1. Cavity solitons in semiconductor
VISTA meeting Santander, May 23-24, 2003
Cavity solitons in semiconductor
microresonators: theory and experiment
Giovanna Tissoni
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy
Jorge Tredicce, Massimo Giudici, Stephane Barland, X. Hachair, L. Furfaro
INLN Nice, France
Salvador Balle
IMEDEA (CSIC-UIB), Palma de Mallorca, Spain
Luigi A. Lugiato, Reza Kheradmand
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy
Massimo Brambilla, Tommaso Maggipinto, Ida Perrini
INFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari, Italy

2. Cavity solitons in semiconductor microcavities:
MENU
What are cavity solitons and why are they interesting?
Cavity solitons in semiconductor microcavities:
the experiment at INLN
THERMAL EFFECTS:
spontaneous motion of patterns and cavity solitons
Guiding thermally induced motion of CS by means of
phase/amplitude gradients: numerical simulations
CS above laser threshold: preliminary results

3. Encoding a binary number in a 2D pattern??1
Problem: different peaks of the pattern are strongly correlated

4. Solution: Localised Structures
Spatial structures concentrated in a relatively small region of an extended system, created by stable fronts connecting two spatial structures coexisting in the system
1D case
Tlidi, Mandel,
Lefever
2D case

5. CAVITY SOLITONS Holding beam Output field Writing pulses
Nonlinear medium
cnl
Writing
pulses
Intensity x y
Intensity profile
In a semiconductor microcavity: Brambilla, Lugiato, Prati, Spinelli, Firth,
Phys. Rev. Lett.79, 2042 (1997).
Cavity solitons persist after the passage of the pulse, and their
position can be controlled by appropriate phase and amplitude
gradients in the holding field
Possible applications:
realisation of reconfigurable
soliton matrices, serial/parallel
converters, etc
Phase profile

6. The experiment at INLN (Nice) and its theoretical interpretation
was published in
Nature 419, 699
(2002)

7. S. Barland, M. Giudici and J. Tredicce (INLN), S. Balle (IMEDEA)
Experimental Set-up
S. Barland, M. Giudici and J. Tredicce (INLN), S. Balle (IMEDEA)
L L
aom
Holding beam
aom M M
Tunable Laser
Writing beam BS
L L BS C
VCSEL
CCD C BS BS
Detector linear array
BS: beam splitter, C: collimator, L: lens, aom: acousto-optic modulator

8. R. Jaeger, T. Knoedl and M. Miller, University of Ulm
The VCSEL
R. Jaeger, T. Knoedl and M. Miller, University of Ulm
p-contact
Bottom Emitter (150m)
Bragg reflector
Active layer (MQW)
Bragg reflector
GaAs Substrate
E R
E In
n-contact
Features
1) Current crowding at borders (not critical for CS)
2) Cavity resonance detuning (x,y)
3) Cavity resonance roughness (layer jumps) See R.Kuszelewicz et al. "Optical self-organisation in bulk and MQW GaAlAs Microresonators", Phys.Rev.Lett. 84, 6006 (2000)

9. Experimental results Above threshold, Below threshold,
Intensity (a.u.)
x (m)
Frequency (GHz) x
Above threshold,
no injection (FRL)
Intensity (a.u.)
x (m)
Frequency (GHz) x
Below threshold,
injected field
Interaction disappears on the right side
of the device due to cavity resonance
gradient (400 GHz/150 mm, imposed
by construction)
Observation of different
structures (symmetry and
spatial wavelength)
in different spatial regions
In the homogeneous region:
spontaneous formation of a single spot
of about 10 mm diameter

10. Control of two independent spots
50 W writing beam
(WB) in b,d. WB-phase
changed by  in h,k
All the circled states
coexist when only the broad
beam is present
Spots can be
interpreted
as CS

11. The Model (x,y) = (C - in) /  + (x,y) Where
L.Spinelli, G.Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, Phys.Rev.A 58 , 2542 (1998)
E = normalized S.V.E. of the intracavity field
EI = normalized S.V.E. of the input field
N = carrier density scaled to transp. value
q = cavity detuning parameter
 = bistability parameter
Where
(x,y) = (C - in) /  + (x,y)
Broad Gaussian (twice the VCSEL)
Choice of a simple model: it describes the basic physics and more refined models
showed no qualitatively different behaviours. Furthermore, we included the more realistic features, like the gradient of the cavity resonance, the spatial profile of the injected current and the spatial inhomogeneities related to the growth process of the device.

12. Reproducing the experimental results
Time averaged transverse intensity profile of a VCSEL driven by a coherent holding beam: A patterned region appears on the left, a homogeneous domain on the right.
Experiment
Numerical simulation
 (x,y)

13. Theoretical interpretation
x (m) 
Patterns (rolls, filaments)
Cavity Solitons
The vertical line corresponds to the MI boundary
CS form close to the MI boundary, on the red side

14. Pinning by inhomogeneities
Broad beam only
Experiment
Add local perturbation
Cavity Solitons
appear close to the MI boundary,
Final Position is imposed by roughness
of the cavity resonance frequency
Numerics
 (x,y)

15. 7 Solitons: a more recent achievement
Courtesy of Luca Furfaro e Xavier Hacier

16. Numerical simulations of CS dynamics in presence of
gradients in the input fields or/and thermal effects
CS in presence of a doughnut-shaped (TEM10 or 01) input beam: they experience
a rotational motion due to the input phase profile e  i (x,y) 
Input intensity profile
Output intensity profile

17. Thermal effects induce on CS a spontaneous translational motion,
originated by a Hopf instability with k  0
Intensity profile
Temperature profile

18. The thermal motion of CS can be guided on a ring,
created by means of an input amplitude modulation
Input amplitude modulation
Output intensity profile

19. The thermal motion of CS can be guided on “tracks”, created
by means of a 1D phase modulation in the input field
1D input phase modulation
Output intensity profile

20. The phase modulation is not strong enough to stop thermal motion.
CS PINBALL
During thermal drift the CS is momentarily captured by the phase maxima.
The phase modulation is not strong enough to stop thermal motion.
2D input phase modulation
Output intensity profile

21. CS in guided VCSEL above threshold: they are “sitting”
on an unstable background
Output intensity profile
By reducing the intensity of the input field, the system passes from the
pattern branch (filaments) to CS

22. CS in guided VCSEL above threshold:
experimental results
Reducing the intensity of the injected field the pattern contracts,
and two CS remain.

23. Conclusions Cavity solitons look like very interesting objects
There is by now a solid experimental
demonstration of CS
in semiconductor microresonators
Theoretical and numerical studies show that
thermal effects induce on CS a spontaneous translational
motion, that can be guided by means of appropriate
phase/amplitude modulations in the holding beam.
The experimental results and preliminary numerical simulations
demonstrate that CS persist also above the laser threshold