cavity solitons in semiconductor microcavities luigi a. lugiato infm, dipartimento di scienze,...
TRANSCRIPT
![Page 1: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/1.jpg)
Cavity solitons in semiconductormicrocavities
Luigi A. Lugiato
INFM, Dipartimento di Scienze, Università dell'Insubria, Como, [email protected]
Collaborators:Giovanna Tissoni, Reza KheradmandINFM, Dipartimento di Scienze, Università dell'Insubria, Como, ItalyJorge Tredicce, Massimo Giudici, Stephane BarlandInstitut Non Lineaire de Nice, FranceMassimo Brambilla, Tommaso MaggipintoINFM, Dipartimento di Fisica Interateneo, Università e Politecnico di Bari, Italy
![Page 2: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/2.jpg)
MENU
What are cavity solitons and why are they interesting?
The experiment at INLN (Nice):
First experimental demonstration of CS insemiconductors microcavities
“Tailored” numerical simulations steering the experiment
Thermally induced and guided motion of CS in presence of phase/amplitude gradients: numerical simulations
![Page 3: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/3.jpg)
Solitons in propagation problems
Temporal Solitons: no dispersion broadening
z
“Temporal” NLSE: 02
22
t
uuu
z
ui
dispersionpropagation
Solitons are localized waves that propagate (in nonlinear media) without change of form
Spatial Solitons: no diffraction broadening
“Spatial” NLSE:
02
22
x
uuu
z
ui 1D
02
2
2
22
y
u
x
uuu
z
ui 2D
x
y
z diffraction
![Page 4: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/4.jpg)
Input
Nonlinear Medium
nl
Cavity Output(Plane Wave) (Pattern)
Nonlinear Medium
nl
Nonlinear media in cavities
Hexagons Honeycomb Rolls
Optical Pattern Formation
Diffraction in the paraxialapproximation:
2
2
2
22
yx
022
injuiuuiuut
ui
diffractiondissipation
“Dissipative” NLSE:
Kerr medium in cavity.Lugiato Lefever, PRL 58, 2209 (1987).
![Page 5: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/5.jpg)
1 1
1 1
1
0
00
0
Encoding a binary number in a 2D pattern??
Problem: different peaks of the pattern are strongly correlated
![Page 6: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/6.jpg)
Spatial structures concentrated in a relatively small regionof an extended system, created by stable fronts connecting
two spatial structures coexisting in the system
Solution: Localised Structures
1D case
![Page 7: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/7.jpg)
Localised Structures Tlidi, Mandel, Lefever
![Page 8: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/8.jpg)
In
tens
ity
x y
CAVITY SOLITONS
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
Phase profile
Intensity profileIn a semiconductor microcavity: Brambilla, Lugiato, Prati, Spinelli, Firth,
Phys. Rev. Lett.79, 2042 (1997).
Nonlinear medium nl
Holding beam Output field
Writingpulses
Possible applications:realisation of reconfigurablesoliton matrices, serial/parallelconverters, etc
![Page 9: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/9.jpg)
Cavity Solitons
Cavity
Mean field limit: field is assumed uniform along the cavity (along z)
CS height, width, number and interaction properties do not depend directly on the total energy of the system
Dissipation
Non-propagative problem: CS profiles
Inte
nsit
y
x y x
y
Cavity Solitons are individual entities, independent from one another
![Page 10: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/10.jpg)
What are the mechanisms responsible for CS formation?
AbsorptionCS as Optical Bullet Holes (OBH):
the pulse locally creates a bleached area where the material is transparent
Interplay between cavitydetuning and diffraction
At the soliton peak the system is closer to resonance with the cavity
Refractive effectsSelf-focusing action of the material:
the nonlinearity counteracts diffraction broadening
![Page 11: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/11.jpg)
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)
1999-2001
![Page 12: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/12.jpg)
Nature 419, 699 (2002)
The experiment at INLN (Nice) and its theoretical interpretation
was published in
![Page 13: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/13.jpg)
Tunable Laser
CCD
Holding beam
Writing beam
Detector linear array
VCSEL
BS
BS BS
BS
aom
aom
C
L L
L L
C
M M
Experimental Set-upS. Barland, M. Giudici and J. Tredicce, Institut Non-lineaire de Nice (INLN)
BS: beam splitter, C: collimator, L: lens, aom: acousto-optic modulator
![Page 14: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/14.jpg)
Active layer (MQW)
E R
Bottom Emitter (150m)
Features1) 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)
n-contact
The VCSELTh. Knoedl, M. Miller and R. Jaeger, University of Ulm
Bragg reflector
Bragg reflector
GaAs Substrate
E In
p-contact
![Page 15: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/15.jpg)
Experimental results
In the homogeneous region: formation of a single spot of about
10 m diameter
Observation of differentstructures (symmetry and spatial wavelength) in different spatial regions
Interaction disappears on the right side of the device due to cavity resonance gradient (400 GHz/150 m, imposed by construction)
Intensity (a.u.)
x (m)
Fre
quen
cy (
GH
z)
x
Above threshold,no injection (FRL)
Intensity (a.u.)
x (m)
Fre
quen
cy (
GH
z)x
Below threshold,injected field
![Page 16: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/16.jpg)
Control of two independent spots
Spots can be interpreted
as CS
50 W writing beam(WB) in b,d. WB-phase changed by in h,k
All the circled statescoexist when only the broad
beam is present
![Page 17: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/17.jpg)
E = normalized S.V.E. of the intracavity fieldEI = normalized S.V.E. of the input fieldN = carrier density scaled to transp. value = cavity detuning parameter = bistability parameter 1 NiN
,),(),(1 2EaiENiyxEEyxit
EI
NdyxIENNt
N 22),(Im
Where
Choice of a simple model: it describes the basic physics and more refined models showed no qualitatively different behaviours.
(x,y) = (C - in) / + (x,y)
),( yxEIn Broad Gaussian (twice the VCSEL)
The ModelL.Spinelli, G.Tissoni, M. Brambilla, F. Prati and L. A. Lugiato, Phys.Rev.A 58 , 2542 (1998)
![Page 18: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/18.jpg)
Theoretical interpretation
-2.25 -2.00 -1.75 -1.50 -1.250
1
2
3112.537.5
x (m)150750
|ES|
x (m)0 37.5 75 112.5 150
-2.25 -2.00 -1.75 -1.50 -1.25
Patterns (rolls, filaments)
Cavity Solitons
The vertical line corresponds to the MI boundary
CS form close to the MI boundary, on the red side
![Page 19: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/19.jpg)
Pinning by inhomogeneities
Broad beam only
Experiment
Add local perturbation
Broad beam only
Cavity Solitonsappear close to the MI boundary, Final Position is imposed by roughnessof the cavity resonance frequency
Numerics
(x,y)
![Page 20: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/20.jpg)
7 Solitons: a more recent achievement
Courtesy of Luca Furfaro e Xavier Hacier
![Page 21: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/21.jpg)
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)
Numerical simulations of CS dynamics in presence of gradients in the input fields or/and thermal effects
Output intensity profileInput intensity profile
![Page 22: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/22.jpg)
Intensity profile Temperature profile
Thermal effects induce on CS a spontaneous translational motion,originated by a Hopf instability with k 0
![Page 23: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/23.jpg)
The thermal motion of CS can be guided on “tracks”, createdby means of a 1D phase modulation in the input field
Output intensity profileInput phase modulation
0 10 20 30 40 50 60
-0,2
-0,1
0,0
0,1
0,2
0,3
X
![Page 24: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/24.jpg)
The thermal motion of CS can be guided on a ring, created by means of an input amplitude modulation
Output intensity profileInput amplitude modulation
![Page 25: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/25.jpg)
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
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.00
1
2
3
4
|ES|
EI
![Page 26: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/26.jpg)
Next step:
Conclusions
Cavity solitons look like very interesting objects
To achieve control of CS position and of CS motion
by means of phase-amplitude modulations in the holding beam
There is by now a solid experimental demonstration of CS
in semiconductor microresonators
![Page 27: Cavity solitons in semiconductor microcavities Luigi A. Lugiato INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy luigi.lugiato@uninsubria.it](https://reader035.vdocuments.us/reader035/viewer/2022062404/55161a5c55034694308b56ec/html5/thumbnails/27.jpg)
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