UNIVERSITA DEGLI STUDI DI PAVIA´3.20 CriticalphasematchingofSHG in LBO.The polarizationdirections...

UNIVERSITA DEGLI STUDI DI PAVIA

FACOLTA DI INGEGNERIADottorato Di Ricerca in Ingegneria Elettronica,

Elettrica ed Informatica - XIX CICLO

Picosecond mode-locked laser sources

for fundamental physics investigations

Supervisor:

Prof. A. Agnesi

Ph. D. Thesis

of Federico Pirzio

Anno Accademico 2006

Contents

Introduction 1

1 Motion Induced Radiation (MIR) experiment 5

1.1 Theoretical situation . . . . . . . . . . . . . . . . . . . . . . . 6

1.2 Experimental approaches . . . . . . . . . . . . . . . . . . . . 7

1.2.1 The mechanical motion approach . . . . . . . . . . . . 7

1.2.2 A novel experimental approach . . . . . . . . . . . . . 8

1.2.3 Experiment feasibility discussion . . . . . . . . . . . . 9

1.3 Layout for the detection of Casimir radiation . . . . . . . . . 11

1.3.1 The laser system - conceptual scheme . . . . . . . . . 12

1.3.2 Preliminary calculations . . . . . . . . . . . . . . . . . 14

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2 High rep-rate passively mode-locked solid state lasers 21

2.1 Review of the theory of picosecond lasers . . . . . . . . . . . 22

2.1.1 SEmiconductor Saturable Absorber Mirrors . . . . . . 25

2.1.2 Critical energy criterion . . . . . . . . . . . . . . . . . 27

2.2 Critical energy reduction by Inverse Saturable Absorption . . 30

2.3 Cavity design of a multi-GHz laser resonator . . . . . . . . . 31

2.3.1 325MHz Nd:YVO4 laser resonator . . . . . . . . . . . 31

2.3.2 720MHz Nd:YVO4 laser resonator . . . . . . . . . . . 32

2.3.3 1.4GHz Nd:GdVO4 laser resonator . . . . . . . . . . . 33

2.3.4 2.6GHz rep-rate Nd:GdVO4 widely tunable laser res-

onator . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

i

ii Contents

2.3.5 Tunability of the 2.6GHz Nd:GdVO4 with SHG-ISA . 41

2.3.6 Nd:YVO4 based 4.8GHz rep-rate resonator . . . . . . 42

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3 IRENE - A laser source for photoconductivity measure-

ments 53

3.1 State of the art of µJ level picosecond sources . . . . . . . . . 54

3.1.1 Multi-pass amplifiers . . . . . . . . . . . . . . . . . . . 54

3.1.2 Regenerative amplifiers . . . . . . . . . . . . . . . . . 55

3.1.3 Cavity dumping . . . . . . . . . . . . . . . . . . . . . 57

3.1.4 Grazing incidence Nd:YVO4 slab amplifiers . . . . . . 58

3.2 Laser system setup . . . . . . . . . . . . . . . . . . . . . . . . 59

3.2.1 Overwiev of system functioning . . . . . . . . . . . . . 60

3.2.2 The 1064nm Master Oscillator . . . . . . . . . . . . . 61

3.2.3 The pulse picking stage . . . . . . . . . . . . . . . . . 66

3.2.4 Amplification stage . . . . . . . . . . . . . . . . . . . . 68

3.2.5 The Second Harmonic Generation stage . . . . . . . . 72

3.2.6 The Optical Parametric Generation (OPG) stage . . . 75

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

A Guidelines for a model of a grazing incidence single-pass

QCW amplifier 87

A.1 Grazing incidence single pass amplifier . . . . . . . . . . . . . 87

A.2 1st order consideration while designing a single pass amplifier 90

B Critical parameters for efficient harmonic and parametric

generation 93

B.1 Second harmonic efficient generation in LBO . . . . . . . . . 93

B.2 Optical parametric generation in KTP . . . . . . . . . . . . . 97

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Issues and workshops 103

List of Figures

1.1 (a) Mirror effective motion: a composite mirror changes its reflec-

tion properties (under intermittent laser light irradiation), and the

microwave reflecting surface switches its position between P1 and

P2 accordingly. (b) Arrangement of the composite mirror in a mi-

crowave resonant cavity. The semiconductor is irradiated by an

optical fiber piercing the cavity . . . . . . . . . . . . . . . . . . . 9

1.2 Detailed experimental setup. There are three main parts: the elec-

tromagnetic cavity already shown in Figure 1.1, the electronic chain

and the laser system. This block diagram displays the interrelations

between laser and radio frequency generator for the control of para-

metric resonance . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3 Laser system blocks scheme . . . . . . . . . . . . . . . . . . . . 13

2.1 Instantaneous and average laser power versus time for (a) a stable

cw mode-locked laser and for (b) a mode-locked laser exhibiting

large Q-switching instabilities. The average laser power (thick line)

is the same for both lasers . . . . . . . . . . . . . . . . . . . . . 23

2.2 Measured data (filled points) and fitted (solid) curve according to

Eq. (2.8) for the nonlinear reflectivity R(FP,A) of a SESAM as a

function of the pulse energy fluence FP,A = EP /Aeff,A. . . . . . . 26

2.3 Setup of the cavity operating @375MHz . . . . . . . . . . . . . . 32

2.4 Setup of the cavity operating @720MHz . . . . . . . . . . . . . . 32

2.5 Autocorrelation trace of the 720MHz frep laser cavity . . . . . . . 33

2.6 RF spectrum analyzer trace for cw-ML (a) and QML (b) . . 34

iii

iv List of Figures

2.7 720MHz cavity setup, a picture . . . . . . . . . . . . . . . . . . 34

2.8 Diode pump output power characteristic . . . . . . . . . . . . . . 35

2.9 Layout of the diode-pumped 1.4 and 2.6 GHz Nd:GdVO4 laser . . 36

2.10 Two mirror plano-concave output power versus incident pump power

characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.11 Fresnel loss from the quasi-Brewster interface as a function of the

angle offset. The inclination of the uncoated face yielding exact

Brewster incidence is θ = 24.52 . . . . . . . . . . . . . . . . . . 38

2.12 Critical output power calculated for cw mode-locking . . . . . . . 39

2.13 Critical Pout calculated for cw mode-locking (a) and waist radii (b)

as a function of frep. The waist radii on the SAM (wa) as well as

on the gain medium (wg) are calculated (both for the tangential (t)

and the sagittal (s) planes), near the 2.6GHz edge of the stability

region. Actually, the tangential waist radius within the laser crystal

has to be multiplied by the refractive index n=2.192 . . . . . . . . 40

2.14 Non-collinear background-free second-harmonic autocorrelation and

spectrum of the passively mode-locked laser (inset) . . . . . . . . 41

2.15 Experimental setup for the oscillator operating around 2.5GHz . . 42

2.16 Cavity setup with LBO placed near SAM . . . . . . . . . . . . . 43

2.17 Autocorrelation trace of the 2.41GHz cw mode-locking pulses emerg-

ing from the cavity of Figure 2.16 . . . . . . . . . . . . . . . . . 43

2.18 Output power versus input current characteristic of the new pump

diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.19 Plano-concave Nd:YVO4 output power performances . . . . . . . 46

2.20 Picture of the 4.8GHz oscillator, white continuous line shows the

cavity path, dash line is the output . . . . . . . . . . . . . . . . 46

2.21 cw Mode-Locking oscilloscope traces with long (a) and short

(b) time span . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

2.22 sech2 shaped autocorrelation trace for the 4.74GHz cw mode-locking

laser pulses. The conversion coefficient for the FWHM pulse dura-

tion is 29.4ps/ms which gives a duration of about 9.7ps . . . . . . 47

2.23 RF spectrum of the cw mode-locking . . . . . . . . . . . . . . . . 48

List of Figures v

3.1 In a multipass amplifier, the beam passes through the gain medium

several times, at a slightly different angle each time . . . . . . . . 54

3.2 A typical regenerative amplifier setup . . . . . . . . . . . . . . . 56

3.3 Nd:YVO4 passively mode-locked cavity dumped oscillator: pulse

extraction is realized through an Electro-Optical Modulator (EOM)

in combination with a Thin Film Polarizer (TFP) . . . . . . . . . 58

3.4 Amplifier module in side-pumped grazing incidence configuration . 59

3.5 Layout of the diode-pumped oscillator-amplifier system. L1, L2,

L3: lenses; PD: photodiode generating the 56-MHz reference clock;

AOPP: acousto-optic pulse-picker; BD: beam dump; LD: quasi-cw

laser diode arrays; HWP: half-wave plate; slabs: Nd:YVO4 graz-

ing incidence high-gain modules; LBO: SHG crystal; HS: harmonic

separator; KTP: OPG crystal . . . . . . . . . . . . . . . . . . . 60

3.6 Temporal operations sequence of the laser system: the timing is

set by the high frequency (≈ 56 MHz) clock signal provided by the

master oscillator; the low frequency repetition rate is set reducing

or increasing the idle time . . . . . . . . . . . . . . . . . . . . . 61

3.7 Output power characteristic of the diode pump . . . . . . . . . . 62

3.8 Master Oscillator cavity setup: R1=R2=250mm, OC=98%, M1

and M2 High Reflectivity plane mirrors . . . . . . . . . . . . . . 62

3.9 Oscilloscope trace of the cw Mode-Locking pulse train . . . . . . . 63

3.10 Output power versus pump current characteristic of the Master

Oscillator; each output beam carries out 50% of the total output

power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.11 Optical spectrum of the cw mode-locking . . . . . . . . . . . . . 64

3.12 SHG non collinear sech2 shaped autocorrelation trace . . . . . . . 65

3.13 Frequency down-scaling stage . . . . . . . . . . . . . . . . . . . 65

3.14 Single pulse selection . . . . . . . . . . . . . . . . . . . . . . . . 67

3.15 Amplification stage setup: a couple of Quasi Continuous-Wave

(QCW) 150W peak power laser diodes pump two slabs of Nd:YVO4;

a collimation lens and Half Wave Plate (HWP) provides the right

polarization and pump spot dimension on the amplifier crystal face 68

vi List of Figures

3.16 Output energy versus input current caracteristic for the QCW 150W

peak power diodes . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.17 Typical 120µs-long pump pulse, a conversion factor of 20A/V gives

a pump current amplitude of ≈ 135A . . . . . . . . . . . . . . . 70

3.18 Background free, non collinear SHG autocorrelation trace of the

amplified pulses . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.19 Comparison between the seed and an amplified pulse train optical

spectrum; slight narrowing and central wavelength shift for the

amplified pulses can be appreciated . . . . . . . . . . . . . . . . 71

3.20 Critical phase matching of SHG in LBO. The polarization directions

of fundamental (ω) and second-harmonic generated wave (2ω) are

perpendicular to the beam direction, and to each other, the crystal

is cut with the α angle for phase-matching at 1064nm . . . . . . . 72

3.21 Phase-matching angle for critical phase matching of frequency dou-

bling in LBO at room temperature, configuration Ordinary - Ordi-

nary - Extraordinary in the XY plane . . . . . . . . . . . . . . . 74

3.22 SHG stage setup . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.23 A picture of the second harmonic beam . . . . . . . . . . . . . . 75

3.24 Oscilloscope traces of the undepleted fundamental and second har-

monic pulses, normalized so that the ratio of the peaks corresponds

to the observed conversion efficiency. In case of 2ω pulse, also the

adjacent small pulses are strongly depressed by the non-linear process 76

3.25 Type-II phase matching in the XZ plane for KTP crystal. The

polarization directions of pump (p), signal (s) and idler (i) are also

reported . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.26 Signal (blue) and idler (green) wavelength as a function of crystal

tilting angle in the vertical plane . . . . . . . . . . . . . . . . . . 77

3.27 Side view of the Optical Paramatric Generation setup . . . . . . . 78

3.28 Spectra of the OPG pulses, obtained at several tuning angles . . . 79

3.29 System setup, see Table 3.2 for legend . . . . . . . . . . . . . . . 81

A.1 Geometry definitions for the side-pumped grazing incidence slab

amplifier medium . . . . . . . . . . . . . . . . . . . . . . . . . . 89

List of Figures vii

A.2 Fluence of ASE Fin normalized with respect to the saturation flu-

ence Fsat as a function of the single pass small signal gain g0 for

an emission solid angle Ω = 4π · 10−4sterad. Dashed curve is ob-

tained with the approximation Fin ≪ Fsat, dotted line refers to

the approximation of Fin ≫ Fsat . . . . . . . . . . . . . . . . . 91

B.1 Walk-off angle as a function of wavelength in LBO . . . . . . . . . 94

B.2 Group Velocity Dispersion in LBO as a function of pump wavelength 95

B.3 Angular acceptance in LBO around 1.064µm . . . . . . . . . . . . 96

B.4 Temperature acceptance in LBO around 1.064µm . . . . . . . . . 96

B.5 Walk-off angle for signal in KTP as a function of wavelength . . . 98

B.6 GVD in KTP for signal with respect to pump (blue curve) and to

idler (green curve) for a signal wavelength ranging from 0.6 to 1µm 99

B.7 Angular acceptance in KTP with respect to signal wavelength in

the range 0.6-1µm . . . . . . . . . . . . . . . . . . . . . . . . . 99

B.8 Signal (blue curve) and idler (green curve) spectral bandwidth ver-

sus wavelength in KTP. The signal bandwidth in the range 0.6-

1µm is lower than the 1nm maximum resolution of the Ocean Op-

tics USB2000 spectrometer employed the OPG characterization re-

ported in Figure 3.28, as expected by the measurements results . . 100

viii List of Figures

List of Tables

2.1 Tunability range of 1.4GHz V-folded cavity . . . . . . . . . . 38

2.2 Results obtained employing LBO . . . . . . . . . . . . . . . . 44

3.1 Constructor specification for the Acousto-Optical Modulator 66

3.2 Legend of Figure 3.29 . . . . . . . . . . . . . . . . . . . . . . 80

A.1 Physical parameters in our working condition (active medium

Nd:YVO4) for a 1st order estimation of g0 . . . . . . . . . . . 92

B.1 Working Conditions: Crystal length l = 1.5cm, λω = 1.064µm 97

ix

x List of Tables

Introduction

Since the discovery of the first laser in 1960, this device knew an enor-

mous growth, becoming very important in many industrial applications,

like telecommunication systems, material processing or remote sensing, as

well as in scientific fields like medicine, chemistry and physics.

Laser that employees a crystal, a ceramic or a doped glass as active

medium are named solid state lasers. Thanks to the relative simplicity

of their complete structure and to their limited cost, these lasers cover a

relevant part of the laser source market and play an active role in the devel-

opment of many fields where they found application.

During the 1990s, the impressive increase of telecommunications market

gave incentive to the spread of optical devices and to the improvements

in semiconductor growth technology, allowing a decisive step forward to

semiconductor diode laser performances.

The availability of new compact, reliable and efficient diode pump mod-

ules made easier the rapid growth of DPSSL (Diode Pumped Solid State

Laser) systems, which became more and more competitive with respect to

flash lamp pumped system not only in laboratory research field, but also in

commercial applications.

In parallel with the development in the field of pump sources, also new

semiconductor based devices such as SEmiconductor Saturable Absorber

Mirrors (SESAMs) became available on the market. Since their introduc-

tion, the pulse durations, average powers, pulse energies and pulse repetition

rates of compact ultrafast solid-state lasers have improved by several orders

of magnitude.

2 Introduction

Picosecond and femtosecond mode-locked solid state lasers progressed

from complicated and specialized laboratory systems, to compact and reli-

able instruments. In particular picosecond solid state sources, which are in-

trinsicly simpler devices with respect to ultra-fast femtosecond lasers, broke

into the market and rapidly found application in many scientific and indus-

trial reality.

For example, lasers with multi-gigahertz repetition rates based on pas-

sively mode-locked solid state sources are now state of the art solutions

available for high-capacity telecommunication systems, photonic switching

devices, optical interconnections and clock distribution. And applications of

the future, such as clocks for very large scale integrated (VLSI) micropro-

cessors, polarized electron beams for electron accelerators and high-speed

electro-optic sampling techniques, will rely on multi-gigahertz pulse trains

with short pulses, low timing jitter and low amplitude noise.

These approaches benefit from the availability of simple and compact

transform-limited optical pulse generators. For example, they eliminate the

need for a modulator to create the pulses and thereby simplify system ar-

chitecture, increase efficiency and reduce costs. Additionally, pulse quality

is typically very good, much better than with modulated CW (continuous

wave) sources. This improves system signal-to-noise ratios and allows scal-

ing to higher repetition rates through optical time-division multiplexing.

Transmission of data at 160 Gbits per second through standard single-mode

fibres has been demonstrated using such laser sources.

Moreover, the high peak intensity of the pulse in lower repetition fre-

quency devices can be used to alter materials by “cold” ablation (when

a material is changed to gas directly from a solid) or to generate other

colours/wavelengths through efficient nonlinear frequency conversion. Diode-

pumped solid-state lasers with high average power have produced femtosec-

ond pulses with a pulse energy larger than 1 µJ with a 30 MHz pulse repe-

tition rate. This is an unprecedented combination of short pulse, high pulse

energy and high average power.

Such high peak intensity sources make “non-thermal” ablation (without

an increase in temperature) possible without any further amplification. The

Introduction 3

ability of intense ultrashort-pulse lasers to fabricate microstructures in solid

targets is very promising, and the quality of ablated holes and patterns is

much better using femtosecond or picosecond pulses instead of nanosecond

pulses.

The Laser Source Laboratory of the University of Pavia is a well ex-

perienced group in the development of innovative solutions in the field of

DPSSL. In the last decade our group has accumulated experience in side-

pumping as well as in end-pumping with diode lasers; various aspects of

pumping schemes, resonator modeling, thermal problems, active and pas-

sive Q-switching and mode-locking techniques have been intensively inves-

tigated.

During these three years of my Ph.D. fellowship (2003-2006) I had the

opportunity to be involved in an exciting project in collaboration with the

INFN, MIR (Motion Induced Radiation) experimental team. The object

of the collaboration, that will be explained better in the first Chapter of

this thesis, is the realization of innovative and highly customized picosecond

mode-locked laser sources for both the MIR experiment itself and spectro-

scopic characterization of semiconductor materials.

Along the way to the goal I had the opportunity to explore the limits of

the state of the art regarding this kind of laser systems and to manage with

a lot of different topics such as passively mode-locked resonators modeling

and design, picosecond pulse continuous and quasi-continuous-wave amplifi-

cation and non-linear conversion processes, just to mention the mains. There

are many other fundamental aspects of this job, I learnt in these years; they

can not be easily enumerated, and are related to being daily a part of a

research group. As well as the matter itself, surely I found that an exciting

experience.

The content of this thesis work is organized as follows:

in Chapter 1 the Motion Induced Radiation (MIR) experiment is de-

scribed. It concerns the detection of the dynamical Casimir effect, a

4 Introduction

fundamental physics phenomenon related to point zero energy fluctu-

ations. The experimental setup is currently under development at the

INFN (Istituto Nazionale di Fisica Nucleare) Labs located in Legnaro

(PD). A particular attention is dedicated to the role and the specifica-

tion of the laser system that will be inserted in the experimental setup

and is currently under construction at the Laser Source Laboratory of

the Electronics Department of the University of Pavia. The study and

realization of such a device occupied a relevant part of my research

activity and it is currently not yet concluded;

in Chapter 2, after an introduction to the critical design parameters for

passively cw mode-locked high repetition frequency laser sources, the

experimental work and the final cavity design of the master oscillator

for the Casimir experiment laser system is shown. All the experimental

work we carried out in order to achieve the required performances and

the scientific relevant results we obtained are here reported;

in Chapter 3 is described realization, functioning and performances of

IRENE (InfraRed ENergy Emitter), the laser source we realized for the

INFN group of Legnaro in order to investigate the photoconductivity

properties of the semiconductor materials candidate to be inserted in

the Casimir experiment cavity. Since in literature are not present

data about semiconductor mobility µ and recombination time τ under

vacuum at cryogenic temperature, the selection of the proper material

to employ in the experiment undergoes to a direct measurements of

such intrinsic properties actually carried out at the INFN national

Labs in Legnaro (PD);

in Appendix A and B an analytical model for the grazing incidence

Quasi-cw single pass amplifier employed in the IRENE’s setup and a

brief description of the critical parameters for an efficient non-linear

conversion stage design, are respectively shown.

Chapter 1

Motion Induced Radiation

(MIR) experiment

For any quantum field, the vacuum is defined as its ground state. Differently

than in the classic case, this ground state, due to the uncertainty principle, is

not empty, but filled with field fluctuations around a zero mean value. More-

over this vacuum state depends on the field boundary conditions: if they

change, there will be a correspondingly different vacuum (whose fluctua-

tions will have a different wavelength spectrum). Thus a quantum vacuum

state may be equivalent to real particles of a new vacuum after a change in

boundary conditions. If we consider the electromagnetic field, the peculiar

nature of the quantum vacuum has experimentally observable consequences

in the realm of microscopic physics, such as natural widths of spectral lines,

Lamb shift, anomalous magnetic moment of the electron and many more.

It is perhaps even more striking that there exist also observable effects at

a macroscopic level. The Casimir force (static Casimir effect[1][2]) is one

of these macroscopic effects which has been observed experimentally. A

dynamic Casimir effect is also predicted to occur when one boundary is

accelerated in a nonuniform way, as, for instance, when a metal surface un-

dergoes harmonic oscillations. In this case a number of virtual photons from

the vacuum are converted into real photons (“Casimir radiation”), while the

moving metal surface loses energy[3][4].

6 Motion Induced Radiation (MIR) experiment

It is worth notice that, whereas the static Casimir effect has been ob-

served by several experiments[5][6], the Casimir radiation is to date unob-

served, in spite of the abundant theoretical work done in this field[7][8][9]

(see [8] for a historical review and a bibliography of the relevant studies).

1.1 Theoretical situation

The simplest system that can produce Casimir radiation is a single mirror,

harmonically oscillating in a direction perpendicular to its surface. In this

case the number N of created photons should be[10]:

N =ωt

2π

(v

c

)2(1.1)

where:

ω is the angular frequency of the mirror motion;

t is the duration of the motion;

v is the maximum speed reached in the oscillation;

c is the speed of light.

Even if we stretch all parameters to their utmost values (ω ∼ 1010rad/s,

t ∼ 1s and v/c ∼ 10−8), the number of produced photons is not detectable.

A great theoretical progress was to realize that when the oscillating mir-

ror is a wall of an electromagnetic resonant cavity, the cavity itself behaves

as a multiplier for the produced radiation if the frequency of the moving

wall is twice one of the proper electromagnetic cavity frequencies (paramet-

ric resonance). It is however disappointing that the formulae developed so

far using different approaches (in the case of parametric resonance) are not

the same and even irreconcilable. Apart from minor differences, the for-

mulae for the produced photons found in literature[8][9][11] can be brought

back to either of two forms:

N =ωt

2π

(v

c

)2Q (1.2)

1.2 Experimental approaches 7

sinh2(

ωtv

c

)

(1.3)

where Q is the quality factor of the cavity.

1.2 Experimental approaches

One possible experimental solution for detection of the Dynamical Casimir

Effect is based on the mechanical motion of a resonant cavity wall. We will

now show that this approach is nowadays impracticable.

1.2.1 The mechanical motion approach

The highest frequency attainable for mechanical motion is in the gigahertz

range[12] and following the parametric amplification request this implies

microwave cavities with dimensions ranging from 1cm to 1m. The motion

of a single wall of such a cavity requires a huge amount of power. In fact a

wall of volume V , made of a material with mass density ρ, vibrating at an

angular frequency ω0, with an amplitude δx, has a maximum kinetic energy

E =1

2ρV ω2

0δx2 which vanishes in a time of order

2π

ω0. If we estimate the

required power for ρ = 3 · 103kg/m3, V = 3cm×3cm×0.1mm = 9 · 10−8m3,ω0

2π= 2GHz, x = 1nm, we obtain about 3 · 108W.

At present there are two known ways to make a body oscillate at gi-

gahertz frequencies and both of them have some disadvantages precluding

their use in a dynamic Casimir experiment.

The first way would exploit acoustic waves in solids. Waves at gigahertz

frequencies were produced in the 60’s by Bommel and Dransfeld in a quartz

rod placed inside a microwave resonant cavity[13]. What makes this tech-

nique ineffective for our purpose is that a large microwave power is needed

and that the rod motion has a maximum displacement δx much less than

1nm. A small amplitude δx implies a small maximum oscillation speed v (for

a harmonic motion v = ω0x where ω0 is the oscillation angular frequency).

Hence the number of photons produced by a mechanical oscillation with

such a speed would be undetectable, as is readily seen from eq.(1.2) and

(1.3).


The second technique is the one applied in acoustic microscopes[12]. A

resonant vibrating mode in a sapphire block is excited at a typical frequency

around 3GHz. The use of a mechanical system with high quality factor Q

reduces power requests in this case. For sapphire at a temperature of 4.3K

the product of the cavity quality factor Q by the oscillation frequency f is

about Qf ≈ 1014Hz[14]. Therefore if f ∼ 109Hz, Q can be as high as 105.

The same oscillation amplitude as in a nonresonant system can be reached

with a power 105 times smaller. But again the oscillation amplitude δx is

about 10−10m and the moved area is quite small (about 100µm2).

1.2.2 A novel experimental approach

Another possible experimental approach is to realize an oscillating mirror

without mechanical methods. The notion of using laser pulses to quickly

change the dielectric properties of a semiconductor can be found in litera-

ture. In 1989 Yablonovitch[15] proposed the use of laser pulses to change the

refraction index of a semiconductor very rapidly. Another work by Lozovik,

Tsvetus and Vinograd[16] studied the parametric excitation of electromag-

netic waves using a dense plasma layer in a cavity; the layer was created by

irradiating a semiconductor film with femtosecond laser pulses.

In the MIR experimental scheme mirror motion is simulated by changing

the actively reflecting surface of a composite mirror. The mirror consists of

a metal plate with a semiconductor wafer fixed on one side (see Figure

1.1 (a)). The semiconductor reflectivity is driven by irradiation from laser

light, with photon energy corresponding to the semiconductor energy gap,

so that it can switch from completely transparent to completely reflective for

microwaves. By sending a train of laser pulses at a given frequency we get

a mirror oscillating from position P1 to position P2. An advantage of this

method is that the distance between P1 and P2 can be made of the order of

a millimeter, compared to about 1nm obtainable by mechanical oscillations.

This leads to a layout as represented in Figure 1.1(b). The composite

mirror becomes a wall of a superconducting cavity. The laser pulses are

guided into the cavity via an optical fiber. A small pickup antenna is also

1.2 Experimental approaches 9

Figure 1.1: (a) Mirror effective motion: a composite mirror changes its reflec-

tion properties (under intermittent laser light irradiation), and the

microwave reflecting surface switches its position between P1 and P2

accordingly. (b) Arrangement of the composite mirror in a microwave

resonant cavity. The semiconductor is irradiated by an optical fiber

piercing the cavity

introduced in the cavity and the signal fed to high sensitivity electronics.

1.2.3 Experiment feasibility discussion

A number of points need to be checked in order to state that the method

shown could be effective:

1. Is the mirror created in P2 as good as the one in P1?

2. Is the Q of the cavity influenced by the presence of the semiconductor?

3. Is the sensitivity of the pickup electronics good enough to detect the

predicted number of created photons?

4. Is it actually feasible to make the mirror appear and disappear in P2

at gigahertz frequencies?


Experiments carried out at the INFN Legnaro (PD) National Labs gave

an answer to the first three questions.

1. Inserting a semiconductor layer in a waveguide and measuring the

reflected and the transmitted power under laser irradiation, it was

shown that the semiconductor can reflect microwaves as effectively as

copper. This test yields also another important parameter, that is

the laser power needed to make a good mirror. This question arises

from the fact that one needs to build a plasma of thickness equal to

at least three skin depths (for the given microwave frequency) in order

that it may be fully reflective. The energy needed was estimated to

be approximatively 1µJ/cm2 per pulse in the microwave range[17].

2. Measurements of the Q value of a niobium cavity brought to 4.6K,

were performed. Determining the decay time of the loaded cavity, a

value of Q ≈ 2 · 106 was obtained. Once the semiconductor wafer was

inserted in the cavity no difference in the decay time (hence in Q) was

detected.

3. In order to answer question (3) a complete electronic chain was con-

nected to the pickup antenna inserted in the cryogenic cavity. The

first amplification stage was placed near the cavity at liquid helium

temperature[19]. The cavity was then loaded with microwave pulses

of decreasing power in order that the minimum detectable signal could

be reached. The minimum signal detected had an energy of 0.1eV, cor-

responding to about 104 microwave (2.5GHz) photons. By taking 100

measurements one arrives at 103 photons. Further improvements in

the electronic chain should allow to detect even feebler signals.

4. The answer to question (4) can be found in literature[18]. The mir-

ror appearance at P1 is fast enough for gigahertz frequencies, since the

transition time of the electrons is some femtoseconds, so that the dom-

inant factor is the rise time of the laser pulse, which is in the hands of

the experimenter. However the disappearance of the mirror depends

on the recombination time of the electrons, which is a property of the

1.3 Layout for the detection of Casimir radiation 11

semiconductor only. If one uses semi-intrinsic semiconductors one can

obtain recombination times as low as 5–10ps[18].

One important expect is the determination of the semiconductor to em-

ploy as “vibrating” mirror. Since its recombination time is an important

issue for the experiment feasibility, this property has to be measure in order

to determine the best material. These measurements are carried out at the

Legnaro INFN National Labs and in Chapter 3 the laser system we realized

for the experiments is described.

1.3 Layout for the detection of Casimir radiation

On the basis of these results a general layout for the detection of Casimir

radiation is shown in Figure 1.2. A niobium cavity at cryogenic tempera-

ture is placed in a vacuum vessel. A cryogenic amplifier is connected by a

transmission line to an inductive pickup loop coupled with the cavity in crit-

ical matching. A directional coupler is inserted between the cavity and the

cryogenic amplifier to enable measurements of the resonance cavity reflec-

tion coefficient and calibration of the electronic chain. The signal output by

the cryogenic amplifier is further amplified at room temperature, then pro-

cessed by a superheterodyne receiver and eventually integrated over time.

The laser light carried by the optical fiber is tuned in the near infrared and

modulated in amplitude at a frequency exactly double the cavity resonance

frequency. The generator drives a frequency doubler whose output turns to

a low power laser master oscillator. The master oscillator yields a continu-

ous signal from which a pulse picker selects the number of pulses required

in each excitation stage. The total energy stored in the laser is limited, so

must be the number of available pulses. The present estimate is between

103 and 104 pulses for each run.

This experimental setup leaves open the possibility of changing many

configuration parameters to help distinguishing real from spurious signals.

The master laser frequency can be changed and thus the oscillation mirror

frequency to slightly detune the parametric resonance condition. Also the

cavity temperature can be varied in order to study possible contributions


Figure 1.2: Detailed experimental setup. There are three main parts: the electro-

magnetic cavity already shown in Figure 1.1, the electronic chain and

the laser system. This block diagram displays the interrelations be-

tween laser and radio frequency generator for the control of parametric

resonance

from thermal radiation. Mirrors made with different semiconductor samples

and with different thickness can be tried.

1.3.1 The laser system - conceptual scheme

In Figure 1.3 is represented the conceptual scheme of the laser system in-

serted in the experimental setup described in Figure 1.2.

Master Oscillator: it should provide a low energy pulsed laser

beam with a repetition frequency slightly tunable around the para-

metric resonance of the microwave cavity (≈ 5GHz with the actual

cavity geometry) and a pulse duration less than 20ps. The laser source

consists in a cw-ModeLocked oscillator operating at 1064nm.


AMPLIFICATION STAGES OPTICAL FREQUENCYDOUBLING STAGE

OUTPUT

10−100mJ PULSE BURST @780−820nm

MASTER OSCILLATOR

5 GHz

HIHG REP−RATE LOW POWER PULSE TRAIN @1064nm

NON LINEAR WAVELENGTHCONVERSION STAGE

SELECTORPULSE BURST

1000−10000 P

ULS

Es B

UR

ST

LOW

EN

ER

GY

Figure 1.3: Laser system blocks scheme

Pulse Burst Selector: from the continuous pulse train, burst

made by 103-104 single pulses should be picked up. Within the single

burst the pulses maintains the same time spacing given by the mas-

ter oscillator. The selector relies on an Acousto-Optical Modulator

(AOM).

Amplification Stages: the low energy single burst is amplified in a

double stages amplifier. The first is a diode pumped pre-amplification

stage, the second a flash lamp pumped power amplifier. An energy

level of about 50-500µJ per single pulse (hence a total energy of 50-

500mJ for a burst made by 103 single pulses) is expected.

Optical Frequency Doubling Stage: the amplified laser beam

at a wavelength of 1064nm is then frequency doubled in order to pump

an optical parametric generation stage.

Nonlinear Wavelength Conversion Stage: an optical paramet-

ric generator provides the output at the desired wavelength of 780-


820nm, selected in function of the semiconductor material deposed on

the vibrating microwave cavity wall. A total energy ranging from 10

to 100mJ per burst is expected.

1.3.2 Preliminary calculations

In order to understand if this scheme leads to observable results it is nec-

essary to insert real numbers in the theoretical formulae and compare the

predicted number of photons with the apparatus sensitivity. Several phys-

ical parameters are essentially already chosen, since a niobium cavity and

an electronic chain have been used satisfactorily in the tests carried on to

answer questions (3) and (4). The niobium cavity has transverse dimensions

of 71mm and 22mm, and length x = 110mm. The cavity mode chosen was

TE101 with eigenfrequency around 2.5GHz. The semiconductor was GaAs

with thickness 2x = 0.6mm. The excitation time duration for a single run, at

5GHz, according to the number of pulses, can be between 0.2-2µs. Typically

a run can be repeated after a few seconds.

The following data can be used to estimate the number of photons pro-

duced by dynamic Casimir effect:

t = 10−6s;

ω0

2π= 2.5 · 109s−1;

v

c=

δx

x=

0.3mm

110mm= 3 · 10−3;

Q = 2 · 106.

With formula (1.2), which is the more pessimistic, a number of ≈ 4 · 104

microwave photons, well above apparatus sensitivity, turns out.

A good knowledge of quantum vacuum is of great importance in cosmol-

ogy, both to the recurrent question of Einstein’s cosmological constant[20],


with its significance to the dark matter problem; and to the critical question

of the birth of density inhomogeneities, ancestors of galaxies, from inflated

quantum vacuum fluctuations[21]. Moreover a sound grasp of quantum vac-

uum dynamics is crucial in understanding some issues on the nature of quan-

tum particles and on the relationships among vacuum noise, the concepts of

information and entropy, and gravitation[21].

Bibliography

[1] H. B. G. Casimir, D. Polder, The Influence of Retardation on the

London-van der Waals Forces, Phys. Rev. 73, 360 (1948)

[2] M. Bordag, U. Mohideen, V. M. Mostepanenko, New develop-

ments in the Casimir effect, Phys. Rep. 353, 1 (2001)

[3] G. T. Moore, Quantum theory of the electromagnetic field in a

variable-length one-dimensional cavity, J. Math. Phys. 9, 2679 (1970)

[4] S. A. Fulling, P. C. W. Davies, Radiation from a moving mirror

in two dimensional space-time - Conformal anomaly, Proc. R. Soc.

London A 348, 393 (1976)

[5] S. K. Lamoreaux, Demonstration of the Casimir Force in the 0.6 to

6 µm Range, Phys. Rev. Lett. 78, 5 (1997)

[6] G. Bressi, G. Carugno, R. Onofrio, G. Ruoso, Measurement

of the Casimir Force between Parallel Metallic Surfaces, Phys. Rev.

Lett. 88, 041804 (2002)

[7] A. Lambrecht, M. T. Jaekel, S. Reynaud, Motion Induced Radi-

ation from a Vibrating Cavity, Phys. Rev. Lett. 77, 615 (1996)

[8] V. V. Dodonov, Modern Nonlinear Optics, edited by M.W. Evans,

Adv. Chem. Phys. Ser. Vol. 119, p. 309 (Wiley, New York, 2001)

[9] M. Crocce, D. A. R. Dalvit, F.D. Mazzitelli, Resonant photon

creation in a three-dimensional oscillating cavity, Phys. Rev. A 64,

013808 (2001)

18 Bibliography

[10] M. T. Jaekel, A. Lambrecht, S. Reynaud, Relativity of Motion

in Quantum Vacuum, Proceedings of the Ninth Marcel Gross-

mann Meeting, edited by V.G. Gurzadyan, R.T. Jantzen and

R. Ruffini, p. 1447 (World Scientific, 2002)

[11] G. Schaller, R. Schutzhold, G. Plunien, G. Soff, Dynamical

Casimir effect in a leaky cavity at finite temperature, Phys. Rev. A

66, 023812 (2002)

[12] Z. Yu, S. Boseck, Scanning acoustic microscopy and its applications

to material characterization, Rev. Mod. Phys. 67, 863 (1995)

[13] H. E. Bommel, K. Dransfeld, Excitation and Attenuation of Hy-

personic Waves in Quartz, Phys. Rev. 117, 1245 (1960)

[14] V. B. Braginsky, C. M. Caves, K. S. Thorne, Laboratory experi-

ments to test relativistic gravity, Phys. Rev. D 15, 2047 (1977)

[15] E. Yablonovitch, Accelerating reference frame for electromagnetic

waves in a rapidly growing plasma: Unruh-Davies-Fulling-DeWitt radi-

ation and the nonadiabatic Casimir effect, Phys. Rev. Lett. 62, pp.

1742-1745 (1989).

[16] Yu. E. Lozovik, V. G. Tsvetus, E. A. Vinograd, Parametric

excitation of vacuum by use of femtosecond laser pulses, JETP Lett.

61, 723 (1995)

[17] C. Braggio, G. Bressi, G. Carugno, A. Lombardi, A. Palmieri,

G. Ruoso, D. Zanello, Semiconductor microwave mirror for a mea-

surement of the dynamical Casimir effect, Rev. of Sci. Instr. 75,

4967 (2004)

[18] J. Mangeney, N. Stelmakh, F. Aniel, P. Boucaud, J.-M. Lour-

tioz, Temperature dependence of the absorption saturation relaxation

time in light- and heavy-ion-irradiated bulk GaAs, Appl. Phys. Lett.

80, 4711 (2002)

Bibliography 19

[19] R. F. Bradley, Cryogenic, low-noise, balanced amplifiers for the

300-1200MHz band using hetreostructure field-effect transistors, Nucl.

Phys. B (Proc. Suppl.), 72 137 (1999)

[20] M. Fukugita, The Dark Side, Nature 422, 489 (2003)

[21] P. C. W. Davies, Quantum vacuum noise in physics and cosmology,

Chaos 11, 539 (2001)

20 Bibliography

Chapter 2

High rep-rate passively

mode-locked solid state lasers

Diode–pumped, ion–doped solid–state lasers are well known for their poten-

tial to deliver high–power mode–locked pulse trains in diffraction–limited

beams[1][2]. They feature efficient, robust, compact and reliable opera-

tion. In high–speed electro–optic sampling[3][4], photonic switching or op-

tical clocking [5][6], high–capacity telecommunication systems or free space

data links[7] and time–resolved ultrafast spectroscopy[8], high–repetition

rate pulse generating lasers are a desirable tool. Even in electron accel-

erators, high repetition rate lasers are used to generate polarized electron

beams[9]. Although the field of current and potential applications is rather

diversified, laser sources for these applications have to meet common require-

ments: compact, reliable and efficient lasing operation is a key goal. Wave-

length tunability and/or phase locking to an external microwave reference

source is often desired. Low phase and amplitude noise are therefore another

must–have. Depending on the specific type of application, multi–gigahertz

pulse trains with average output powers between tens of milli–watts to sev-

eral watts, delivered in a diffraction–limited beam, are required.

In high repetition rate applications, passive mode-locking is preferred

against active mode-locking, because potentially shorter pulses and thus a

higher extinction ratio between the pulses can be achieved, besides the fact

22 High rep-rate passively mode-locked solid state lasers

that the modulators add costs and complexity to the setup and limit the

maximum achievable cavity compactness.

Short cavities need to be built in order to generate high repetition rate

(frep) pulse trains, since the round-trip time TR =1

frepfixes the time spacing

between two consecutive pulses. Besides mechanical and geometrical prob-

lems which can arise from building very small laser cavities, Q–switched

mode locking (QML) becomes the main problem. QML means that the out-

put pulse train consists of pulses of different energies instead of pulses that

all have the same energy. An unwanted regime of operation for most applica-

tions of course. Because of their typically low emission cross–sections (com-

pared to semiconductor gain media, for example), passively mode–locked

ion–doped solid–state lasers show an increased tendency for Q–switching

instabilities when the repetition rate is increased.

We will now briefly review the theory describing the transition from

Q–switched mode-locking to continuous wave mode-locking, in order to

give some practical design parameters for passively mode-locked picosecond

lasers.

2.1 Review of the theory of picosecond lasers

Figure 2.1 illustrates qualitatively the two laser-operation regimes of inter-

est. The instantaneous laser power is shown versus time. In the cw mode-

locking regime (Figure 2.1(a)) the laser generates a train of mode-locked

pulses with high amplitude stability, while Q-Switching-Mode-Locking (Fig-

ure 2.1(b)) means that the pulse energy is modulated with a strongly peaked

Q-switching envelope. To derive a stability criterion against QML we start

from the rate equations for the intracavity power, gain, and saturable ab-

sorption. We call “stable” the operating conditions in which the relaxation

oscillations are damped.

The rate equations for the mode-locked laser can be written as[10]:

dP

dt=

g − l − qP (EP )

TRP (2.1)

2.1 Review of the theory of picosecond lasers 23

Figure 2.1: Instantaneous and average laser power versus time for (a) a stable

cw mode-locked laser and for (b) a mode-locked laser exhibiting large

Q-switching instabilities. The average laser power (thick line) is the

same for both lasers

dg

dt= −g − g0

τL− P

Esat,Lg (2.2)

dq

dt= −q − q0

τA− P

Esat,Aq (2.3)

where:

P is the average intracavity laser power;

TR = 1/frep is the cavity round-trip time;

EP = P · TR is the mode-locked intracavity pulse energy;

g is the time-dependent round-trip power gain and g0 the correspon-

dent value for P = 0;

q is the time-dependent round-trip saturable absorption coefficient and

q0 the correspondent value for P = 0;

l is the linear loss per round-trip;


τL,A are the upper-state lifetime of laser medium and absorber recovery

time respectively;

Esat,L = Fsat,L · Aeff,L is the saturation energy of the gain, which

is defined as the product of saturation fluence Fsat,L =hν

mσand the

effective laser mode area inside the active medium Aeff,L = πw2L, with

m the number of passes through the gain element per cavity round trip;

Esat,A = Fsat,A · Aeff,A is the absorber saturation energy and is de-

fined by the product of absorber saturation fluence Fsat,A and effective

laser mode area on the saturable absorber Aeff,A = πw2A. Fsat,A cor-

responds to the pulse fluence that is necessary to bleach the saturable

absorption to 1/e of its maximum amount q0.

It is worth notice that while eq. (2.1) and eq. (2.2) describes long time

scale phenomena (many round-trip), eq. (2.3) has to be solved in the laser

pulse time scale.

qP (EP ) in eq. (2.1) represents the round-trip loss in average laser power

(or pulse energy) introduced by the saturable absorber for a given intra-

cavity pulse energy. In our conditions we can make two assumptions to to

determine qP . First, we have a slow absorber, i.e., the duration τP of the

mode-locked pulses is shorter than the absorber recovery time τA, although

the results remain valid even for τA ≈ τP [10]. Second, τA is much shorter

than the cavity round-trip time TR. With these assumptions we can neglect

the relaxation term in Eq. (2.3) during the time necessary for a mode-locked

pulse to pass the saturable absorber and we can assume that the absorber

is always fully recovered before it is hit by the next pulse. Then, for qP (EP )

we obtain:

qP (EP ) = q0Fsat,AAeff,A

EP

[

1 − exp

(

− EP

Fsat,AAeff,A

)]

(2.4)

Therefore we can now describe the mode-locked laser by the following two

coupled rate equations:

TRdEP

dt= [g − l − qP (EP )]EP (2.5)


dg

dt= −g − g0

τL− EP

Esat,LTRg (2.6)

By linearizing these equations for small deviations δEP and δg from the

steady-state values EP and g we obtain the criterion for stability against

QML:

EP

∣∣∣∣

dqP

dEP

∣∣∣∣EP

<Tr

τLr =

TR

τL+

EP

Esat,L(2.7)

where we have used r = 1+P

Psat,L. If the absorber is nearly fully saturated,

which is normally the case, r is identical to the usual pump parameter that

describes how many times above threshold the laser operates.

The physical background of relation (2.7) can be understood as follows.

If the pulse energy rises slightly owing to relaxation oscillations, this pulse

energy fluctuation first grows exponentially because of the stronger bleaching

of the absorber. However, the increased pulse energy starts to saturate the

gain. The laser is stable against QML if the gain saturation is sufficiently

strong to stop the exponential rise.

2.1.1 SEmiconductor Saturable Absorber Mirrors

The non-linear intracavity elements we used to mode-lock our picosecond

laser sources were semiconductor saturable absorber mirrors (SESAMs, or

simply SAMs)[11][12][13]. A typical non-linear reflectivity response of such

a device is reported in Figure 2.2. The fitting curve has the following

expression:

R(EP ) = Rns

ln

1 + exp(−∆R)

[

exp

(EP

Esat,A

)

− 1

]

EP /Esat,A(2.8)

in which ∆R is the maximum change in nonlinear reflectivity, which is also

referred to as the maximum modulation depth of the SESAM device, Rns is

the reflectivity for high pulse energies and determines the nonsaturable loss

∆Rns = 1 − Rns.

For absorber with ∆R smaller than approximately 10%, as always in our


Figure 2.2: Measured data (filled points) and fitted (solid) curve according to Eq.

(2.8) for the nonlinear reflectivity R(FP,A) of a SESAM as a function

of the pulse energy fluence FP,A = EP /Aeff,A.

case, we can simplify eq. (2.8) to:

R(EP ) = Rns

1 − ∆RFsat,AAeff,A

EP

[

1 − exp

(

− EP

Fsat,AAeff,A

)]

(2.9)

The nonlinear reflectivity R(EP ) of the SESAM is related to the pulse energy

loss per round trip qP (EP ). Note that we did not include any nonsaturable

losses in q(t) (Eq.(2.3)) or qP (EP ) (Eq.(2.4)). Therefore the maximum mod-

ulation depth is given by ∆R = 1− exp(q0) ≈ q0 for ∆R ≪ 1 as in passively

mode-locked solid-state lasers we can usually assume. In addition, the non-

saturable losses should be as low as possible because they only degrade the

laser performance, which results in the additional condition that ∆Rns ≪ 1,

hence Rns ≈ 1. Under these conditions we have:

R(EP ) ≈ exp (−qP (EP )) ≈ 1 − qP (EP ) (2.10)

and we can rewrite eq. (2.7) in terms of the SESAM parameters:

EPdR(EP )

dEP

∣∣∣∣EP

<Tr

τLr =

TR

τL+

EP

Esat,L(2.11)


2.1.2 Critical energy criterion

To benefit from the full modulation depth of the saturable absorber, in cw

mode-locked lasers the pulse energy must be high enough to bleach the ab-

sorber. To meet that condition, the pulse fluence on the SESAM should be

approximately five times the absorber saturation fluence. With this approx-

imation and the assumption that Rens ≈ 1, as well as with relations (2.10)

and (2.4), we obtain for the nonlinear reflectivity of the SESAM:

R(FP,A) ≈ 1 − ∆RFsat,A

FP,A(2.12)

where FP,A =EP

Aeff,Ais the pulse fluence (energy per unity of area) incident

on the saturable absorber. At lower fluences the residual saturable absorp-

tion would contribute to the cavity loss and act against self-starting and

efficient mode-locked operation.

If the laser operates far above threshold (r ≫ 1), which is the case in

most mode-locked lasers, we can neglect the first term on the right-hand

side of relation (2.11), and the stability criterion against QML becomes in-

dependent of the upper-state lifetime of the considered laser material. The

saturation energy is then the only relevant parameter of the gain medium. A

laser material with a large stimulated-emission cross section σL is therefore

desirable for stable cw mode-locking. It also could help to choose, if possi-

ble, a resonator geometry with multiple passes through the gain medium to

decrease the gain saturation fluence. Selecting inhomogeneously broadened

gain materials with the same averaged σL would also reduce the gain satu-

ration fluence because the class of laser ions with the highest cross sections

dominates the gain saturation. Reducing the spontaneous lifetime, e.g., by

lifetime quenching effects, does not affect the stability condition against

QML.

With the approximations listed above, stability condition (2.11) can be

written in the following equivalent forms:

EP >√

Esat,LEsat,A∆R (2.13)


FP,A >

√

Fsat,LFsat,A∆RAeff,L

Aeff,A(2.14)

P > frep

√

Fsat,LAeff,LFsat,AAeff,A∆R (2.15)

With respect to the experimental verification of the theory, it is helpful

to introduce the QML parameter relating Esat,L, Esat,A, ∆R, because it

contains all the parameters that determine the laser dynamics. We then

define the critical intracavity pulse energy EP,c as the square root of the

QML parameter:

EP,c = (Esat,LEsat,A∆R)1/2

This is the minimum intracavity pulse energy which is required for ob-

taining stable cw mode-locking; i.e., for EP > EP,c we obtain stable cw

mode-locking, and for EP < EP,c we have to expect QML instability. Note

that, if we neglect the lifetime dependent term in relation (2.11) and set

the bracketed term in eq. (2.9) as 1, both approximations lead to a slightly

stricter stability criterion: a laser fulfilling the stability condition with these

approximations will always fulfill the exact condition.

As can be seen from eq. (2.15), the intracavity power required for sta-

ble cw mode-locking regime increases linearly with the laser repetition fre-

quency. At higher pulse repetition rates the tendency for QML will increase.

In addition, for very short laser cavities we also have to take into account

the tendency for pure Q-switching[11], which is negligible in 100-MHz-type

laser oscillators with a saturable absorber recovery time τA ≪ TR. Since

the pulse energy scales inversely with the pulse repetition rate (for funda-

mental mode locking and a given intracavity power), a pulse repetition rate

that is ten times higher requires an intracavity laser power that is ten times

higher, if we leave the QML parameter fixed. At the same pump level, the

intracavity power can be increased with reduced output coupling, but only

at the expense of efficiency and output power.

We can reduce the absorber modulation depth ∆R by using a thinner

absorber layer. However, this leads to longer pulses and to a weaker self-

starting tendency of the mode-locking process, neglecting the fact that by

now SESAM with ∆R < 0.7% are not commercially available. Tighter


focusing onto the SESAM reduces the absorber saturation energy since,

Esat,A = Aeff,AFsat,A. The tradeoffs are that operation of the laser at pulse

energies far above the absorber saturation energy can lead to pulse breakup

or can damage the device.

Another variable that affects the QML parameter is the gain saturation

energy. Esat,L is determined by the gain cross section of the laser material,

the laser mode area inside the gain medium, and the type of laser resonator.

To minimize the gain saturation energy it is desirable to use a laser ma-

terial with a large gain cross section, e.g., Nd:YVO4, or Nd:GdVO4 rather

than Nd:YAG or Nd:YLF. Broadband gain media, suitable for subpicosec-

ond pulse generation, usually have low emission cross sections (with the

exception of Ti:sapphire) and thus have a stronger tendency for QML.

The laser mode area Ap inside the gain medium should be chosen relying

in the following considerations. In order to assure an efficient pump absorp-

tion, crystal length lc should be longer than the pump absorption depth; we

can assume lc ≈2

αp, where αp is the active medium absorption coefficient at

the pump wavelength λp. Efficient pump absorption requires a pump waist

rayleigh range zRp ≈πW 2

p np

λpM2p

comparable with the crystal length. As can be

seen zRp depends on the pump focusing (Wp), on the refractive index of the

active medium at the pump wavelength (np) and on the beam quality fac-

tor of the pump beam M2p which roughly increases proportionally to pump

power. Hence we can finally find that:

Ap ≈ πW 2p ≈

2λpM2p

αpnp

with the constrain that in order to suppress higher-order transverse modes

oscillation and to achieve maximum efficiency, wL & Wp.

Therefore QML can be more difficult to suppress in lasers pumped by

high-power laser diodes (with their poor beam quality), while the use of

highly doped gain media can be advantageous because the reduced absorp-

tion length allows for tighter focusing.

When the stability condition given by eq. (2.15) is not achievable in

practice, it is necessary to investigate some method to obtain a reduction


in critical energy. One possible strategy is to introduce inside laser cavity

some element capable to produce Inverse Saturable Absorption (ISA).

2.2 Critical energy reduction by Inverse Saturable

Absorption

As shown in [14], the critical energy required for starting cw mode-locking

can be reduced significantly in the presence of inverse saturable absorption

such as two-photon absorption, free-carrier absorption, and Second Har-

monic Generation (SHG). Dependending on the working conditions (soliton

or non-soliton mode-locking regime, slow or fast saturable absorber) the

amount of reduction in critical energy is different. In the case of our in-

terest (slow absorber in non-soliton regime), eq. (2.13) in presence of ISA

becomes:

Ec =

√√√√√

Esat,A∆R

2β +1

Esat,L

(2.16)

where, in case of Second Harmonic Generation induced ISA[15]:

β =4π2Z0(deffL)2

3n3λωASHGτ(2.17)

with:

Z0 = 377Ω is the vacuum impedance;

deff is the non-linear effective coefficient of the SHG crystal;

L is the minimum between the length of the crystal and the Rayleigh

range of the focused laser beam;

ASHG is the beam area in the SHG crystal;

τ is the pulse duration;

n and λω have the usual meaning.

2.3 Cavity design of a multi-GHz laser resonator 31

If β >1

EsatL

suppression of QML becomes relatively independent of the

properties of the gain medium. Independence of the gain medium will allow

suppression of QML in lasers with very large Esat,L, i.e. lasers with large

mode volumes such as diode-pumped high-powered lasers, lasers with a low

gain cross-section that is related to a long upper-state lifetime, as shown in

[15][16].

Both the direct nonlinear loss owing to SHG, as well as the gain reduction

due to self-phase modulation SPM contribute to the effective stabilization

of the cw mode locking while providing the minimum pulse duration allowed

by the passive mode locking alone[15][19][20].

Also, lasers with a limited intracavity pulse energy, which hardly reaches

the critical value Ec, as is the case for high-repetition-rate lasers, may greatly

benefit from ISA induced critical energy limiting.

2.3 Cavity design of a multi-GHz laser resonator

Since our workgroup had no experience before in design GHz repetition rate

passively mode-locked resonators, our strategy was to procede step by step

from hundred MHz regime, up to thousand MHz laser sources. In this path

we tested many different laser cavity before determining our way to high

rep-rates. I’ll discuss now of the principals steps we made.

2.3.1 325MHz Nd:YVO4 laser resonator

At first we set up a laser resonator employing an 1% doped, 3mm long a-

cut Nd:YVO4 crystal, pumped by a 750mW maximum output power laser

diode emitting around 807nm. The cavity scheme is shown in Figure 2.3.

The length L1 + L2 ≈ 280mm while L3 ≈ 100, hence the cw mode-locking

repetition frequency was ≈ 325MHz. The ABCD simulation of the TEM00

intracavity resonating mode gives the following dimensions for the funda-

mental mode inside the active medium and over the saturable absorber mir-

ror: wL ≈ 180µm, wA ≈ 60µm. Employing the ∆R = 1% saturable losses

mirror, with the saturation fluence given by the constructor, eq. (2.13) gives


OC 98,4%

R 1 = 150mm

SAM 1% / 4% LBO

Nd : YVO 4 PUMP L 1

L 2

L 3

Figure 2.3: Setup of the cavity operating @375MHz

a critical energy Ec ≈ 30nJ per pulse.

Without employing SHG-ISA method, we were not able to obtain stable

cw mode-locking. Hence we introduced a 15mm long LBO crystal near the

SAM, as shown in Figure 2.3. Opportunely tilting the LBO crystal out

of phase matching we obtain stable and self-starting cw mode-locking with

an intracavity pulse energy Eic ≈ 10nJ (significantly lower than the limit

predicted without SHG ISA) and average output power of ≈ 120mW (60mW

for each of the two laser cavity outputs).

We also tested the laser resonator with a ∆R = 4% SAM, which further

increases of a factor 2 the critical intracavity energy. In these conditions we

experimented cw mode-locking with Eic ≈ 5nJ (more than a factor 10 below

the critical energy) and an average output power of about 72mW (36mW

for each harm).

2.3.2 720MHz Nd:YVO4 laser resonator

OC 98,4%

R 1 = 80mm

SAM 1% LBO

Nd : YVO 4 PUMP L 1

L 2

L 3

Figure 2.4: Setup of the cavity operating @720MHz


Subsequently we scaled up the resonator repetition frequency oppor-

tunely reducing the optical cavity length and consequently reducing the

folding mirrors radius of curvature. With the Z-folded cavity shown in Fig-

ure 2.4 we obtained stable cw mode-locking at 720MHz.

The new simulated TEM00 mode dimensions inside active medium an

SAM were respectively wL ≈ 160µm and wA ≈ 50µm, also in these condi-

tions we had to employ LBO SHG-ISA in order to avoid QML instabilities.

The average output power was ≈ 160mW, 80mW for each output.

Figure 2.5: Autocorrelation trace of the 720MHz frep laser cavity

In Figure 2.5 is shown the autocorrelation trace of the output pulses.

We measured a FWHM duration τp ≈ 6.6ps with a time-bandwidth product

∆ν∆τ ≈ 0.43, tipical of this kind of resonators in which the active medium

is placed on one end of the cavity.

We report in Figure 2.6(a) and Figure 2.6(b) respectively the radiofre-

quency spectrum analyzer trace in case of cw mode-locking and QML regime.

A picture of the cavity setup is shown in Figure 2.7.

2.3.3 1.4GHz Nd:GdVO4 laser resonator

The Z-folded cavity scheme employed for our resonators operating at 325 and

720MHz pulse repetition rates was not further scalable for shorter cavities,


(a) Cw-Ml (b) Qs-Ml

Figure 2.6: RF spectrum analyzer trace for cw-ML (a) and QML (b)

Figure 2.7: 720MHz cavity setup, a picture

due to mechanical limitations. Therefore we decided for a V-folded cavity

employing a 1% doped, plane-brewster vanadate laser crystal, coated on one

side AR at 808nm and HR at 1063nm, whereas the second face was cut with

a slight offset δ from the Brewster angle. The available a-cut Nd:GdVO4

laser crystal was already investigated as a promising candidate for high

repetition-rate sources[17], owing to its superior thermal conductivity that

allows for power up-scaling, while the absorption peak is broader than that

of Nd:YVO4 and is especially attractive for diode-pumping.

The pump was a readily available 1W, 100µm single emitter diode laser


tuned at 808nm, beam-shaped for end-pumping with aspheric lenses and an

anamorphic prism pair. The pump spot radius was measured to be 36µm.

The output power versus current characteristic is shown in Figure 2.8.

400 600 800 1000 12000

100

200

300

400

500

600

700

Ial (mA)

Po

ut (

mW

)

Figure 2.8: Diode pump output power characteristic

Laser resonator design criteria

Eq. (2.13) suggests straightforward criteria for achieving cw mode-locking[21]:

1. tightly focus the resonant mode both in the laser crystal and on the

SAM device;

2. use small ∆R;

3. use a lowloss oscillator with high intracavity power (and pulse energy).

The smallest modulation depth ∆R offered with commercial devices is

generally around 1% and cannot be reasonably reduced to a small frac-

tion of such a value without accepting large variations in production runs

and significantly increased costs. The ultimate low-loss oscillator for such

an application should employ only high reflectivity (HR) mirrors and no

anti-reflection (AR) optics, since these kind of coatings always brings in a

non-vanishing Fresnel loss of 0.1% - 0.2% per pass, of the order of the out-

put coupling that is generally tolerated, which is also comparable to the


non-saturable losses of the SAM. These considerations led us to propose

the design for the high-frequency passively mode-locked oscillator shown in

Figure 2.9. L1 and L2 are aspheric lenses for collimation and focussing,

respectively, and APP is the prism pair for slow-axis expansion.

Figure 2.9: Layout of the diode-pumped 1.4 and 2.6 GHz Nd:GdVO4 laser

An HR concave mirror, with R = 50mm radius of curvature, folded the

nearly-symmetric resonator. The folding angle was kept as small as possible,

≈ 6, in order to allow maximum overlap of the tangential and sagittal

stability regions. The SAM (supplied by BATOP Gmbh, Weimar, Germany)

was the second end-mirror: the saturable modulation depth was specified

to be ∆R = 0.7% (nonsaturable loss ¡ 0.3%), with saturation fluence of

30µJ/cm2 and recovery time ¡ 10ps.

To determine the amount of the loss from the Nd:GdVO4 quasi-Brewster

face, a simpler two-mirror plano-concave cavity was separately set up with

a 25mm radius of curvature, 2% transmissivity output coupler. The laser

emitted up to 250mW in TEM00 mode with 700mW of incident pump power,

whereas the external reflection from the Brewster face was measured to be ≈0.2% of the intracavity power. In Figure 2.10 the output power characteristic

versus pump power for the plano-concave cavity is reported.

Since the working tolerance for crystal cutting is often within 0.5 and

the reflectivity dependence from the offset angle δ is parabolic near the

Brewster condition, it is easy to specify some offset angle to introduce an

acceptable amount of output coupling (see Figure 2.11; see the inset for angle


definitions). The shortcoming of this approach is the loss for the internal

reflection, and correspondingly reduced laser efficiency, but this is of little

concern as long as few tens of milliwatts can be considered a sufficient output

power as in our case.

Numerical computation results summarized in Figure 2.12 show the vari-

ation of the resonant mode size and of the critical output power (critical

energy multiplied by the repetition rate frequency), considering the 0.2%

effective coupling through the quasi-Brewster face, as a function of the rep-

etition rate. In agreement with the numerical modeling, cw mode-locking

could be readily achieved only near the edge of the stability region.

Experimental results

In Table 2.1, the results obtained for different pulse frep are reported. A

little tunability of the repetition frequency was experimented (∆frep/frep ≈3MHz ∼ 2 ). The output beam was, as expected, linearly polarized.

0 100 200 300 400 500 600 7000

50

100

150

200

250

300

Ppump

[mW]

Pou

t [mW

]

Measured dataLinear fitting

Slope 38%

Figure 2.10: Two mirror plano-concave output power versus incident pump power

characteristic


Figure 2.11: Fresnel loss from the quasi-Brewster interface as a function of the

angle offset. The inclination of the uncoated face yielding exact Brew-

ster incidence is θ = 24.52

frip[GHz] Ppump [mW ] Pout Brewster[mW ]

(1) 1.399 465 (cw ML threshold) 25.5

680 (max.) 43

(2) 1.401 420 (cw ML threshold) 31

680 (max.) 55

(3) 1.402 620 (cw ML threshold) 43

660 47

680 (max.) 51

Table 2.1: Tunability range of 1.4GHz V-folded cavity

2.3.4 2.6GHz rep-rate Nd:GdVO4 widely tunable laser res-

onator

Once the feasibility of the cavity scheme reported in Figure 2.9 was demon-

stred, the realization of the 2.6GHz pulse repetition rate source was straight-

forward. We simply substituted the R = 50mm folding concave mirror with

a R = 25mm mirror and consequently reduce the length of L1 and L2 in

order to match the stability condition for the new laser cavity. The results

of our simulations about critical energy condition and fundamental mode

transversal dimension in the active medium and over the saturable absorber


1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.4720

40

60

80

100

120

140

160

180

frep

[GHz]

Crit

ical

out

put p

ower

[mW

]

Figure 2.12: Critical output power calculated for cw mode-locking

mirror are shown in Figure 2.13.

The output power from the quasi-Brewster face was up to ≈ 60mW, the

repetition rate was centered at 2.6GHz with pulse duration of 4.4ps (Figure

2.14). The time-bandwidth product was 0.47, slightly above the sech2 limit

as often occurs in lasers with the gain element at the end[18]. The output

beam was TEM00 with horizontal polarization. The repetition rate could

be varied only slightly (few MHz) by translating the SAM longitudinally

without compromising the stability of cw mode-locking. Once the cw mode-

locking was started, the laser could be used several days without any damage

of the SAM.

We used a radio-frequency spectrum analyzer (HP 8562A) to monitor the

quality of mode-locking and to measure carefully the repetition frequency.

Owing to the limited photodetector sensitivity we were limited to a S/N

ratio of 30dB, with no trace of relaxation oscillations in the background

noise (the signal on a 500-MHz oscilloscope did not show any significant

train modulation at low frequency).

The flexibility of this cavity design can be appreciated when a broader

repetition rate tuning range is required. In fact, a significantly broader

tuning range, of ≈ 200 MHz, has been achieved by unbalancing the resonator

arms, varying the length of the SAM arm within 30% - 50% of the total


intracavity path in air, which physically corresponds to right-left shifting

the graph in Figure 2.13(a). Such a tuning range is important, for example,

for matching the pulse frequency to the resonance of a given microwave test

device, and cannot be done with linear plano-concave resonators without

compromising the cw mode-locking stability.

Reducing the pump power we found that the critical output power for

cw mode-locking was ≈ 30mW, corresponding to 470mW of pump power

(for comparison, the pump threshold for laser emission with the SAM was

Figure 2.13: Critical Pout calculated for cw mode-locking (a) and waist radii (b)

as a function of frep. The waist radii on the SAM (wa) as well as on

the gain medium (wg) are calculated (both for the tangential (t) and

the sagittal (s) planes), near the 2.6GHz edge of the stability region.

Actually, the tangential waist radius within the laser crystal has to

be multiplied by the refractive index n=2.192


Figure 2.14: Non-collinear background-free second-harmonic autocorrelation and

spectrum of the passively mode-locked laser (inset)

80mW). The intracavity critical energy is comparable with that reported in

[17] and is in fair agreement with the prediction of eq. (2.13) [see Figure

2.13(a)]. It is worth noting that the pulse duration of 4.4ps is significantly

shorter than the 12ps value previously obtained, which may be explained by

the larger modulation depth of the SAM used in the present experiment.

A picture of the experimental setup is shown in Figure 2.15.

2.3.5 Tunability of the 2.6GHz Nd:GdVO4 with SHG-ISA

In order to test our SHG-ISA stabilization technique in such a high rep-rate

system, we inserted intracavity a 4mm long, type I LiB3O5 (LBO) crystal,

as shown in Figure 2.16. Simply varying the length of the L2 cavity arm

was possible to obtain stable cw mode-locking regime with the threshold

and maximum output powers listed in Table 2.2.

At frep = 2.41GHz a pulse autocorrelation measurement was carried out.

A pulse duration of ≈ 4.2ps was measured with a FWHM spectrum of about

0.38nm with a correspondant product ∆λ∆ν = 0.42. The autocorrelation

trace is shown in Figure 2.17.


Figure 2.15: Experimental setup for the oscillator operating around 2.5GHz

2.3.6 Nd:YVO4 based 4.8GHz rep-rate resonator

The results obtained with the Nd:GdVO4 based oscillators were the pre-

liminary condition for further steps. Since the 1063nm centered Nd:GdVO4

emission wavelength does not match the gain bandwidth of the amplification

stages of the laser system, based on Nd:YVO4 slabs, further cavity setups

rely on Nd:YVO4 active medium. A 1% doped, plane-brewster a-cut, 3mm

long crystal was chosen. Due to its higher emission cross section and con-

sequently lower saturation fluence, in according with eq. (2.14) Nd:YVO4

reduces the intracavity critical pulse energy. Also the pump diode was sub-

stituted with the aim to achieve a better absorption peak wavelength match-

ing and higher pump power. The diode output power versus input current

characteristic is reported in Figure 2.18, showing a ≈ 20% available pump

power in excess if compared with the characteristic shown in Figure 2.8.

The diode emission is centered at 808nm with a FWHM of about 2nm.

Once again, in order to determine the amount of the loss from the

Nd:YVO4 quasi-Brewster face, a two-mirror plano-concave cavity was set


L 1 L g

HR, R= 25mm

SAM 1%

L 2

2 a

a

LBO

4mm

Figure 2.16: Cavity setup with LBO placed near SAM

Figure 2.17: Autocorrelation trace of the 2.41GHz cw mode-locking pulses emerg-

ing from the cavity of Figure 2.16

up with a 25mm radius of curvature, 2% transmissivity output coupler. The

output power performances as a function of the incident pump power are

reported in Figure 2.19 and show a significant improvement with respect to

the previously tested Nd:GdVO4 setup (see Figure 2.10 for a comparison).

A slope efficiency of about 50% was achieved, while quasi-brewster face loss

was ≈ 1 .

The conceptual scheme of the laser cavity operating at 4.8GHz repeti-

tion frequency is the same we employed for the Nd:GdVO4 based oscillator

descripted before (see Figure 2.9). The main difference is obviously relying


frip[GHz] Ppump [mW ] Pout Brewster[mW ]

2.415 610 (cw ML thres.) 53

690 65

2.43 530 (cw ML thres.) 34

690 45

2.45 580 (cw ML thres.) 42

690 52

2.47 560 (cw ML thres.) 48

690 63

2.49 605 (cw ML thres.) 42

690 47

2.51 630 (cw ML thres.) 40

690 43

2.53 690 (cw ML thres.) 53

2.545 690 (cw ML thres.) 50

2.57 690 (cw ML thres.) 45

2.60 690 (cw ML thres.) 48

Table 2.2: Results obtained employing LBO

on the cavity length and hence the curvature radius of the folding mirror. A

mirror coated HR at 1064nm with R=12mm was employed. The cavity opti-

cal length of ≈ 31mm (≈ 24mm in air) related to this frep needs an accurate

mechanical design of the oscillator in order to minimize the folding angle

(and consequently HR mirror losses and induced astigmatism in the cavity

mode) and carefully manage the available space to put every component in

place. It is worth notice that we used only commercially available compo-

nents, without any expensive customization. In Figure 2.20 is reported a

picture of the oscillator.

Obtaining a stable cw mode-locking regime in these conditions was not

so simple. Only with tricky and accurate alignment of the mirrors very close

to the cavity stability edges we reached our goal. Once the laser operates

in cw mode-locking it shows good stability. It works for hours without any


200 400 600 800 10000

200

400

600

800

Ial (mA)

Pou

t (m

W)

Figure 2.18: Output power versus input current characteristic of the new pump

diode

alignment correction and it is also self starting. Once again it was possible

to tune the cavity mode-locking repetition frequency adjusting the ratio

between the length of the two V-folded cavity arms. We measured repetition

frequencies ranging from 4.72 to 4.88GHz, with a best performance of 25mW

average output power at 4.74GHz.

In Figure 2.21 are reported both the long time scale and the short time

scale oscilloscope cw mode-locking traces. The instrument employed is 6-

GHz oscilloscope (Tektronix TDS 6604B) while the optical sensor is a 5-GHz

InGaAs photodiode (Thorlabs SIR5-FC, 70-ps FWHM pulse response).

In Figure 2.22 is reported the sech2 profile of the cw mode-locking

pulses autocorrelation trace. Taking into account a conversion constant of

29.4ps/ms for the instrument (Femtochrome FR-103XL Autocorrelator), it

comes out a duration of ≈ 9.7ps, more than two times longer that the 4.4ps

obtained whit the 2.6GHz repetition rate, Nd:GdVO4 based oscillator. This

behaviour can be explained taking into account the narrower gain band-

width for Nd:YVO4 and a lower saturation for the 1% SAM, in according

with the reduced intracavity energy due to the approximately doubled frep.


Figure 2.19: Plano-concave Nd:YVO4 output power performances

In Figure 2.23 is reported a typical Radio Frequency (RF) spectrum of

the cw mode-locking. A S/N ratio of 40dB, with no trace of relaxation

oscillations in the background noise was obtained.

Figure 2.20: Picture of the 4.8GHz oscillator, white continuous line shows the

cavity path, dash line is the output


(a) 10µs/div (b) 500ps/div

Figure 2.21: cw Mode-Locking oscilloscope traces with long (a) and short

(b) time span

Figure 2.22: sech2 shaped autocorrelation trace for the 4.74GHz cw mode-locking

laser pulses. The conversion coefficient for the FWHM pulse duration

is 29.4ps/ms which gives a duration of about 9.7ps


Figure 2.23: RF spectrum of the cw mode-locking

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Chapter 3

IRENE - A laser source for

photoconductivity

measurements

A crucial point regarding the feasibility of the Motion Induced Radiation

(MIR) experiment, as described in Chapter 1, is the possibility to make

appear and disappear at high frequency the end mirror of the Casimir ex-

periment microwave cavity. This possibility relies on physical properties of

the semiconductor layer that, optically switching its conductivity, acts as a

vibrating wall for the electromagnetic field. The experimental tests of the

photoconductive behavior of different semiconductors materials at cryogenic

temperatures are performed at the INFN National Labs of Legnaro (PD),

by using a laser source realized at the Laser Source Lab of the Electronics

Department of the University of Pavia. These measurements require a low

repetition rate source, able to provide short pulses (τp < 10ps) with en-

ergy of the order of few microjoule at 532nm and tens of nanojoule around

790nm. In this Chapter, I will describe the laser system (IRENE - InfraRed

ENergy Emitter), its realization and its performances.

54 IRENE - A laser source for photoconductivity measurements

3.1 State of the art of µJ level picosecond sources

Many laser systems consist of an oscillator followed by one or more ampli-

fier stages. These optical amplifiers can take several very different forms,

including that of a single-pass amplifier, a multipass amplifier or a regen-

erative amplifier. A number of interdependent factors determine which of

these configurations is the best suited for a particular application. These

factors include the amplification required, the gain and saturation properties

of the active medium, the input power from the oscillator, the desired beam

quality, system cost, complexity and reliability. Microjoule-level picosecond

pulses are interesting for a variety of applications, including micromachin-

ing and nonlinear optics. Laser systems delivering microjoule pulse energy

have been reported relying either on multi-pass gain elements[1] or, more

often, on regenerative amplification[2][3]. Also less complex soultions that

in principle do not need amplification stages like cavity dumping have been

employed[4]. We will now briefly go into each of these techniques in order

to point out their capabilities and drawbacks.

3.1.1 Multi-pass amplifiers

A possible scheme for multipass amplification systems is represented in Fig-

ure 3.1.

Figure 3.1: In a multipass amplifier, the beam passes through the gain medium

several times, at a slightly different angle each time

3.1 State of the art of µJ level picosecond sources 55

In this setup optics (usually mirrors) are arranged so that input beam

makes several passes through the amplifier gain medium before exiting. In

practice, each pass through the gain medium may travel through the same

optically pumped spot in the center of the amplifier material, but with

different paths. A folded path allows the beam to enter and exit the amplifier

after a finite number of passes. The optimum number of passes and hence

the number of folds in the amplifier path, depends on the gain per pass,

the amount of overall gain required, the saturated gain coefficient for the

material and the amount of optical complexity tolerable. The greater the

number of passes needed the more complex the design must be. The design is

limited also in the difficulty of focusing each pass through the gain medium.

Typically four to eight passes are made, with cascading multipass amplifiers

used for a greater number of passes. The technique is desirable as it is

relatively inexpensive, but it needs time-consuming adjustments. The gain

medium must also be used close to the damage threshold to have a high gain

per pass ratio.

3.1.2 Regenerative amplifiers

Practical issues of optical complexity limit the number of passes feasible

for a multipass amplifier, so the net gain of such an amplifier cannot be

increased beyond a certain level. For some applications, this gain level is

not sufficient. This happens when the input signal from the laser oscillator is

very weak, or when several passes are not enough to reach saturation. Both

instances are often the result of a low cross-section for stimulated emission.

One possible alternative solution is represented by regenerative ampli-

fiers. The operation principle can be understood as follows:

first, the gain medium is pumped for some time, so that it accumulates

energy;

then, the initial pulse is injected into the cavity through a port which

is opened for a short time (shorter than the round-trip time) with an

electro-optic (or sometimes acousto-optic) switch;


after that, the pulse can undergo many (possibly hundreds) of cavity

round trips, being amplified to a high energy level;

finally, the pulse is again released from the cavity. This can either hap-

pen with a second electro-optic switch, or with the same one previously

used for coupling in.

This principle allows to achieve very high gain and thus pulse energies in

the millijoule range with amplifiers of moderate size, or even higher ener-

gies with larger devices. Typical pulse repetition rates are of the order of

1kHz (although repetition rates of 100kHz are sometimes possible), while

the highest pulse energies are achieved at lower repetition rates.

The pulse is usually trapped using a Pockels cell and a broadband po-

lariser. Figure 3.2 represent a typical set-up of a regenerative amplifier. In

PUMP

ACTIVE MEDIUM

OUT

IN

POLARIZER

POCKELLS CELL

Figure 3.2: A typical regenerative amplifier setup

terms of output characteristics, one of the major advantages of a regenera-

tive amplifier is that the spatial profile and pointing of the output beam is

defined by the cavity. With a well-designed cavity, the regenerative ampli-

fier is capable of delivering transform-limited pulses in a very high-quality

beam. On the other end, fast and synchronized electronic switching in and

out of the pulses add costs and complexity to the setup.

The power efficiency of a regenerative amplifier can be severely reduced

by the effect of intracavity losses (particularly in the electro-optic switch).

The sensitivity to such losses is particularly high in cases with low gain,

3.1 State of the art of µJ level picosecond sources 57

because this increases the number of required cavity round trips to achieve

a certain overall amplification factor.

Regenerative amplifiers can also have a reduced gain and power efficiency

due to a finite lower state lifetime, leading to a significant population of the

lower laser level during amplification of a pulse, and thus to reabsorption

on the laser transition. This problem occurs primarily in amplifiers for very

short pulses.

3.1.3 Cavity dumping

Cavity dumping is an efficient method to generate relatively high pulse en-

ergies, sufficient for many applications such as ultrafast spectroscopy, micro-

machining, and nonlinear frequency conversion directly from a laser oscil-

lator and thus avoiding complex amplifier schemes[5][6][7]. In the past the

main focus of research was on cavity-dumped TEM00-pumped Ti:sapphire

laser systems[8]. However, since these lasers are pumped in the green spec-

tral region, where no laser diodes are available, their application is quite

limited due to the high cost of the green pump lasers. One way to reduce

the complexity is the usage of directly diode-pumped laser media such as

ytterbium- and neodymium-doped materials in combination with highly re-

liable mode-locking techniques using semiconductor saturable absorber mir-

rors (SESAMs). A possible cavity scheme for such a device is represented

in Figure 3.3. The basic idea is to keep the cavity losses small for most of

the time, so that the circulating pulse can become rather intense, and then

to extract this pulse with an optical switch. This switch, usually realized

with an electro-optic or acousto-optic modulator and a polarizer in the laser

cavity, allows to couple out a large fraction of the energy of the circulating

pulse. After pulse extraction, the cavity must be kept in a low-loss state

for many cavity round trips to allow the pulse to accumulate energy again.

One important factor is that the switching time has to be small compared

with a cavity round-trip time, and the trigger for the optical switch must

be synchronized with the circulating pulse.

The achieved pulse energy is typically about an order of magnitude

higher than with an ordinary mode-locked laser, and the pulse repetition


Figure 3.3: Nd:YVO4 passively mode-locked cavity dumped oscillator: pulse ex-

traction is realized through an Electro-Optical Modulator (EOM) in

combination with a Thin Film Polarizer (TFP)

rate can be several megahertz. The average output power of cavity-dumped

lasers is usually quite low due to the effect of parasitic cavity losses.

3.1.4 Grazing incidence Nd:YVO4 slab amplifiers

The development of very high gain diode-pumped amplification modules

offers new reliable, cheap and simple solutions also for picosecond pulse

amplification. Owing to the effective gain confinement near the pump side in

highly absorbing media with large stimulated emission cross section, grazing-

incidence side-pumped slabs offer high gain per pass as well as effective

averaging of gain in the direction of the pump absorption[9][10]. Indeed,

Nd:YVO4 slab amplifiers with single-pass gain ranging from 103 to 105 have

been reported[11], that are perfectly suitable for the application considered

here.

A typical scheme of such an amplifier module is represented in Figure

3.4. A collimated diode array is coupled into an high gain active medium

directly or through a cylindrical fast-axis focusing optics. Owing to the

high pump absorption coefficient, population inversion is confined in a thin

foil near to the pumped face. The seed laser beam is injected inside the

amplifier in such a way that it experiences a grazing incidence total inter-

nal reflection at the pumped crystal face. Thanks to this it passes through

the highest gain region, and the half path reflection make possible to op-

3.2 Laser system setup 59

PUMP MODULE

PUMP BEAM

SEED

AMPLIFIED BEAM

ACTIVE MEDIUM

Figure 3.4: Amplifier module in side-pumped grazing incidence configuration

portunely average gain and thermal distortions in the pumping plane. We

demonstrated very high small signal gain for such a configuration both in

continuous wave[12] and quasi-continuous wave[13] pumped modules, with

simple and cost effective setups that make this solution very attractive for

high stability, low energy picosecond pulses amplification.

3.2 Laser system setup

A conceptual scheme of the laser system setup is described in Figure 3.5.

It is in principle possible to identify five different stages in the setup:

1. the high repetition frequency master oscillator;

2. the repetition frequency downscaling stage relying on the acousto-

optical pulse picker;

3. the single pass double stages amplifier employing a couple of Nd:YVO4

slabs in a grazing incidence one bounce configuration;

4. the Second Harmonic Generation (SHG) stage which provides both

the green output and the pump for the final stage;

5. the Optical Parametric Generation (OPG) stage for the 790nm output.


Figure 3.5: Layout of the diode-pumped oscillator-amplifier system. L1, L2, L3:

lenses; PD: photodiode generating the 56-MHz reference clock; AOPP:

acousto-optic pulse-picker; BD: beam dump; LD: quasi-cw laser diode

arrays; HWP: half-wave plate; slabs: Nd:YVO4 grazing incidence high-

gain modules; LBO: SHG crystal; HS: harmonic separator; KTP: OPG

crystal

3.2.1 Overwiev of system functioning

Before going into the specifications and the performances of any single stage,

we will describe qualitatively the operation of the whole laser system. The

core element for the correct device functioning is the synchronization of

pulse picking and amplification with the master oscillator pulses train. The

temporal operations sequence is described in Figure 3.6.

All the operations are coordinated by a microprocessor. The clock for

the processor is recovered by the master oscillator output through an oppor-

tunely reshaped monitor photodiode signal. The first event to occur is the

amplifier pump pulse formation. In order to exploit the maxium available

gain, the deflection signal is sent to the pulse-picker exactly at the end of the

amplifier pump pulse. Once the deflection window is properly centered in


0

0

0

Amplifier Pump Pulse Amplifier Pump Pulse

Master oscillator provided high freq. clock signal

Idle time − set by low freq. repetition rate

Deflectionsignal

Deflectionsignal

t

t

t

τp ≈ 120µs τp ≈ 120µs

τdefl ≈ 15nsτdefl ≈ 15ns

Figure 3.6: Temporal operations sequence of the laser system: the timing is set by

the high frequency (≈ 56 MHz) clock signal provided by the master os-

cillator; the low frequency repetition rate is set reducing or increasing

the idle time

order to optimize the single pulse selection (as will be more clearly explained

in 3.2.3), the time reference given directly by the master oscillator guaran-

tees the time-locking between amplification, deflection window and selected

pulse. The desired repetition frequency can now be selected operating on

the duration of the idle time between two consequent amplification pump

pulses.

3.2.2 The 1064nm Master Oscillator

The low-power master oscillator is based on a Nd:YVO4 2%-doped plane-

Brewster crystal pumped by a 1-W cw laser diode emitting at 808nm. The

output power versus input current characteristic of the pump source is shown

in Figure 3.7. Passive mode-locking was achieved with a semiconductor

saturable absorber mirror with 2% loss modulation at 1064nm.


400 800 12000

200

400

600

800

1000

Ial (mA)

Pou

t (m

W)

Figure 3.7: Output power characteristic of the diode pump

Since the Brewster cut of the laser crystal expands the cavity mode

diameter of a factor ≈ 2 in the polarization plane, in order to realize the

correct matching between pump and fundamental mode waists, a couple of

aspheric lenses of focal length f1 = 4.5mm (NA = 0.55) and f2 = 8mm (NA

= 0.5) was employed to re-image the diode emission (100µm × 1µm) into

the laser crystal.

The cavity setup is described in Figure 3.8. The curved mirror R1 pro-

duce a fundamental mode size wg ≈ 70µm inside the active medium, while

the curved mirror R2 produces a waist wa ≈ wg over the saturable absorber.

R1

R2

M1

OC

M2

SAM

Nd:YVO4

Figure 3.8: Master Oscillator cavity setup: R1=R2=250mm, OC=98%, M1 and

M2 High Reflectivity plane mirrors


Figure 3.9: Oscilloscope trace of the cw Mode-Locking pulse train

The R = 98% output coupler is a folding mirror for the standing wave cav-

ity, hence we had a double non collinear output beams, each carring out

50% of the output average power. The output laser beams are substantially

collimated with a 1/e diameter w ≈ 750µm.

400 600 800 10000

40

80

120

Pump Current (mA)

Tot

al P

out (

mW

)

Figure 3.10: Output power versus pump current characteristic of the Master Os-

cillator; each output beam carries out 50% of the total output power


The cavity optical length is ≈ 2.7m giving a cw mode-locking repetition

frequency of about 56MHz (see Figure 3.9). Due to the relatively low repe-

tition frequency, the critical intracavity pulse energy stability condition (see

Chapter 2, 2.1.2) was fulfilled at relatively low pump power. The output

power versus pump current characteristic of the master oscillator is shown

in Figure 3.10.

The stable cw Mode-Locking pump current threshold is approximatively

750mA: at this current level, each of the two output beams carries out ≈25mW average power.

The optical spectrum of the cw mode-locking is reported in Figure 3.11,

we measures a full width half maximum ∆λ ≈ 0.3nm and a central wave-

length λ0 = 1064.3nm.

1063.6 1064.1 1064.6 1065.10.0

0.4

0.8

1.2

Wavelength (nm)

Am

plitu

de (

a. u

.)

∆λ=0.3 nm

Figure 3.11: Optical spectrum of the cw mode-locking

In Figure 3.12 the second harmonic non-collinear sech2 shaped autocor-

relation trace of the pulses is shown. The pulse duration obtained is about

6.7ps. The time-bandwidth product ∆ν∆τ ≈ 0.52 is far from the Fourier

transform limit, but this behaviour is typical for the resonator layout[14].


Figure 3.12: SHG non collinear sech2 shaped autocorrelation trace

PULSE PICKER

FOCUSING LENS

MONITOR PHOTODIODE

COLLIMATING LENS

BEAM STOPPER

Figure 3.13: Frequency down-scaling stage


3.2.3 The pulse picking stage

The system frequency down-scaling is realized employing an Acousto-Optical

modulator (A-A Opto-Electronic MT200) as single pulse picker. The char-

acteristics of the device and its driver are reported in Table 3.1.

Parameter Specification

Carrier Drive Frequency f0 200MHz

Aperture (vert. × hor.) 0.2×2 mm2

Polarization IN/OUT Linear perp.

Max. Power Density 5W/mm2

Laser frequency shift ± 200MHz

Static extinction ratio 2000:1

Rise time 160ns/mm

Rise time (min) 10ns (diam 64µm)

Refraction index 2.2

AO wave velocity 4200m/s

Optical transmission ¡98%

1st order efficency ¿75%

RF Power 2.2W

Table 3.1: Constructor specification for the Acousto-Optical Modulator

As represented in Figure 3.13, one of the two laser beams arriving from

the Master Oscillator stage is the signal input for the Monitor Photodiode

(MP), while the other passes through the acousto-optical modulator.

As previously described, the monitor photodiode signal, opportunely am-

plified, provides a clock signal for a custom electronic controller based on a

microprocessor. The controller synchronizes the pulse picker deflection win-

dow with the amplification stage, in order to create the population inversion

inside the amplifier slabs with the correct timing with respect to the seeded

single pulse. A focusing lens resize the input beam inside the acousto-optical

modulator in order to minimize the deflection rise-time, while a second lens,

opportunely placed after the modulator, collimates to the right dimension


the emerging laser beam.

Since the time spacing between two adjacent pulses is fixed by the repe-

tition rate of the master oscillator to ≈ 18ns, we operated close to the best

performances of the pulse picker in terms of rise and fall time. In other

words only an accurate alignment and a proper choice of the beam diameter

inside the device, make possible to select a single pulse inside the deflection

window. Also the deflection efficency was reduced by the single pulse se-

lection constrain. In our best conditions we estimated ≈ 65% pulse-picking

efficency after the AOM.

−40 −30 −20 −10 0 10 20 30 40−0.2

0

0.2

0.4

0.6

0.8

1

1.2

delay (ns)

Am

plitu

de (

a.u.

)

Figure 3.14: Single pulse selection

An amplitude ratio between the selected and the adjacent pulses of about

20:1 was the best result we achieved. The behaviour of the system is clearly

explained by Figure 3.14.

The relatively low extinction of the adjacent pulses was not an issue in

our case since nonlinear frequency conversion required in subsequent stages

improves drastically this parameter. However, if single pulses with higher

contrast were required at 1064nm, a faster pulse picker, or two acousto-

optic pulse pickers in series, or an oscillator running at a lower repetition

rate could have been employed. We chose to use an acousto-optic pulse

picker since its driving electronics is easier to develop and customize than

that for electro-optic devices, which require fast switching of high voltages,

generating electromagnetic noise that is more difficult to suppress. Fur-


thermore, acousto-optic pulse pickers are cheaper and more flexible allowing

operation from single-shot to hundreds of kHz repetition rate. We tested the

laser system with pulse repetition rate up to 100Hz, but in principle there is

no limitation in frequency selection, and even user-defined sequences pulses

could be generated.

3.2.4 Amplification stage

The amplification stage setup is represented in Figure 3.15.

HWP

QCW DIODES

MICROLENSESCOLLIMATION

SEED

BEAMAMPLIFIED

Nd:YVO slabs4

Figure 3.15: Amplification stage setup: a couple of Quasi Continuous-Wave

(QCW) 150W peak power laser diodes pump two slabs of Nd:YVO4;

a collimation lens and Half Wave Plate (HWP) provides the right

polarization and pump spot dimension on the amplifier crystal face

The amplification stage is based on a couple of 4×2×12mm3 Nd:YVO4

slabs, 1% doped, 5 wedge, in a grazing-incidence configuration. Each slab

was pumped by a 150W peak power quasi-cw laser diode array with emitting

size 10mm×1µm, tuned at 808nm and collimated by a microlens. The input

and output faces were antireflection-coated at 1064nm, while the pump side

was left uncoated. Half-wave plates were used to align the polarization of


the pump diode arrays with the Nd:YVO4 c-axis (perpendicular to the plane

of Figure 3.15). The slabs were placed few millimeters apart for maximum

compactness, furthermore the pump diodes could be connected in series with

minimum parasitic inductance, and driven by a single power supply unit.

The beam diameter of the injected seed pulse was ≈ 1mm (full width

at 1/e2), slightly larger than the 0.8-mm thin gain sheet provided by the

microlens-collimated diode arrays. The seed polarization was also parallel

to the crystal c-axis, for maximum gain.

The output energy versus input current caracteristic of the Quasi-cw

pump diodes is reported in Figure 3.16.

0 40 80 1200

5

10

15

20

Ial (A)

Ep

um

p (

mJ)

Diode 1

Diode 2

Figure 3.16: Output energy versus input current caracteristic for the QCW 150W

peak power diodes

The two diodes show a similar slope efficiency but different thresholds,

hence the output energy at the same input current level was different. In par-

ticular the first amplification module was more efficient. A Peltier Thermo-

Electroc-Cooler (TEC) module provided the correct temperature set point

to the system in order to match the spectral emission of the QCW diodes

with the absorption peak of the active media.

The typical pump current pulse is reported in Figure 3.17. It is a squared

current pulse of maximum amplitude ≈ 135A and width ∆τpump ≈ 120µs.

The pump pulse duration was selected in order to maximize the amplifier


gain, since no particular thermal load constrain was experienced at our low

repetition rate.

Figure 3.17: Typical 120µs-long pump pulse, a conversion factor of 20A/V gives

a pump current amplitude of ≈ 135A

Guidelines for a numerical modeling of the amplifier behaviour are re-

ported in Appendix A.

Amplification results

Small-signal single-pass gain as high as 1.3·105 was measured at the maxi-

mum pump level, with a maximum output energy of about 10µJ per pulse

(saturated gain ≈ 105), still with 1-mm beam diameter. Both the pulse

duration and the smooth TEM00 beam profile of the seed pulse were well

preserved (M2 ¡ 1.2). Owing to the extremely high single-pass gain, the

amplifier setup was prone to self-lasing with the slightest scattering along

the beam path, therefore two diaphragms had to be placed before and after

the amplifier in order to avoid such shortcomings. These are not especially

dangerous, but subtract gain (and energy) to the amplifying process. An

optical isolator was not required to shield the oscillator.

The duration of the amplified pulses was measured. In Figure 3.18 the

background free, non collinear SHG autocorrelation trace of the pulses is


reported.

-30 -20 -10 0 10 20 300.0

0.5

1.0

∆t (ps)

SH

G A

utoc

orr.

Sig

nal (

a.u.

)

8.2 ps

Figure 3.18: Background free, non collinear SHG autocorrelation trace of the

amplified pulses

1063.6 1064.0 1064.4 1064.80.0

0.4

0.8

Wavelength (nm)

A.U

.

Amplified Pulse

MO Pulse

0.3 nm

0.2 nm

Figure 3.19: Comparison between the seed and an amplified pulse train optical

spectrum; slight narrowing and central wavelength shift for the am-

plified pulses can be appreciated


A duration ∆τp ≃ 8.2ps was obtained from the 6.7ps seed pulses. Also

the optical spectrum of the pulses was measured after the amplification

stage. In order to show more clearly the spectral narrowing and the central

peak wavelength slight shift, in Figure 3.19 we plot on the same scale the

spectrum already reported in Figure 3.11, relative to the seed pulses, and

the amplified pulses optical spectrum.

Even if the pulse duration after amplification was increased, nevertheless

the relatively great spectral narrowing contributed to reduce significantly the

time-bandwidth product for the amplified pulses to a value ∆ν∆τ ≈ 0.43.

3.2.5 The Second Harmonic Generation stage

The Second Harmonic Generation stage relies on a 15mm long AntiReflec-

tion coated LBO crystal cut for Type-I critical phase matching at 1064nm.

In Figure 3.20 an example of the beam direction and the polarization

directions for phase-matched second-harmonic generation in LBO based on

the Type-I scheme with polarizations ordinary-ordinary-extraordinary in the

XY plane is shown.

Y

Z

X

LBO

α

ω

2ω

kω,2ω

Figure 3.20: Critical phase matching of SHG in LBO. The polarization directions

of fundamental (ω) and second-harmonic generated wave (2ω) are

perpendicular to the beam direction, and to each other, the crystal

is cut with the α angle for phase-matching at 1064nm

In critical phase matching (also called angle phase matching) the inter-


acting beams are aligned at some angle(s) to the axes of the index ellipsoid.

In almost all cases, there are one or two waves polarized along one axis of

the index ellipsoid (→ ordinary beam), while another one or two waves are

polarized at some variable angle with the plane spanned by the other two

axes (→ extraordinary beam). Adjustment of the propagation angle allows

to modify the refractive index of the extraordinary beam (called extraordi-

nary refractive index), while the ordinary index stays constant. For some

angular position, phase matching may be achieved.

The phase matching condition for the wave vectors of fundamental and

SH field implies a condition for the refractive ordinary and extraordinary

indexes at the frequency ω and 2ω. For collinear phase matching, in which

the beams at ω and 2ω are parallel:

2kω = k2ω → n(o)ω = n

(e)2ω

Due to dispersion, usually n(o)ω 6= n

(e)2ω , however phase matching condition

can be achieved opportunely choosing the angle α (Figure 3.20) in a way

that:

1

n22ω(α)

=sin2(α)

n2x,2ω

+cos2(α)

n2y,2ω

≡ 1

n2z,ω

where nx,y,z(λ) are given by the Sellmeier equations[15].

In our case beam propagates within the XY plane, the fundamental field

polarization is ordinary (o, here in Z direction) and the second-harmonic

polarization is extraordinary (e, with an angle α to the X axis). This is

Type-I phase matching in which the two fundamental photons have the

same polarization, perpendicular to that of the double frequency generated

one.

Referring to Figure 3.21 we can obtain the required parameter for the

crystal cut. For a pump wavelength of 1064nm the phase-matching angle α

would be ≈ 9.5. In order to make the system non-sensitive to room tem-

perature variations, the LBO crystal was mounted in a thermally controlled

copper holder and warm up to ≈ 35C during laser operations.


Figure 3.21: Phase-matching angle for critical phase matching of frequency dou-

bling in LBO at room temperature, configuration Ordinary - Ordi-

nary - Extraordinary in the XY plane

Experimental results

The SHG stage scheme with the fundamental, undepleted fundamental and

second harmonic beam polarization, is shown in Figure 3.22. Since the huge

small signal gain allows self lasing in the amplification stage, a scattered

light stopper pinhole was placed next to the LBO crystal. An harmonic

separator mirror divides the undepleted fundamental beam from the 532nm

output.

The excellent second harmonic beam profile is shown in Figure 3.23.

A conversion efficency of ≈ 55%, corresponding to a maximum energy of

≈ 5.5µJ per pulse at 532nm, was obtained without the need to focus the fun-

damental beam inside the second harmonic generation crystal. Moreover the

non-linear process contributed to further increase the ratio between the am-

plified selected pulses and the adjacent not completely extinguished pulses

shown in Figure 3.14.

The oscilloscope traces of both the amplified infrared pulse and its sec-

ond harmonic are shown in Figure 3.24. Subnanosecond InGaAs and silicon


NO

N D

EP

LET

ED

IR

BEAM STOPPER

AMPLIFIED FUNDAMENTAL BEAM

GREEN OUTPUT

HARMONICS SEPARATOR

LBO

SCATTERING STOPPERDIAPHRAGM

SHG FIELD POL.FUND. FIELD POL.

Figure 3.22: SHG stage setup

Figure 3.23: A picture of the second harmonic beam

photodiodes were used for these measurements, along with a 1-GHz oscillo-

scope (Tektronix TDS5104B). It is worth noting that notwithstanding the

weakly saturated amplification process, relatively stable pulses with ampli-

tude fluctuations as small as 2% (one-sigma) were recorded.

3.2.6 The Optical Parametric Generation (OPG) stage

The final system stage is represented by an Optical Parametric Generation

stage, necessary to provide the few picosecond pulses with a wavelength

near 800nm needed for the photoconductivity measurements. To this end,


Figure 3.24: Oscilloscope traces of the undepleted fundamental and second har-

monic pulses, normalized so that the ratio of the peaks corresponds

to the observed conversion efficiency. In case of 2ω pulse, also the

adjacent small pulses are strongly depressed by the non-linear process

a traveling-wave OPG was set up using a 15mm long and uncoated KTP

crystal cut for Type-II phase-matching in the XZ plane. In this scheme,

reported in Figure 3.25, an ordinarily polarized pump photon is splitted

into an ordinary idler photon and an extraordinary signal photon, with the

following constrain about the energy:

op −→ es + oi;1

λp=

1

λs+

1

λi

A parametric generator is an optical parametric amplifier with quite

high gain (many tens of dB), so that a significant output power is gener-

ated even without any input signal. The physical origin of this emission is

parametric fluorescence, amplified to high levels. This phenomenon is sim-

ilar to amplified spontaneous emission (ASE) in a laser amplifier; in both

cases, quantum fluctuations of the vacuum (the so called vacuum noise) are

amplified to macroscopic power levels.

Compared with an Optical Parametric Oscillator (OPO), the setup of

a parametric generator is simpler, because it does not need a cavity. One

may simply tune the wavelengths of signal and idler by influencing the phase-


X

Y

Z

s

p,iθ

KTP

kp,s,i

Figure 3.25: Type-II phase matching in the XZ plane for KTP crystal. The

polarization directions of pump (p), signal (s) and idler (i) are also

reported

matching conditions, which corresponds in our critical Type-II phase match-

ing scheme in an angular rotation of the KTP crystal in the vertical plane.

Of course OPO can have a much lower threshold pump power and the re-

Figure 3.26: Signal (blue) and idler (green) wavelength as a function of crystal

tilting angle in the vertical plane


quired high intensities in OPG setups sometimes force one to operate not

that far below the optical damage threshold of the nonlinear material, as

it was in our case. The theoretical idler and signal accordability range is

shown in Figure 3.26

A side view of the final stage setup is represented in Figure 3.27.

TUNABLE OUTPUT BEAM

KTP CRYSTAL

PUMP BEAM 532nm

FOCUSING LENS

f = 100mm

UNDEPLETED GREEN PUMP

Figure 3.27: Side view of the Optical Paramatric Generation setup

Parametric superfluorescence was readily observed by pumping with

5.5µJ energy, 532nm pulses and using a 100mm focal lens. The spot radius

was calculated to be w0 ≈ 40µm, and the peak intensity ≈ 25 GW/cm2, rea-

sonably below to the threshold of surface optical damage at 8ps pulsewidth

for the uncoated crystal (35 GW/cm2 using an inverse-square law scaling

rule from the specified threshold of 1 GW/cm2 at 10ns[16]).

With this setup the OPG was pumped at about twice its threshold level

at 790nm, and was readily tunable in the range 770nm – 1020nm (signal

wavelength λs, see Figure 3.28) and 1110nm – 1720nm (idler wavelength λi).

The signal bandwidth was ≈ 1nm, close to the resolution of the monochro-

mator used for OPG characterization (Ocean Optics USB2000), and the

conversion efficiency was of few percents. The OPG tuning range was

actually limited by mechanical constraints, and might be readily extended

down to ≈ 650nm, where the idler absorption starts limiting the conversion

process.

The pump intensity threshold condition for the OPG can be written

as[17]:

I2ω,th = 4.6ǫ0cn

3λsλi

d2effL2

eff

(3.1)


Figure 3.28: Spectra of the OPG pulses, obtained at several tuning angles

where:

ǫ0 is the vacuum permittivity;

c is the speed of light;

n = 1.8 is the average refractive index;

deff = 3.2 pm/V is the nonlinear coefficient.

In eq. (3.1) the spatial walk-off angle (see Appendix B, B.2) ρ ≈ 2.7

and the gaussian beam diffraction (confocal parameter b = 2πnw20/λ2ω) are

included as in [18] for SHG, defining a squared effective interaction length:

L2eff = L2 b

Ltan−1

(L

b

)

tanh

(La

L

)

(3.2)

The experimental results are reasonably reproduced by this model if

one defines a walk-off length La = 2√

πw0/ρ in eq. (3.2), twice the value

assumed heuristically for second-harmonic generation in [18]. Since the opti-

cal parametric generator operated at only two times above pump threshold,

it was not as stable as the pump pulse, but exhibited ≈ 30% amplitude

fluctuations.


A picture of the whole laser system is shown in Figure 3.29. The footprint

of the laser box is 45cm×60cm.

LEGEND

1 1W CW Diode Pump

2 CW-ML Laser cavity

3 Monitor output (to monitor PhotoDiode)

4 Acousto-optical Pulse Picker

5 Non deflected beam stopper

6 QCW Amplification stage

7 SHG generation stage (LBO crystal)

8 Harmonic separator

9 OPG stage (KTP crystal)

10 532nm and 800nm output beams

Table 3.2: Legend of Figure 3.29


Figure 3.29: System setup, see Table 3.2 for legend

Bibliography

[1] P. Heinz, A. Seilmer, A. Piskarskas, Picosecond Nd:YLF laser-

multipass amplifier source pumped by pulsed diodes for the operation of

powerful OPOs, Opt. Commun. 136, 433-436 (1997)

[2] M. Siebold, M. Hornung, J. Hein, G. Paunescu, R. Sauer-

brey, T. Bergmann, G. Hollemann, A highaverage power diode-

pumped Nd:YVO4 regenerative laser amplifier for picosecond-pulses,

Appl. Phys. B 78, 287-290 (2004)

[3] J. Kleinbauer, R. Knappe, R. Wallenstein, 13-W picosecond

Nd:GdVO4 regenerative amplifier with 200-kHz repetition rate, Appl.

Phys. B 81, 163-166 (2005)

[4] A. Killi, J. Dorring, U. Morgner, M. J. Lederer, J. Frei, D.

Kopf, High speed electro-optical cavity dumping of mode-locked laser

oscillators, Opt. Express 13, 1916-1922 (2005)

[5] X. Liu, D. Du, G. Mourou, Laser ablation and micromachining

with ultrashort laser pulses, IEEE J. Quantum Electron. QE-33,

1706–1716 (1997)

[6] R. Osellame, S. Taccheo, M. Marangoni, R. Ramponi, P. La-

porta, D. Polli, S. De Silvestri, G. Cerullo, Femtosecond writing

of active optical waveguides with astigmatically shaped beams, J. Opt.

Soc. Am. B 20, 1559–1567 (2003)

[7] G. Cerullo, S. De Silvestri, Ultrafast optical parametric amplifiers,

Rev. Sci. Instrum. 74, 1–18 (2002)

84 Bibliography

[8] G. N. Gibson, R. Klank, F. Gibson, B. E. Bouma, Electro-

optically cavity-dumped ultrashort-pulse Ti:sapphire oscillator, Opt.

Lett. 21, 1055–1057 (1996)

[9] J. E. Bernard, A. J. Alcock, High-efficiency diode-pumped Nd:YVO4

slab laser, Opt. Lett. 18, 968-970 (1993)

[10] M. J. Damzen, M. Trew, E. Rosas, G. J. Crofts, Continuous-

wave Nd:YVO4 grazing-incidence laser with 22.5W output power and

64% conversion efficency, Opt. Comm. 196, 237-241 (2001)

[11] G. Smith, M. J. Damzen, Spatially-selective amplified spontaneous

emission source derived from an ultra-high gain solid-state amplifier,

Opt. Express 14, 3318-3323 (2006)

[12] A. Agnesi, L. Carra, F. Pirzio, G. Reali, A. Tomaselli,

D. Scarpa, C. Vacchi, Amplification of a Low-Power Picosecond

Nd:YVO4 Laser by a Diode-Laser Side-Pumped Grazing-Incidence Slab

Amplifier, IEEE J. Quantum Electron., 42, pp. 772-776 (2006)

[13] A. Agnesi, L. Carra, F. Pirzio, D. Scarpa, A. Tomaselli, G.

Reali, C. Vacchi, C. Braggio, High-gain diode-pumped amplifier for

generation of microjoule-level picosecond pulses, Opt. Exp. 14, 9244-

9249 (2006)

[14] B. Braun, K. Weingarten, F.X. Kartner, U. Keller, Continuous-

wave mode-locked solid-state lasers with enhanced spatial hole-burning.

Part I. Experiments, Appl. Phys. B 61, 429-437 (1995)

[15] S P. Velsko, M. Webb, L. Davis, C. Huang, Phase matched har-

monic generation in Lithium Triborate (LBO), IEEE J. Quantum

Electron., 27, pp. 2182-2193 (1991)

[16] W. Koechner, Solid State Laser Engineering, 5th ed., Berlin, Ger-

many: Springer (1999)

Bibliography 85

[17] R. L. Byer, Optical parametric oscillators, in Quantum Electron-

ics: A Treatise, H. Rabin and C. L. Tang, pp. 587–702, (Aca-

demic, New York, 1975)

[18] P. L. Ramazza, S. Ducci, A. Zavatta, M. Bellini, and F. T.

Arecchi, Second-harmonic generation from a picosecond Ti:Sa laser

in LBO: conversion efficiency and spatial properties, Appl. Phys. B

75, 53-58 (2002)

86 Bibliography

Appendix A

Guidelines for a model of a

grazing incidence single-pass

QCW amplifier

In order to better understand the behavior of the grazing-incidence amplifier,

we introduce a simplified model based on standard QCW amplifier theory.

A.1 Grazing incidence single pass amplifier

Let’s start from the rate equation for the amplifier during pumping:

dn

dt= Wp −

n

τf(A.1)

with:

Wp =λp

λl

αp

wL

Pinc(0)e−αpx

ℏωp(A.2)

where in eq. (A.1) and (A.2) we introduced the following quantities:

n is as usual the population inversion;

τf is the fluorescence life-time of the amplifying material (sec);

Wp is the pump rate;

87

88 Guidelines for a model of a grazing incidence single-pass QCW amplifier

αp is the active medium pump absorption coefficient at the pumping

wavelength (cm−1);

x is the pump propagation direction in a side-pumping scheme;

w and L are respectively the height of the pumped region and the

crystal length;

λp, λl and ωp have the usual meaning.

Assuming a pump pulse duration τp, in order to find the population inversion

as a function of τp we have to integrate eq. (A.1):

∫ ni

0

dn

n − Wpτf= −

∫ τp

0

dt

τf= − τp

τf(A.3)

from which we obtain:

ln

(ni − Wpτf

−Wpτf

)

= − τp

τf=⇒ ni = Wpτf

[

1 − e−τp/τf

]

(A.4)

which reduces to the steady state solution wit CW pumping for τp → ∞.

Let’s introduce now the geometry of our system and the new working

coordinates. The side-pumped slab is represented in Figure A.1. The crystal

length is L, the internal bounce angle is θ and it is assumed to be “small”, al-

lowing all the usual trigonometrical approximations. The pump propagation

direction is x, while the amplified beam propagation direction is given by

s. A local coordinate ξ in the transverse direction of the propagating beam

is defined. Coordinates x can be given in function of s and xi according to

this transformation:

x(s, ξ) =θL

2+ ξ + sθ

The output fluence after a single pass amplification is given by[1][2]:

Fo = Fs ln[

1 + eg0

(

eFi/Fs − 1)]

(A.5)

where Fs =σ

ℏωlis the saturation fluence for the active medium and g0 is

the small signal gain.

A.1 Grazing incidence single pass amplifier 89

x

y

θ

s

θL/2

ξ

0

L/2

∝ e−αp|x|

Figure A.1: Geometry definitions for the side-pumped grazing incidence slab am-

plifier medium

Considering the situation represented in Figure A.1, we can evaluate the

gain experienced by the laser beam during its bouncing propagation inside

the active medium:

g0 =

∫ L

0σndz = σWpτf

[

1 − e−τp/τf

]

Ψ (A.6)

in which σ is the active material emission cross section an Ψ is the path gain

integral, defined as follows:

Ψ =

∫ L

0e−αp|x|ds (A.7)

Using the expression of x(s, ξ) and integrating along the beam path, we

obtain:

Ψ =2

αpθ

[

1 − e−αpθL/2cosh(αpξ)]

(A.8)

For an easier understanding of the physical behaviour of the system we can

make some approximations and imagine a flat-top profile for the seed laser

beam entering the amplifier. This assumption leads to a new expression for

Ψ, averaged along the ξ direction. Introducing the flat-top input beam waist


wi, we have:

< Ψ >wi=

1

2(wi/2)2

∫ wi/2

0Ψ(ξ)dξ =

=2

αpθ

[

1 − e−αpθL/2 2

wi

∫ wi/2

0cosh(αpξ)dξ

]

=

=2

αpθ

[

1 − e−αpθL/2 2

wiαpsinh

(αpwi

2

)]

(A.9)

This leads to the final approximated expression for the small signal gain:

< g0 >wi≈ σ < Wp > τf

[

1 − e−τp/τf

]

=

=λp

λl

Einc

wLFs

τf

τp

[

1 − e−τp/τf

]

︸︷︷︸

ηT

2

θ

[

1 − e−αpθL/2 2

wiαpsinh

(αpwi

2

)]

(A.10)

where:

Einc is the pump energy entering in the active medium;

Fs =σ

ℏωlis the saturation fluence of the active medium;

ηT depends on the ratio between pump pulse duration and fluorescence

time and measures the fraction of deposed pump energy available for

extraction;

w, L and θ represent respectively the height of the pumped region, the

crystal length and the internal bounce angle;

αp is the absorption coefficient at the pump wavelength;

wi is the flat-top shaped input beam waist.

A.2 1st order consideration while designing a sin-

gle pass amplifier

In high gain amplification modules the first constrain to consider for effi-

cient operation is the limit set by Amplified Spontaneous Emission (ASE)

A.2 1st order consideration while designing a single pass amplifier 91

to single-pass small signal gain g0. The ASE rising, roughly speaking, fixes

a limit to the maximum achievable gain. When amplified laser beam fluence

becomes comparable to ASE, any further increasing in single-pass small sig-

nal gain means to transfer energy not to the seed beam, but to the ASE

itself.

In order to have a more quantitative idea of the situation, we can refer to

Figure A.2, in which ASE fluence normalized with respect to active medium

saturation fluence is given as a function of single pass small signal gain[3].

Figure A.2: Fluence of ASE Fin normalized with respect to the saturation flu-

ence Fsat as a function of the single pass small signal gain g0 for

an emission solid angle Ω = 4π · 10−4sterad. Dashed curve is ob-

tained with the approximation Fin ≪ Fsat, dotted line refers to the

approximation of Fin ≫ Fsat

Considering a non-saturated amplifier in which the amplified beam flu-

ence is few percent of the saturation fluence, the small signal single pass

gain should fall in the range 5 ÷ 10 in order to avoid that ASE becomes


predominant. If we use the g0 expression given by (A.10) with the physical

parameters summarized in Table A.1 (that applies to our working condition)

we obtain a rough value g0 ≈ 9.

Experimental working conditions

λp 808nm λl 1064nm

w ≈ 1mm L 12mm

Einc ≈ 18mJ Fsat 0.15J/cm2

τf 90µs τp 120µs

αp 25cm−1 wi ≈ 400µm

θ 4

Table A.1: Physical parameters in our working condition (active medium

Nd:YVO4) for a 1st order estimation of g0

Appendix B

Critical parameters for

efficient harmonic and

parametric generation

B.1 Second harmonic efficient generation in LBO

Second harmonic generation efficiency can be defined in terms of energy as

follows[1]:

η =E2ω

Eω= tanh2

√

8π2Z0

d2eff

n3λ2ω

l2Iωsinc

(∆kl

2

)

(B.1)

where:

Z0=377Ω is the vacuum impedance;

deff is the effective non-linear coefficient of the material;

l is the crystal length;

Iω is the intensity (W/cm2) of the fundamental beam;

∆k is the phase mismatch.

93

94 Critical parameters for efficient harmonic and parametric generation

In order to optimize the design of the SHG stage some critical parameters

have to be taken into account:

Spatial walk-off :

- the direction of the power flow, given by the Poynting vector, is

in general different for the E2ω field with respect to the Eω field. The

walk-off angle ρ is defined as follows:

ρ = | tan−1

(

n22ω,y

n22ω,x

tan α

)

− α|

where α is the phase-matching angle.

The walk-off angle as function of the fundamental field wavelength is

reported in Figure B.1.

Figure B.1: Walk-off angle as a function of wavelength in LBO

Temporal walk-off :

- it is a consequence of group velocity dispersion (GVD); temporal

walk-off per unit length of the crystal is defined as follows:

tw−off = | 1

vg,2ω− 1

vg,ω|

B.1 Second harmonic efficient generation in LBO 95

Figure B.2: Group Velocity Dispersion in LBO as a function of pump wavelength

Figure B.2 shows the behaviour of LBO crystal around 1.064µm fun-

damental field wavelength.

Angular acceptance :

- it is a measure of how accurately the crystal has to be oriented in

order to achieve the maximum conversion efficency. Since the conver-

sion efficency is proportional to sinc2

(∆kl

2

)

(see Eq. (B.1)), the an-

gular acceptance is set to the value ∆α that makes sinc2

(∆kl

2

)

=1

2:

αp.m. + ∆α =⇒ ∆kl

2= 0.443π (B.2)

Furthermore, since the transversely limited wavefronts of width 2w

have a diffraction angle ϑ =2λ

πw, this should be smaller than the

crystal angular acceptance.

Figure B.3 shows the behaviour of LBO around 1.064µm.

Temperature acceptance :


Figure B.3: Angular acceptance in LBO around 1.064µm

Figure B.4: Temperature acceptance in LBO around 1.064µm

- it is a measure of how accurately the crystal has to be thermally

controlled in order to achieve the maximum conversion efficency. Ac-

B.2 Optical parametric generation in KTP 97

cording to the definition of angular acceptance, we have:

Tp.m. + ∆T =⇒ ∆kl

2= 0.443π

In Figure B.4 the temperature acceptance around the fundamental

1.064µm wavelength is reported.

In Table B.1 the values of all of these parameters in our working condition

are summarized.

SHG critical parameters

Spatial walk-off ρ ≈ 0.33

Temporal walk-off tw−off ≈ 0.67ps

Angular acceptance ∆α ≈ 3.3mrad

Temperature acceptance ∆T ≈ 3.7C

Table B.1: Working Conditions: Crystal length l = 1.5cm, λω = 1.064µm

B.2 Optical parametric generation in KTP

As previously discussed for LBO, also for KTP crystal, critical parameters

for efficient non-linear conversion are walk-off angle, Group Velocity Dis-

persion (GVD) and angular acceptance.

Spatial walk-off :

- as we already said for second harmonic generation, it measures

the angle between the Poynting vector of the pump beam and of the

signal generated beam.

In Figure B.5 the walk-off angle for the signal beam in the range from

0.6 to 1µm wavelength is reported.

As reported in 3.2.6, in our working conditions the spatial walk-off

angle ρ ≈ 2.7. In addiction to walk-off length, also Rayleigh range

(defined asπw2

0

λp≈ 9mm in our working conditions) of focused pump


Figure B.5: Walk-off angle for signal in KTP as a function of wavelength

beam should be taken into account while designing the OPG stage,

since it fixes the maximum non-linear interaction lenght.

Group Velocity Dispersion:

- gives the temporal delay, measured in picosecond, that pump,

idler and signal accumulate while propagating in a unity length of

non-linear crystal.

In Figure B.6 the behaviour of KTP crystal is shown.

Angular acceptance:

- it measures how accurately the crystal has to be oriented in order

to achieve the maximum conversion efficiency at the desired signal and

idler wavelength. Its definition is given in eq. (B.2) and the behaviour

of KTP is shown in Figure B.7.

Once again, since the transversely limited wavefronts of width 2w have

a diffraction angle ϑ =2λ

πw, this should be smaller than the crystal

angular acceptance.

B.2 Optical parametric generation in KTP 99

Another parameter that should be considered is the spectral bandwidth of

both signal and idler generated beams. In Figure B.8 the behaviour of

Figure B.6: GVD in KTP for signal with respect to pump (blue curve) and to

idler (green curve) for a signal wavelength ranging from 0.6 to 1µm

Figure B.7: Angular acceptance in KTP with respect to signal wavelength in the

range 0.6-1µm


KTP over the entire generable bandwidth with 532nm pump wavelength is

reported.

Figure B.8: Signal (blue curve) and idler (green curve) spectral bandwidth ver-

sus wavelength in KTP. The signal bandwidth in the range 0.6-1µm

is lower than the 1nm maximum resolution of the Ocean Optics

USB2000 spectrometer employed the OPG characterization reported

in Figure 3.28, as expected by the measurements results

Bibliography

[1] W. Koechner, Solid State Laser Engineering, 5th ed., Berlin, Ger-

many: Springer (1999)

[2] A. E. Siegman, Lasers, University Science Books (1986)

[3] O. Svelto, Principles of lasers, 4th edition, Plenum (1998)

Issues and workshops

Issues

1. A. Agnesi, F. Pirzio, A. Tomaselli, G. Reali, C. Braggio, Multi-GHz

tunable-repetition-rate mode-locked Nd:GdVO4 laser, Optics Express,

Vol. 13, pp. 5302-5307, (2005)

Abstract: We report on a simple design for a multi-GHz tun-

able repetition-rate diode-pumped picosecond laser. Using a plano-

Brewster Nd:GdVO4 crystal in a V-folded cavity employing only read-

ily available commercial components, we achieved passive mode-locking

with 4.4-ps pulses tunable in the range 2.5-2.7 GHz. This laser is meant

to be employed in the MIR experiment that aims at the detection of

the Schwinger radiation (dynamical Casimir effect)

2. A. Agnesi, L. Carra, F. Pirzio, G. Reali, A. Tomaselli, D. Scarpa, C.

Vacchi, Amplification of a Low-Power Picosecond Nd:YVO4 Laser by

a Diode-Laser Side-Pumped Grazing-Incidence Slab Amplifier, IEEE

Journal of Quantum Electronics, Vol. 42, pp. 772-776, (2006)

Abstract: An optimized diode-laser side-pumped grazing inci-

dence Nd:YVO4 amplifier was used to increase the power of a 50-mW

150-MHz continuous-wave (CW)-pumped mode-locked oscillator up to

6.1 W in single pass, with 22% optical-to-optical efficiency, or up to

8.4W in double pass, with 30% efficiency. Both beam quality (M2 ¡1.4

from TEM00 seed pulses) and pulse duration (7.5 ps from 6.9 ps) were

preserved. Single- or double pass small-signal gain greater than 40 dB

104 Issues and workshops

was achieved. These experimental results have been corroborated by

a numerical model analysis of the amplifier.

3. A. Agnesi, F. Pirzio, G. Reali, G. Piccinno, Sub-nanosecond diode-

pumped passively Q-switched Nd:GdVO4 laser with peak power ¿1MW,

Applied Physics Letters, Vol. 89, pp. 101120-1 101120-3 (2006)

Abstract: The authors report on a passively Q-switched diode

pumped Nd:GdVO4 miniature laser generating 0.5mJ pulses at 1063nm,

with 420ps time duration and 1.2MW peak power, at a repetition rate

up to 200Hz and with a nearly diffraction limited beam quality M2¡1.1.

4. A. Agnesi, L. Carra, F. Pirzio, D. Scarpa, A. Tomaselli, G. Reali, C.

Vacchi, High gain diode pumped amplifier for generation of microjoule-

level picosecond pulses, Optics Express, Vol. 14, pp. 9244-9249

(2006)

Abstract: A diode-pumped single-pass amplifier system relying

on two grazing-incidence Nd:YVO4 slabs was developed to increase

the energy of low-repetition-rate pulses from a decimated low-power

cw mode-locked oscillator. Single-pass unsaturated gain up to 1.3·105

was achieved, and amplified pulses of 10-µJ energy and 8.0-ps duration

were obtained. Efficient second harmonic generation (SHG) at 532nm

was achieved, as well as traveling-wave parametric conversion in the

range 770-1020nm (signal) and 1110-1720nm (idler).

Workshops

1. A. Agnesi, F. Pirzio, A. Tomaselli, F. Bonfigli, T. Marolo, Thermal

lens characterization of a side-pumped Nd:YVO4 laser

XV International Symposium on Gas Flow, Chemical Lasers,

and High-Power Lasers - Prague (CZ) - Poster Session Septem-

ber 2004.

2. A. Agnesi, A. Guandalini, A. Lucca, F. Pirzio, A. Tomaselli, G. Reali,

E. Sani, A. Toncelli, M. Tonelli, Passive stabilization technique applied

Issues and workshops 105

to continuous-wave picosecond mode-locked Yb:YAG and Nd:BaY2F8

lasers

CLEO - Baltimore (US) - Oral Session, May 2005

3. A. Agnesi, L. Carra, F. Pirzio, G. Reali, D. Scarpa, A. Tomaselli,

C. Vacchi, Amplification of a low power picosecond Nd:YVO4 laser to

multiwatt level with a side pumped grazing incidence slab

EUROPHOTON CONFERENCE - Pisa (IT) - Poster Ses-

sion, September 2006

4. A. Agnesi, L. Carra, F. Pirzio, G. Reali, D. Scarpa, A. Tomaselli,

C. Vacchi, C. Braggio, Novel amplification scheme for generation of

microjoule-level picosecond pulses

EUROPHOTON CONFERENCE - Pisa (IT) - Oral Session,

September 2006

UNIVERSITA DEGLI STUDI DI PAVIA´3.20 CriticalphasematchingofSHG in LBO.The polarizationdirections...

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