Applications of Cavity Solitons
T. Ackemann
SUPA and Department of Physics, University of Strathclyde
Glasgow, Scotland, UK
Email: thorsten.ackemann@strath.ac.uk
13/05/2006
Spring School ‚Solitons in Optical Cavities‘
1
Agenda
 Paul: „This is a school, not a workshop“  everything known
 now: not so well established, partially more like Science Fiction
 but like every good piece of Science Fiction, it is based on facts
What is special about CS?
Some remarks:
 bistable
all-optical processing
all-optical network
 parallelism
 motion
„plasticity“
optical interconnects
novel ingredient
some early processing schemes: Rosanov 1990s
2
Outline
 optical memory
 all-optical delay line
 buffering information in telecom
 soliton forve microscope
 characterization of structures
 all-optical processing, routing
 telecommunications
+ input from:
• B. Schäpers, W. Lange (WWU Münster)
• F. Pedaci, S. Barland, M. Giudici, J. R. Tredicce + others (INLN, Nice)
• G. Tissoni, L. L. Lugiato, M. Brambilla + others (INFM, Como, Bari)
• A. Scroggie, W. J. Firth, G.-L. Oppo + others (U Strathclyde, Glasgow)
+ apologies to people working on LCLV (e.g. poster of Gütlich et al.)
3
Writing information for optical memory
an ideal homogeneous system has
translational symmetry
 ability to choose position in plane at will
 all states are equally likely
 code arbitrary information  memory
Can you really write arbitrary
configurations?
 interactions: minimum and discrete distances
 not all configurations of clusters are stable
Harkness et al., CNQO, U Strathclyde (1993)
4
Memories and arbitrary configurations
appearance of states with N peaks
hom.
state
wins
width of this region
in general unknown
and system
dependent,
but seems to be
comfortable wide in
worked out models
 memory is
feasible !(?)
fully decomposable  memory
(questioned by Champneys and Firth)
destruction of states with N peaks
pattern
wins
appearance of
states with N
holes
McSloy et al. PRE 66, 046606(2002)
Gomila and Firth (2005)
Pomeau front
destruction of states with N holes
5
Coullet et al., PRL 84, 3069 (2000); Chaos 14, 193 (2004)
“Arbitrary” ensembles of spots !?
For a memory you should be able to create arbitrary arrangements of CS
Firth + McSloy
saturable absorber model
(private communication)
Logvin et al.
sodium vapor + feedback
PRE 61, 4622 (2000)
Taranenko et al.
exp.: driven SC microresonator
PRA 65, 013812 (2002)
6
but rather unstable ...
 in systems with translational symmetry translation is a neutral mode
 no energy is needed for translation
 any perturbation couples easily to neutral mode and induces motion
plasticity
 neutral mode is derivate of soliton and odd
 any odd perturbation (gradient) will cause drift
 until you are in a local extremum (even)
where CS at rest / trapped
Maggipinto et al., Phys. Rev. E 62, 8726, 2000; McSloy et al. PRE 66, 046606(2002)
7
Noise
in a homogeneous system: white noise  diffusive motion
 CS will perform random walk
amplifier model, time between frames 7440/k  90 ns
but actually in reality this is not a problem ...
Spinelli et al., PRA 58, 2542 (1998)
8
Inhomogeneities
semiconductor amplifier
after addressing beam is switched off, CS
moves to a position ‚slightly‘ away from
ignition point
interpretation: CS is moving and finally trapped in small-scale irregularities
of wafer structure
 good news: CS won‘t diffuse in real structure
 bad news: CS can‘t be positioned arbitrarily and this is essentially uncontrolled
Hachair et al., INLN, Nice; similar to X. Hachair et al., PRA 69 (2004) 043817
9
(Radial) Gradients
what happens typically in
single-mirror feedback system
addressing
beam on
adressing beam
AOM
Na
holding beam
addressing
beam on
B
addressing
beam on
 CS/FS can exist at any locations equivalent by symmetry
 in a system with a circular pump beam of Gaussian
shape this is not translational symmetry
but rotational symmetry
 ring
(or center)
Schäpers et al., WWU Münster; similar: PRL 85, 748 (2000); IEEE QE 39, 227(2003)
10
Application: Pixel array
a) code arbitrary information  ability to choose position in plane at will
system should be as homogeneous as possible
b) robust against noise
Solution: Pinning of positions of LS by intentional small-amplitude modulations
 defined positions
 diffusive movement due to
noise suppressed
 accuracy requirements for
aiming relaxed
Firth + Scroggie, PRL 76 1623 (1996); saturable absorber model; see also Rosanov 1990
11
Simulations: Pixel array
semiconductor amplifier model
trap CS at lattice sites
Spinelli et al., PRA 58, 2542 (1998)
12
Experiment: Pixel array
experiment: single-mirror feedback system
insert square aperture, slightly truncating input beam (diffractive ripples)
input beam
pinning of positions of LS by amplitude modulations
 defined positions, diffusive movement due to noise suppressed
 pixel array,
however not all cells are bistable at the same time (residual inhomogeneities)
Schaepers et al., Proc. SPIE 4271, 130 (2001)
13
CS-based optical memory ?
 so it seems that a CS-based optical memory will work
 but: CS are „large“ - some micrometers
medium
Gbit/inch2
bit/mm2
CD
0.7 GB
DVD 4.7 GB
blu-ray 25 GB
blu-ray 100 GB
holografic storage
very best hard discs
0.05
0.35
1.9
7.5
515
300
0.1
0.5
2.9
11.6
800
470
 simple memories won‘t compete with existing technology
 need to exploit other, unique (!?) features
14
Enhancing CS arrays
 combine with processing
 e.g. all-optical routing
 remember that it is light
 cavity soliton laser as
self-luminescent
optically-addressable
display
 exploit plasticity
 all-optical delay line
unique feature
 best bang for the bug
15
„Slow light“
this is cycling speed !
Boyd et al., OPN 17(4) 18 (2006)
Hau et al., Nature 397, 594 16
(1999)
All-optical buffers and delay lines
 buffers can enhance performance of
networks
 future high-performance photonic
networks should be all-optical
 need for all-optical buffers with
controllable delay
Boyd et al., OPN 17(4) 18 (2006)
17
All-optical delay line
parameter gradient
inject train of
solitons here
 time delayed version of input train
read out at
other side
all-optical delay line
buffer register
 for free: serial to parallel conversion and beam fanning
 note: won‘t work for non-solitons / diffractive beams
movie
Harkness et al., CNQO, U Strathclyde (1998)
18
Experimental realization
sodium vapor driven
in vicinity of D1-line
with single feedback
mirror
t = 0 ms
adressing beam
AOM
Na
tilt of mirror
 soliton drifts
holding beam
B
t = 16 ms
t = 32 ms
t = 48 ms
t = 64 ms
t = 80 ms
ignition of soliton by addressing beam
proof of principle, quite slow, but in a semiconductor microresonator this is different !
Schäpers et. al., Proc. SPIE 4271, 130 (2001)
19
First experiments in semiconductors
spatio-temporal
detection
system:
6 local
detectors
+ synchronized
digital
oscilloscopes
BW about 300
MHz
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
VCSEL (UP)
200 µm diameter
quite homogeneous
cavity resonance
pumped above
transparency
but below threshold
 amplifier
20
Preparation of holding beam
with 6 detectors you cannot investigate twodimensional spatio-temporal structures
 create quasi-1D situation
by introducing Mach-Zehnder interferometer
 stripes with modulation depth of  1
 there is also a gradient along the stripes
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
21
Results: Noise-driven events
 anti-phase oscillation
possible interpretation: structure oscillating
back and forth in a potential well
 intentional (bang on table) or intrinsic perturbations
trigger release of pulse
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
22
An animation
strong indication of a
drifting structure
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
23
Reproducibility
noise triggered events appear
at fairly random time intervals
superposition of 50 events

deterministic propagation
compatible with interpretation of a noise triggered drifting CS
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
24
A theoretical analog !?
model: passive semiconductor microcavity + temperature dynamics
 self-propelled CS
 some oscillation
 followed by ‚eruption‘ of CS
 Caution: this is only to illustrate
that similar things can happen in a
model
 it is not claimed that this is the
explanation
25
J. McSloy, PhD thesis, 2002; cf. also Scroggie, PRE 66, 036607 (2002); Tissoni, Opt. Exp. 10_1009(2002).
Optical addressing
100 s
optically
addressed
drifting
structure
gate addressing beam with an
electro-optical modulator
rise/fall times < 1 ns
delay  12 ns
distance  25 µm
velocity  2.1 µm/ns
delay / width  2-4
this is an embryonic all – optical delay line !
F. Pedaci, S. Barland, M. Giudici, J. Tredicce, INLN, Nice, unpublished
26
Velocity
 experiment suggests velocity of about 2 µm / ns = 2000 m / s = 7200 km / h
> supersonic jet !
 theoretical expectation
here amplifier model
(‚standard‘ parameters)
 perturbative regime
 saturation
speed limit  1.5 µm/ns
 semi-quantitative agreement fortutious
(at present stage)
Tissoni et al., unpublished; see also Kheramand et al., Opt. Exp. 11, 3612(2003)
27
Bandwidth and bit rate
 velocity: 2 µm / ns
 CS diameter typically 10 µm  a local detector would see a signal of length
10 µm/(2 µm/ns) = 5 ns  bit rate 100 Mbit/s
 not great, but certainly a start
 limit: time constant of medium (carriers)
typically assumed to be about 1 ns  d-response some ns
10 µm / 3 ns = 3.3 µm /ns
 origin of numerically observed saturation behaviour
 even this makes sense with experiment
28
„Slow media“: Non-instantaneous Kerr cavity
g  0.01  semiconductor
log (velocity / gradient)
 velocity determined by response time
 saturation for instantaneous medium g
 faster medium will speed up response !
slope 1
 response time can be engineered by growers:
low-temperature growth, ion implantation,
QW close to surface, quantum dots
log (g)
A. Scroggie, Strathclyde, unpublished
 need to pay for it by increase of power
(1D, perturbation analysis)
29
„Conventional“ approaches to slow light
 modification of group velocity in vicinity of a resonance
 two-level atom
 electro-magnetically induced
transparency
 cavity resonance
 ....
 large effect needs steep slope,
narrow resonance
 bandwidth limited by
• absorption
• high-order dispersion
Hau et al., Nature 397, 594 30
(1999)
Comparison to other systems
 slow light in the vicinity of resonances:
electro-magnetically induced transparency, linear cavities, photonic crystals
interplay of useful bandwidth and achievable delay
system
speed
length
delay
bandwidth
bandwidth
delay product
EIT in cold vapor1 6
17 m/s
230 µm
~ 10 µs
300 kHz
2.1
EIT in SC QD1 4 (calc)
125000 m/s
1 cm
8 ns
10 GHz
81
SC QW (PO, calc) 5
9600 m/s
0.2 µm
0.02 ns
2 GHz
0.04
SBS in fiber3
70500 km/s
2m
18.6 ns
30-50 MHz
>1
2 km
0.16 ns
10 GHz
> THz
2 (demonstr.)
> 160 (pot.)
Raman in fiber2
CS (demonstrated)
2000 m/s
25 µm
12 ns
300 MHz
3.6
CS (optimize delay)
2000 m/s
200 µm
100 ns
300 MHz
30
CS (optimize BW)
40000 m/s
200 µm
5 ns
6 GHz
30
et al., Electron. Lett. 41, 208 (2005); 2Dahan, OptExp 13, 6234(2005); 3GonsalezHerraez, APL 87 081113 (2005); 4ChangHasnain Proc
31IEE
91 1884 (2003); 5Ku et al., Opt Lett 29, 2291(2004); 5Hau et al., Nature 397, 594 (1999)
1Tucker
Résumé: CS-based delay line
other:
 drifting CS are a quite different approach to slow light
wavelength-conversion by
 pros and contras should be assessed
FOPA
 potentially very large delays
+ dispersive fiber
 lot‘s of things to do
+ back-conversion
• theory:
saturation behaviour
• fabrication:
• experiment:
patterning effects
t N = - A N – B N2 – C N3 +...
homogeneity
control gradients, improve ignition, larger distances ...
 in a cavity soliton laser there are (at least) two other twists
• relaxation oscillations are faster than carrier decay time and modulation
frequency of modern SC lasers is certainly faster (at least 10 Gbit/s)
• possibility of fast spontaneous motion (Rosanov, since about 2002)
McSloy, Strathclyde
32
Material parameters from nonlinear dynamics
 nonlinear dynamics often depends sensitively on parameters
 old idea: use this to determine material parameters
 not many examples: e.g. ferro-fluids
 apparently not much done in optics (remarks welcome)
• relaxation and diffusion constant from below threshold patterns
(Agez et al., PhD thesis, 2005, Lille; Opt. Commun. ?)
• defect characterization by looking at symmetry breaking of SHG conical
emission (Chen et al., PRL 96, 033905, 2006)
• characterize homogeneity of cavity resonance of a microcavity
(INLN, Nice)
33
Broad-area microcavity laser
150 µm diameter VCSEL
free-running
with injection
left-right asymmetry
 gradient in detuning
 gradient in cavity resonance
this gradient was mapped
out by other (tedious)
experiments to be
400 GHz/150 µm
Another clever way?
Barland et al., Nature 419, 699 (2002)
34
Probing the gradient
„fine“ structure
„coarse“ structure
wavenumber should scale as
square root of detuning
qualitative right but not
suitable for quantitative
analysis
modulational instability threshold
Barland et al, APB 83, 2303 (2003)
35
Quantitative
linear relation  351 GHz / 150 µm
Barland et al, APB 83, 2303 (2003)
36
Local probing
 the patterns allow only for large-scale and „directed“ inhomogeneities
 What about local probing?
 the trapped CS indicate extrema of
phase/amplitude
 Can we find depth of potential well?
Soliton force microscope
map relative – possibly absolute – gradients in transverse plane by measuring
the displacement between CS and a (small-amplitude) steering beam
W. J. Firth, Strathclyde
Hachair et al., INLN, Nice;
37
similar to X. Hachair et al., PRA 69 (2004) 043817
Idea of soliton force microscopy
CS in a trap
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
-0.2
-0.2
-0.4
-0.4
-1.0
-1.0
-0.5
-0.5
0.0
0.0
0.5
0.5
1.0
1.0
add focused
steering beam
(addressing beam)
space
space xx
blow up
0.010
trapping potential
trapping "potential"
1.0
1.0
0.008
0.006
0.004
0.002
0.000
-0.002
-0.10
-0.05
0.00
0.05
0.10
space x
CS moves to new equilibrium
 measure displacement  infer relative local curvature (for fixed amplitude)
 changing amplitude + calibrations  „absolute“ local curvature
„inverse“ problem: disentangle phase- and amplitude contributions
identify origin of inhomogeneity
38
All-optical processing
 pulse trains with a high repetition rate are needed in optical communications
• time-division multiplexing (TDM)
• demultiplexing
• regeneration
• routing
 self-pulsing CSL, ideally a mode-locked CSL
• array of self-pulsing laser sources
 carrier pulse trains with high repetition rate in a large number of output channels
• all-optical control
 „high-frequency carrier pulse train on demand“
e.g. Stubkjaer, IEEE Sel. Top. QE 6, 1428 (2000)
39
Anticipated scheme
control beams
• de-multiplexing
• optical regeneration
self-pulsing
CSL
• time scales  packet manipulation
int ensit y (arb. unit s)
pulse train
• routing
• advanced schemes might use
plasticity of CLB
 processing, direct routing
1.0
0.8
0.6
0.4
0.2
0.0
0
10
20
t im e (ns)
30
40
time
40
Summary: Cavity solitons versus „pixels“
broad-area laser with CS
array of micro-fabricated bistable elements
bistable
 memory
 switch
 optical
processing
• continuous
• discrete
 utilize plasticity
• all-optical delay line (different access to slow light)
• soliton force microscope
 continue to think hard about combination of parallelism, all-optical
switching/processing/routing and plasticity
41
Desirable Features and Systems
 compact
 integration
 fast
 robust (monolithic)
 moderate power requirements
 cascadable
 robust (phase-insensitive)
semiconductor microcavity
active system
amplifier or laser
self-sustained laser
incoherent switching of CS
(or propagation in amplifier)
cavity soliton laser
42
Relevance of modulated backgrounds
a) advantageous
improve accuracy and robustness of optical memories
in general modulations of the pump or the refractive index can be used
It is generally believed that cavity solitons get stuck at the maxima of the
background modulation.
b) limiting
provides pinning mechanism for drifting CS
43
Pinning of drift motion
motion of CS might be affected
– in extreme case pinned –
by modulations or localized
inhomogenities
 study motion of CS on
noisy backgrounds
dashed line:
solid line:
perturbation
speed of CS
soliton averages over scales < CS width
A. Scroggie, unpublished (USTRAT)
position along device 
44
Transition between locking and drift
example:
single-mirror feedback system with
Na as nonlinear medium
locking of hexagonal patterns
(not solitons !)
at large-scale envelope
produced by pump profile
 transition discontinous
 possibly we are close in
semiconductors !?
Seipenbusch et. al., PRA 56, R4401 (1997); AG Lange, WWU Münster
45