1. Realization of a cavity-soliton laser
Control of bistability in broad-area vertical-cavity surface-emitting lasers with frequency-selective feedback
Realization of a cavity-soliton laser
using broad-area VCSELs
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, UK
2Institute of Physics, Academy of Sciences of Belarus, Minsk, Belarus
3ULM Photonics, Lise-Meitner-Str. 13, Ulm, Germany
Funding:
FP6 STREP FunFACS
U Strathclyde Faculty starter grant
happy to be here
also thanks to: W. J. Firth, L. Columbo
28/06/2006
Laser Optics 2006, workshop „Dissipative Solitons“ WeW5-11

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. Motivation for a cavity soliton laser
cavity soliton = (spatially) localized, bistable solitary wave in a cavity
prerequisite: coexistence between different states
optical bistability between homogeneous states or
bistability between pattern and homogeneous state
symmetry-breaking pitchfork bifurcation
 look for bistable nonlinear optical systems
driven cavity: need for light field of high temporal and spatial coherence
nonlinear
medium
mirror
laser:
extracts energy from incoherent source
but „normal“ laser: continuous turn-on no cavity solitons
pump level 
output 
bad news

4. Cavity soliton laser II
bistable laser schemes
laser with
injected signal
laser with
frequency-selective feedback
gain
filter
laser with
saturable absorber
gain SA
gain
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 TiPtAu contact pad p-Bragg oxide aperture
33 stacks + metallic mirror,
R >
20.5 stacks, R > 0.992
p-Bragg
oxide aperture
QWs (3  InGaAs/GaAs)
emission wavelength
 980 nm
n-Bragg
GaAs substrate
GeNiAu contact
AR coating
bottom emitter (more homogeneous than top emitter)
output
e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061

6. Near field intensity distribution
free-running laser (below threshold)
with feedback (tuned slightly off-axis)
not lasing cw (thermal roll-over)
defect lines
apart from that “rather homogeneous“
some more defects apparent

7. Setup: Scheme Detection part Writing beam self- imaging Littrow
f1=8mm
f2=300mm
Grating
VCSEL
HWP1
HWP2
Littrow
self- imaging
self-imaging  maintains high Fresnel number of VCSEL
high anisotropy of grating  polarization selective

8. 33 propagation matrices
usual 2x2 ABCD matrix
spatial chirp
for grating: =
xout
out 1
A B E
C D F
xin
in A
D F0
angular dispersion
cos2
cos1
A =
( 1 –(1/n)(F0 tan2))
 Littrow frequency
 detuning from Littrow frequency
d spacing between grooves
2 and 1 angles of reflection and incidence from the grating
c velocity of light
n refractive index).
cos1
cos2
D =
( 1 +(1/n)(F0 tan2))
F0 = -(2pcn2Dw)/(w2d cos2)
O. Martinez, IEEE J. Quantum Electron. 24, 12, 1988

9. At Littrow frequency Dl = 0, on-axis „normal“ mirror
Dl = 0, 5 deg. angle
perfect reproduction after one round-trip
all rays/beams return to same position with same angle

10. Detuned from Littrow frequency
Dl = 1nm, on-axis
still same location, but angle different 
no closed path;
rejected by VCSEL cavity
Dl = 1nm, 5 deg. angle
angular dispersion  0.15 rad/nm; estimated width of resonance rad  bandwidth of feedback  55 GHz

11. A loophole Dl = 1nm, 4.21 degrees angle
this is not a closed path in external cavity after one round-trip!
beam is exactly retroreflected into itself:   - 
but reflection at boundaries and nonlinearities couple wavevectors k - k within VCSEL  spurious feedback

12. Setup: Details
tunable laser
1800/mm
Main external cavity L  m

13. Near field: Increasing current
Movie_nf_currentUp.wmv
feedback tuned close to longitudinal resonance

14. Near field: Decreasing current
Movie_nf_currentDown.wmv
feedback tuned close to longitudinal resonance

15. Current dependence: Spots
Increasing current
bistable localized spots
370mA
381.5mA
386mA
391mA
decreasing current

16. Hysteresis loop local detection around single spot clearly bistable
„kinks“ related to jumps between external cavity modes
LI_spot3_17deg_all.png

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
 equal or blue-detuned: red-shift (carrier effect)
blue-detuned: switch-off excitation of background

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)
we start with spin-flip model (though spin not important for idea)
feedback
noise
delayed feedback terms (Littman)
single round-trip (Lang-Kobayashi approximation)
feedback anisotropic
Naumenko et al., Opt. Commun. 259, 823 (2006)

27. Results: Steady-states + simulations
feedback favoring weaker pol. mode
green:
analytic solutions for stationary states / external cavity modes
black:
simulations
(red/blue for other polarization).
~ current
thermal shift of solitary laser frequency
bistability between lasing states and off-states; abrupt turn-on; small hysteresis

28. Interpretation: Mechanism of OB
laser originally blue detuned with respect to grating
increase of power,
decrease of carriers 
feedback induced
red-shift
positive
feedback
green/black
weaker pol.
red/blue
stronger pol. 
laser better in resonance with grating
operating frequency with feedback
frequency of solitary laser
~ current (Joule heating)

29. Conditions for OB in 80 µm device „stabilization“ of small-area laser
with intra-cavity aperture in near field
OB should exist for:
phase-amplitude coupling
bandwidth of feedback
feedback strength
exp. threshold for OB: 45%
= 3  1.2
= 5  2.0
makes sense !

30. Master equation
offset Gaussian aperture
idea: derive a closed equation for dynamics of nonlinear non-plano-planar resonators by using ABCD matrix to decribe intra-cavity elements
master equation
thin lens
thin lens
nonlinear medium
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

31. Examples fundamental mode of linear cavity: off-axis t
 related to misalignment, proportional to aperture offset
fundamental mode of linear cavity: off-axis
initial conditions
on-axis t
pattern formation
people involved: A. Yao, W. J. Firth, L. Columbo (Bari)

32. though defects might play a role in nucleation and trapping
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

33. Control of spots a a b c d e f g h i
b) 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
Increasing current
bistable localized spots
395.4mA
397.7mA
400mA
decreasing current

35. Rays in external cavity
telescope with 1 lens (unfolded) f f
on-axis soliton ok, but off-axis  inversion
telescope with 2 lenses
f1 + f2

36. Spurious feedback not relevant, too large angles
but possibly here, if resonances have finite width