28/06/2006 laser optics 2006, workshop „dissipative solitons“ wew5-111 realization of a...
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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
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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
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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
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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
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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
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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
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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
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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).
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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
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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
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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
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Setup: Details
Main external cavity L 0.603 m
1800/mm
tunable laser
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Near field: Increasing current
feedback tuned close to longitudinal resonance
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Near field: Decreasing current
feedback tuned close to longitudinal resonance
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Current dependence: Spots
370mA 381.5mA 386mA 391mA
Increasing current
decreasing current
bistable localized spots
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Hysteresis loop
• clearly bistable• „kinks“
related to jumps
between external cavity
modes
local detection around single spot
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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)
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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!
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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)
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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
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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
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„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
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„Pushing“ by aperture
shift by about 5 µm
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Dragging with comb
• spots exist in a broad
range with small
perturbations
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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
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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)
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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
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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
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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 !
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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
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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)
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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: [email protected]
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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
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Current dependence: Spots II
395.4mA 397.7mA 400mA
Increasing current
decreasing current
bistable localized spots
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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
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-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