Transcript Nessun titolo diapositiva - Photonics Italian Chapter

Cavity solitons in semiconductor
microcavities
Luigi A. Lugiato
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy
[email protected]
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
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
Solitons in propagation problems
Solitons are localized waves that propagate (in nonlinear media) without change of form
Temporal Solitons: no dispersion broadening
u
 2u
2
i  u u  2 0
z
t
“Temporal” NLSE:
z
propagation
dispersion
Spatial Solitons: no diffraction broadening
u
 2u
2
i  u u 2 0
z
x
x
z
“Spatial” NLSE:
diffraction
u
 u  u
2
 u u  2  2 0
z
x  y
2
i
y
1D
2
2D
Optical Pattern Formation
Nonlinear media in cavities
Diffraction in the paraxial
approximation:
2
2
2
  2  2
x  y
Nonlinear
Medium
Nonlinear Medium
ccnlnl
Input
Cavity
(Plane Wave )
Hexagons
Honeycomb
Output
(Pattern )
Kerr medium in cavity
.Lugiato Lefever, PRL 58, 2209 (1987).
Rolls
“Dissipative” NLSE:
i
u
2
 u u iu  2 u  i uinj  0
t
dissipation
diffraction
Encoding a binary number in a 2D pattern??
1
0
1
0
0
1
1
1
0
Problem: different peaks of the pattern are strongly correlated
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
Localised Structures
Tlidi, Mandel, Lefever
CAVITY SOLITONS
Holding beam
Output field
Nonlinear medium
cnl
Writing
pulses
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
Intensity
Intensity profile
x
y
Possible applications:
realisation of reconfigurable
soliton matrices, serial/parallel
converters, etc
Phase profile
Cavity Solitons
Cavity Solitons are individual entities, independent from one another
Cavity
Dissipation
CS height, width, number and
interaction properties do not depend
directly on the total energy of the
system
Non-propagative problem:
Intensity
Mean field limit: field is assumed
uniform along the cavity (along z)
CS profiles
y
x
y
x
What are the mechanisms responsible for CS formation?
Absorption
Refractive effects
Interplay between cavity
detuning and diffraction
CS as Optical Bullet Holes (OBH):
the pulse locally creates a bleached
area where the material is transparent
Self-focusing action of the material:
the nonlinearity counteracts
diffraction broadening
At the soliton peak the system
is closer to resonance with the cavity
Long-Term Research Project PIANOS
1999-2001
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)
The experiment at INLN (Nice)
and its theoretical interpretation
was published in
Nature 419, 699
(2002)
Experimental Set-up
S. Barland, M. Giudici and J. Tredicce, Institut Non-lineaire de Nice (INLN)
L
aom
L
Holding beam aom
M
M
Tunable Laser
Writing beam
BS
L
VCSEL
L
BS
C
CCD
C
BS
BS
Detector linear array
BS: beam splitter, C: collimator, L: lens, aom: acousto-optic modulator
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
n-contact
ER
E In
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 selforganisation in bulk and MQW GaAlAs Microresonators", Phys.Rev.Lett. 84, 6006 (2000)
Experimental results
Below threshold,
injected field
Above threshold,
no injection (FRL)
x
x
Intensity (a.u.)
Interaction disappears on the right side
of the device due to cavity resonance
gradient (400 GHz/150 m, imposed
by construction)
Observation of different
structures (symmetry and
spatial wavelength)
in different spatial regions
Frequency (GHz)
Frequency (GHz)
Intensity (a.u.)
x (m)
x (m)
In the homogeneous region:
formation of a single spot of about
10 m diameter
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
The Model
L.Spinelli, G.Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, Phys.Rev.A 58 , 2542 (1998)


E
2
  1  i  ( x, y )  E  E I ( x, y )  i  c N  E  i a  E ,
t

N
2
2
  N  Im c N  E  I ( x, y )  d   N
t
Where
c N     i N  1

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
 = cavity detuning parameter
 = bistability parameter
(x,y) = (C - in) /  + (x,y)
EIn ( 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.
Theoretical interpretation
Patterns (rolls, filaments)
Cavity Solitons
37.5
0
75
3
x (m)
112.5
150
-1.50
-1.25
x (m)
0 37.5 75 112.5 150
|ES|
2
1
0
-2.25
-2.00
-1.75

-2.25 -2.00 -1.75 -1.50 -1.25

The vertical line corresponds to the MI boundary
CS form close to the MI boundary, on the red side
Pinning by inhomogeneities
Experiment
Numerics
 (x,y)
Broad beam only
Add local perturbation
Broad beam only
Cavity Solitons
appear close to the MI boundary,
Final Position is imposed by roughness
of the cavity resonance frequency
7 Solitons: a more recent achievement
Courtesy of Luca Furfaro e Xavier Hacier
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
Thermal effects induce on CS a spontaneous translational motion,
originated by a Hopf instability with k  0
Intensity profile
Temperature profile
The thermal motion of CS can be guided on “tracks”, created
by means of a 1D phase modulation in the input field
0,3
0,2
0,1
0,0
-0,1
-0,2
0
10
20
30
40
50
60
X
Input phase modulation
Output intensity profile
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
CS in guided VCSEL above threshold: they are “sitting”
on an unstable background
4
|ES|
3
2
1
0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0
EI
Output intensity profile
By reducing the input intensity, the system passes from the pattern
branch (filaments) to CS
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
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