28/06/2006

Laser Optics 2006, workshop „Dissipative Solitons“ WeW5-11 1

Realization of a cavity-soliton laser using broad-area VCSELs

with frequency-selective feedback

Control of bistability in broad-area

vertical-cavity surface-emitting lasers with

frequency-selective feedback

T. Ackemann1, Y. Tanguy1, A. Yao1,

A. V. Naumenko2, N. A. Loiko2 , R. Jäger3

1Department of Physics, University of Strathclyde, Glasgow, Scotland, UK2Institute of Physics, Academy of Sciences of Belarus, Minsk, Belarus3ULM Photonics, Lise-Meitner-Str. 13, 89081 Ulm, Germany

Funding:• FP6 STREP 004868 FunFACS• U Strathclyde Faculty starter grantalso thanks to: W. J. Firth, L. Columbo

2

Outline

motivation for pursuing a cavity soliton laser

setup• devices• design of external cavity

results

interpretation • mechanism of optical bistability• master equation for general cavities

summary

3

driven cavity: need for light field of high temporal and spatial coherence

nonlinearmedium

mirror mirror

Motivation for a cavity soliton laser

prerequisite: coexistence between different states optical bistability between homogeneous states or bistability between pattern and homogeneous state symmetry-breaking pitchfork bifurcation

cavity soliton = (spatially) localized, bistable solitary wave in a cavity

look for bistable nonlinear optical systems

but „normal“ laser: continuous turn-on no cavity solitons

pump level ou

tput

laser: extracts energy from incoherent source

bad news

4

Cavity soliton laser IIbistable laser schemes

laser with injected signal

gain

laser with frequency-selective feedback

gain filter

laser with saturable absorber

gain SA

extract energy solely from incoherent source

„better“ cavity soliton laser

go for VCSEL with frequency-selective feedback

look for incoherent manipulation robustness active device cascadability

5

Devices

GaAs substrate

p-Bragg

TiPtAu contact pad

oxide apertureQWs (3 InGaAs/GaAs)

AR coatingGeNiAu contact

n-Bragg

output

e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061

• bottom emitter (more homogeneous than top emitter)

emission wavelength

980 nm

33 stacks + metallic mirror,

R > 0.9998

20.5 stacks, R > 0.992

6

Near field intensity distribution

free-running laser (below threshold)

• not lasing cw (thermal roll-over)• defect lines• apart from that “rather homogeneous“

with feedback (tuned slightly off-axis)

• some more defects apparent

7

Setup: Scheme

VCSEL

Grating

HWP1

self- imaging

HWP2

f1=8mm f2=300mm

Detection partWriting beam

• self-imaging maintains high Fresnel number of VCSEL• high anisotropy of grating polarization selective

Littrow

8

33 propagation matrices

O. Martinez, IEEE J. Quantum Electron. 24, 12, 1988

=

xout

out

A B E

C D F

0 0 1

xin

in

usual 2x2 ABCD matrix

angular dispersion

spatial chirpfor grating:

cos2

cos1

A = ( 1 –(1/n)(F0 tan2))

cos1

cos2

D = ( 1 +(1/n)(F0 tan2))

A 0 00 D F0

0 0 1

F0 = -(2cn2d cos2)

Littrow frequency detuning from Littrow frequency d spacing between grooves 2 and 1 angles of reflection and incidence from the gratingc velocity of lightn refractive index).

9

mm

-100 0 100 200 300 400 500 600 700-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

mm

-100 0 100 200 300 400 500 600 700-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

At Littrow frequency

= 0, on-axis

mm

-2 0 2 4 6 8 10 12-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

= 0, 5 deg. angle

all rays/beams return to same position with same angle

perfect reproduction

after one round-trip

mm-2 0 2 4 6 8 10 12

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

„normal“

mirror

10

mm-100 0 100 200 300 400 500 600 700

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

mm-100 0 100 200 300 400 500 600 700

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Detuned from Littrow frequency

= 1nm, on-axis

= 1nm, 5 deg. angle

mm-5 0 5 10 15 20

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

mm-4 -2 0 2 4 6 8 10 1214 16

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

still same

location, but

angle

different

no closed

path;

rejected by

VCSEL cavity

angular dispersion 0.15 rad/nm; estimated width of resonance 0.026 rad

bandwidth of feedback 55 GHz

11

A loophole

mm

-100 0 100 200 300 400 500 600 700-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

= 1nm, 4.21 degrees angle

mm-2 0 2 4 6 8 10 12 14

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

beam is exactly retroreflected into itself: -

this is not a closed path in external cavity after one round-trip!

but reflection at boundaries and nonlinearities couple wavevectors k - k

within VCSEL spurious feedback

12

Setup: Details

Main external cavity L 0.603 m

1800/mm

tunable laser

13

Near field: Increasing current

feedback tuned close to longitudinal resonance

14

Near field: Decreasing current

feedback tuned close to longitudinal resonance

15

Current dependence: Spots

370mA 381.5mA 386mA 391mA

Increasing current

decreasing current

bistable localized spots

16

Hysteresis loop

• clearly bistable• „kinks“

related to jumps

between external cavity

modes

local detection around single spot

17

Switch-on of spots

• independent switch-

on of two spots• „independent entities“

• cavity solitons ?

• does not depend critically

on frequency detuning of

WB to emerging spot• robust• need resonance in

external cavity

(but question of power)

18

Spectra

low resolution spectrum (plano-planar SFPI) • frequencies of spots

different

0.05 nm 20 GHz• further indication for

independence• probably related to

inhomogeneities

• linewidth (confocal FPI)

10 MHz

• These are small lasers!

19

Spectra with writing beam

WB injected directly onto the spot, at different frequencies.

• red-detuned: injection locking

• blue-detuned: switch-off excitation of background

• equal or blue-detuned: red-shift (carrier effect)

20

Switch-off by excitation of background

• under some conditions

for blue-detuning:

- switch-off

- excitation of

background wave

• not very well understood

but nevertheless:

incoherent manipulation

21

Switch-on/off by position

• switch-on:

hit it head-on (or on some

locations in

neighbourhood)

• switch-off: hit at

(other locations in)

neighbourhood

• complete manipulation

CS !

• incoherent, robust

22

„Plasticity“ / „Motility“

CS ought to be self-localized, independent of boundary conditions

can easily couple to external perturbation motion (on gradients)

trapping (in defects)

possibilities:

writing beam aperture diffractive ripples comb

23

„Pushing“ by aperture

shift by about 5 µm

24

Dragging with comb

• spots exist in a broad

range with small

perturbations

25

Intermediate summary

experiment:

bistable localized spots can exist at several points,

though preferentially at defects independent manipulation indications for motility

these guys have the properties of

cavity solitons,

though defects might play a role in

nucleation and trapping

some interpretation:

why bistability? approach to model details of the external cavity dynamical model: Paulau et al. Talk WeW5-14, 17.30

26

Theoretical model (without space)

• delayed feedback terms (Littman)• single round-trip

(Lang-Kobayashi approximation)

• feedback anisotropic

feedback

noise

Naumenko et al., Opt. Commun. 259, 823 (2006)

we start with spin-flip model (though spin not important for idea)

27

Results: Steady-states + simulations

green: analytic solutions for stationary states / external cavity modes

black:simulations

(red/blue for other polarization).

feedback favoring weaker pol. mode

bistability between lasing states and off-states; abrupt turn-on; small hysteresis

~ current

thermal shift of solitary laser frequency

28

Interpretation: Mechanism of OBlaser originally blue detuned with respect to grating

green/blackweaker pol.

red/bluestronger pol.

~ current (Joule heating)frequency of solitary laser

oper

atin

g fr

eque

ncy

with

feed

back

increase of power, decrease of carriers

feedback induced

red-shift

laser better in

resonance with grating

positivefeedback

29

Conditions for OB

OB should exist for: phase-amplitude

coupling

feedback

strength

in 80 µm device

„stabilization“

of small-area

laser

with intra-

cavity

aperture

in near

fieldbandwidth

of feedback

exp. threshold for OB: 45% = 3 1.2 = 5 2.0

makes sense !

30

Master equation

idea:

derive a closed equation for dynamics

of nonlinear non-plano-planar

resonators by using ABCD matrix to

decribe intra-cavity elements

master equation

benefits / aims:

ability to model complex real-world cavities (e.g. VECSELs) address effects of small deviations from self-imaging condition in external cavity

describe misaligned cavity describe properly action of grating in VEGSEL

Dunlop et al., Opt. Lett. 21, 770 (1996); Firth and Yao, J. Mod. Opt., in press

nonlinear medium

offset Gaussian aperture

thin lens

thin lens

31

Examples

i

R

EE

EiE

SkB

iE

ESk

xB

Sk

x

E

k

Bi

T

ET

22

2

22

2

2

~1

~1~

1

~

~

1

1~

sin2

~

related to misalignment, proportional to aperture offset

likHABGDAS 21;2

t

fundamental mode of linear cavity: off-axis

pattern formation

initial conditions

on-axis

people involved: A. Yao, W. J. Firth, L. Columbo (Bari)

32

Summary

experiment:

bistable localized spots can exist at several points,

though preferentially at defects independent manipulation

(switch-on/off) indications for motility

these guys are

cavity solitons

though defects might play a role in

nucleation and trapping

some interpretation:

why bistability approach to model details

of the external cavity

Email: thorsten.ackemann@strath.ac.uk

33

Control of spots

aa b c d

e f g h

ib) And d): Switch-on of two independent spots, they remain after the WB is blocked.

f) And h): Switch-off, by injecting the WB beside the spot locations.

phase insentivbe

34

Current dependence: Spots II

395.4mA 397.7mA 400mA

Increasing current

decreasing current

bistable localized spots

35

Rays in external cavity

on-axis soliton ok, but off-axis inversion

f f

telescope with 1 lens (unfolded)

telescope with 2 lenses

f1 + f2

36

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 10.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

experiments free-running fit free-running line with spurious feedback

wa

ve n

umbe

r (1

/µm

)

detuning (nm)

Spurious feedback

not relevant, too large angles

but possibly here, if

resonances have finite

width