1. Cavity solitons in semiconductor microcavities
Luigi A. Lugiato
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy
Collaborators:
Giovanna Tissoni, Reza Kheradmand
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy
Jorge Tredicce, Massimo Giudici, Stephane Barland
Institut Non Lineaire de Nice, France
Massimo Brambilla, Tommaso Maggipinto
INFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari, Italy

2. MENU What are cavity solitons and why are they interesting?
The experiment at INLN (Nice):
First experimental demonstration of CS in
semiconductors microcavities
“Tailored” numerical simulations steering the experiment
Thermally induced and guided motion of CS in presence of
phase/amplitude gradients: numerical simulations

3. Solitons in propagation problems
Solitons are localized waves that propagate (in nonlinear media) without change of form
Temporal Solitons: no dispersion broadening z
“Temporal” NLSE:
dispersion
propagation
Spatial Solitons: no diffraction broadening
“Spatial” NLSE: 1D 2D x y z
diffraction

4. Optical Pattern Formation
Input
Nonlinear Medium c nl
Cavity
Output (
Plane Wave )
Pattern
Nonlinear media in cavities
Diffraction in the paraxial
approximation:
diffraction
dissipation
“Dissipative” NLSE:
Kerr medium in cavity
.Lugiato Lefever, PRL 58, 2209 (1987).
Hexagons
Honeycomb
Rolls

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

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

7. Localised Structures
Tlidi, Mandel, Lefever

8. CAVITY SOLITONS Holding beam Output field Writing pulses
Nonlinear medium
cnl
Writing
pulses
Intensity profile
In a semiconductor microcavity: Brambilla, Lugiato, Prati, Spinelli, Firth,
Phys. Rev. Lett.79, 2042 (1997).
Intensity
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 x y
Possible applications:
realisation of reconfigurable
soliton matrices, serial/parallel
converters, etc
Phase profile

9. Cavity Solitons Cavity Dissipation Non-propagative problem:
Cavity Solitons are individual entities, independent from one another
CS height, width, number and interaction properties do not depend directly on the total energy of the system
Cavity
Dissipation
Non-propagative problem:
CS profiles
Intensity x y
Mean field limit: field is assumed
uniform along the cavity (along z)

10. What are the mechanisms responsible for CS formation?
CS as Optical Bullet Holes (OBH):
the pulse locally creates a bleached
area where the material is transparent
Absorption
Self-focusing action of the material:
the nonlinearity counteracts
diffraction broadening
Refractive effects
Interplay between cavity
detuning and diffraction
At the soliton peak the system
is closer to resonance with the cavity

11. Long-Term Research Project PIANOS
Processing of Information with Arrays of Nonlinear Optical Solitons
France Telecom, Bagneux (Kuszelewicz, now LPN, Marcoussis )
PTB, Braunschweig (Weiss, Taranenko)
INLN, Nice (Tredicce)
University of Ulm (Knoedl)
Strathclyde University, Glasgow (Firth)
INFM, Como + Bari, (Lugiato, Brambilla)

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

13. Experimental Set-up
S. Barland, M. Giudici and J. Tredicce, Institut Non-lineaire de Nice (INLN)
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

14. Th. Knoedl, M. Miller and R. Jaeger, University of Ulm
The VCSEL
Th. Knoedl, M. Miller and R. Jaeger, 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)

15. 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:
formation of a single spot of about
10 mm diameter

16. 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

17. 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.

18. 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

19. 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)

20. 7 Solitons: a more recent achievement
Courtesy of Luca Furfaro e Xavier Hacier

21. 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

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

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

24. 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

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

26. Conclusions Cavity solitons look like very interesting objects
There is by now a solid experimental demonstration of CS
in semiconductor microresonators
Next step:
To achieve control of CS position and of CS motion
by means of phase-amplitude modulations in the holding beam

27. Thermal effects induce on CS a spontaneous translational
motion, that can be guided by means of appropriate
phase/amplitude modulations in the holding beam.
Preliminary numerical simulations demonstrate that
CS persist also above the laser threshold