Modelocked Modelocked Ti:sapphireTi:sapphire LaserLaser

Lasers

A laser is an oscillator, all oscillators have1) Amplification/Gain2) Feedback

In a laserAmplification: stimulated emission in gain medium (gas, liquid solid)Feedback: mirrors (cavity)

LightAmplification byStimulatedEmission ofRadiation

Gain

Ener

gy OutputPartiallyTransmissive“Output coupler”

Gain by stimulated emission

Impossible to invert two 2 level system:

3-level systemrequires strong pump

Requires “inversion”greater population in upper state than lower stateotherwise absorption balances stimulated emission

Photon

Photon

Absorption

Photon

Stimulated Em

ission

4-level systembest

Pum

p

Fast relaxation

Slow relaxation

Lasi

ng

Pum

p

Fast relaxation

Slow relaxation

Lasi

ng

Fast relaxation

Resonator Stability

Need the resonator to be “stable”, i.e. the light stays in the cavity

Use ABCD matrices, resonator stable if round-trip matrix satisfies

stable conditionally stablerequires perfect alignment

unstable

20 14

A D+ +≤ ≤

Flat mirrors, just free space, A = D = 1, gives conditionally stable

Equality conditionally stable

Pulse generationA pulse forming mechanism is needed

otherwise lasers run “continuous wave” (CW)

Three types of pulsed operation

Gain switched (micro or millisecond pulses typically)

turn gain on and off (flash lamps, modulate pump)

Q-switched (nanosecond pulses

modulate cavity loss on times scales > round trip time

Modelocked (picosecond to femtosecond pulses

modulate cavity loss periodically at roundtrip time

Historical Progress in Ultrashort Pulses

Nd:glass

S-P DyeDye

CW Dye

Diode

Nd:YLF

Cr:YAG

Cr:liS(C)AFEr:fiber (telecom)Cr:forsteriteNd:fiber

Ti:sapphire

CPM

w/Amplification& Compression(Low Rep. Rate)

ColorCenter

1965 1970 1975 1980 1985 1990 1995

10

10

10

10

-11

-12

-13

-14

ADVANCES IN SHORT PULSE GENERATION

DyePuls

ewid

th(s

ec)

Year

Nd:YAG

Courtesy of E.P. Ippen

Modelocking

0 1 2 3 4 5

Inte

nsity

Time (ns)

Laser Cavity

Modelocking

0 1 2 3 4 5

Inte

nsity

Time (ns)

Laser Cavity

Modelocking

0 1 2 3 4 5

Inte

nsity

Time (ns)

Laser Cavity

Modelocking

• Constructive interference between phase locked cavity modes 0 1 2 3 4 5

30 Modes (Random)

30 Modes (locked)

Inte

nsity

Time (ns)

Laser Cavity

How do you modelock?

• Active modelocking– Acoustooptic modulator, drive with RF– Minimum pulsewidth limited (ps’s)

• Saturable absorption– Use pulse to “gate” itself

• Pulse shortening rate increases with shortening of pulse• Often limited by processes that stretch pulse (dispersion)

– Real: finite population of absorbers• Dye molecules• Semiconductors• Finite relaxation time

– Effective: nonlinear phase shifts converted to amplitude• Nonlinear lensing + aperture• Nonlinear polarization rotation + polarizer• Essentially instantaneous

Kerr Lens Modelocking• Kerr Lens & Aperture gives

increased transmission at high intensity

• Increased transmission at high intensity = saturable absorption

• Short, intense pulse preferred in laser

• Kerr effect instantaneous• Not self starting

GaussianLaser Beam

High Intensity

Gaussian Beam =Gaussian Index Profile =Gradient Index Lens

GaussianLaser Beam

Low Intensity

Kerr Mediumn = n0 + n2I

Kerr Lens Modelocked Ti:sapphire

• Ti:sapphire has large bandwidth• Supports shortest pulses• Simple (amazingly)

M.T. Asaki, et al, Opt. Lett. 18, 977 (1993)

Output coupler High reflector

Pump

Ti:Sapphirecrystal

Prisms(Dispersion compensation)

Beam profile

CW Modelocked

Dispersion Compensation

High reflector

Prisms(

Elements in cavity have group velocity dispersion, velocity depends on frequency

In “visible”, red travels faster than blue (“normal” dispersion)Need to generate “anomalous” dispersion to counter act this

Blue lightis refractedmore than red

Red lighttravels throughtore glass thanblue light

Pump Laser

FocusingLens

Ti:sapphcrystal

Curved mirrors

Output coupler

Prisms

Highreflector

Details

The crystal is at Brewster’s angle

A focus through a dielectric interface at an angle causes astigmatism

compensated by having the curved mirrors at an angle

“Focus” (distance between curved mirrors and crystal) depends on distance to end mirrors

2

1

tan nn

θ =