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

Control of of
bistability
in broad-area
Realization
a cavity-soliton
laser
using broad-area
VCSELs
vertical-cavity
surface-emitting
lasers with
with
frequency-selective
feedback
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 Funding:
• FP6 STREP 004868
2Institute of Physics, Academy of Sciences of Belarus, Minsk, Belarus
FunFACS
3ULM Photonics, Lise-Meitner-Str. 13, 89081 Ulm, Germany
• U Strathclyde
Faculty starter grant
also thanks to: W. J. Firth, L. Columbo
28/06/2006
Laser Optics 2006, workshop „Dissipative Solitons“ WeW5-11
1
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
2
Motivation for a cavity soliton laser
cavity soliton = (spatially) localized, bistable solitary wave in a cavity
 look for bistable
nonlinear optical
systems
prerequisite: coexistence between different states
 optical bistability between homogeneous states or
 bistability between pattern and homogeneous state
 symmetry-breaking pitchfork bifurcation
mirror
laser:
extracts energy from incoherent source
but „normal“ laser: continuous turn-on
no cavity solitons
output 
driven cavity:
need for light field of high temporal and spatial coherence
mirror
nonlinear
medium
bad news
pump level 
3
Cavity soliton laser II
bistable 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
 active device
 robustness
 cascadability
4
Devices
TiPtAu contact pad
33 stacks + metallic mirror,
R > 0.9998
p-Bragg
oxide aperture
QWs (3  InGaAs/GaAs)
emission
wavelength
 980 nm
n-Bragg
20.5 stacks, R > 0.992
GaAs substrate
GeNiAu contact
•
AR coating
bottom emitter
(more homogeneous than top emitter)
output
e.g. IEEE Photon. Tech. Lett. 10 (1998) 1061
5
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
6
Setup: Scheme
Detection part
Writing beam
f1=8mm
f2=300mm
Grating
VCSEL
HWP1
HWP2
Littrow
self- imaging
• self-imaging
• high anisotropy of grating
 maintains high Fresnel number of VCSEL
 polarization selective
7
33 propagation matrices
usual 2x2 ABCD matrix
spatial chirp
for grating:
xout
A
B
E
xin
out
C
D
F
in
0
0
1
1
1
=
A
0
0
0
D
0
0
F0
1
angular dispersion
w
Littrow frequency
Dw
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).
A = cos2 ( 1 –(1/n)(F tan ))
0
2
cos1
D = cos1 ( 1 +(1/n)(F tan ))
0
2
cos2
O. Martinez, IEEE J. Quantum Electron. 24, 12, 1988
F0 = -(2pcn2Dw)/(w2d cos2)
8
At Littrow frequency
2.0
Dl = 0, on-axis
1.5
0.8
0.6
0.4
1.0
0.2
0.5
0.0
-0.2
0.0
-0.4
-0.6
-0.5
mm
-0.8
-2
0
2
4
6
8
10
12
-1.0
„normal“
mirror
-1.5
mm
-2.0
-100
0
100
200
300
400
500
600
2.0
700
2.0
Dl = 0, 5 deg. angle
1.5
1.5
1.0
0.5
1.0
0.0
-0.5
0.5
-1.0
0.0
-1.5
-2.0
-2
-0.5
mm
0
2
4
6
8
10
12
-1.0
-1.5
perfect reproduction
after one round-trip
mm
-2.0
-100
0
100
200
300
400
500
all rays/beams return to same position with same angle
600
700
9
Detuned from Littrow frequency
Dl = 1nm, on-axis
2.0
2.0
1.5
1.5
1.0
0.5
1.0
0.0
0.5
-0.5
0.0
-1.0
-0.5
-1.5
-1.0
-5
0
mm
-2.0
-100
0
100
200
300
400
500
600
5
10
15
mm
20
700
Dl = 1nm, 5 deg. angle
2.0
1.4
1.5
1.2
1.0
1.0
0.5
0.8
0.0
0.6
-0.5
0.4
-1.0
0.2
-1.5
0.0
mm
-2.0
-100
0
100
200
300
400
500
600
700
still same
location, but
angle
different

no closed
path;
rejected by
VCSEL cavity
mm
-0.2
-4 -2 0 2 4 6 8 10 12 14 16
angular dispersion  0.15 rad/nm; estimated width of resonance 0.026 rad
 bandwidth of feedback  55 GHz
10
A loophole
Dl = 1nm, 4.21 degrees angle
2.0
1.5
1.4
1.2
1.0
1.0
0.5
0.8
0.6
0.0
0.4
0.2
-0.5
0.0
-1.0
-0.2
-2
0
2
4
6
8
mm
10 12 14
-1.5
mm
-2.0
-100
0
100
200
300
400
500
600
700
 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
11
Setup: Details
tunable laser
1800/mm
Main external cavity L  0.603 m
12
Near field: Increasing current
feedback tuned close to longitudinal resonance
13
Near field: Decreasing current
feedback tuned close to longitudinal resonance
14
Current dependence: Spots
Increasing current
370mA
381.5mA
bistable localized spots
386mA
391mA
decreasing current
15
Hysteresis loop
local detection around single spot
• clearly bistable
• „kinks“
related to jumps
between external cavity
modes
16
Switch-on of spots
• independent switchon 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)
17
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!
18
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
19
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
20
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
21
„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
22
„Pushing“ by aperture
shift by about 5 µm
23
Dragging with comb
• spots exist in a broad
range with small
perturbations
24
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
25
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)
26
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
27
Interpretation: Mechanism of OB
operating frequency with feedback
laser originally blue detuned with respect to grating
green/black
weaker pol.
increase of power,
decrease of carriers

feedback induced
red-shift
red/blue
stronger pol.

laser better in
resonance
with grating
positive
feedback
frequency of solitary laser
~ current (Joule heating)
28
Conditions for OB
OB should exist for:
bandwidth
of feedback
phase-amplitude
coupling
feedback
strength
exp. threshold for OB: 45%
=3
 1.2
=5
 2.0
 makes sense !
in 80 µm device
with intracavity
aperture
in near
field
„stabilization“
of small-area
laser
29
Master equation
offset Gaussian aperture
thin lens
thin lens
nonlinear medium
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
30
Examples
~
E
i
TR

T 2 sin 
~
 E 
(
 B  2 E~ k 1  S 2


2
B
 k x
)  x 


2
 ~ 
 E 
k (1  S )  

~
i 2 ~  (1  iD )E
E
 Ei
2
~
2
kB(1  S )
1 D  E
S  ( A  D) 2 ;   (BG  (1  A)H ) 2  ik l
 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)
31
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]
32
Control of spots
aa
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
33
Current dependence: Spots II
Increasing current
bistable localized spots
395.4mA
397.7mA
400mA
decreasing current
34
Rays in external cavity
telescope with 1 lens (unfolded)
f
f
on-axis soliton ok, but off-axis  inversion
telescope with 2 lenses
f1 + f 2
35
Spurious feedback
4.0
not relevant, too large angles
wave number (1/µm)
3.5
3.0
2.5
2.0
but possibly here, if
resonances have finite
width
1.5
1.0
experiments free-running
fit free-running
line with spurious feedback
0.5
0.0
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
detuning (nm)
36