Cavity solitons in semiconductormicrocavities

Luigi A. LugiatoINFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy

luigi.lugiato@uninsubria.it

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

MENUWhat 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

Solitons in propagation problems

Temporal Solitons: no dispersion broadening

z

“Temporal” NLSE: 02

22

tuuu

zui

dispersionpropagation

Solitons are localized waves that propagate (in nonlinear media) without change of form

Spatial Solitons: no diffraction broadening

“Spatial” NLSE:

02

22

xuuu

zui 1D

02

2

2

22

yu

xuuu

zui 2D

x

y

z diffraction

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

injuiuuiuutui

diffractiondissipation

“Dissipative” NLSE:

Kerr medium in cavity.Lugiato Lefever, PRL 58, 2209 (1987).

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

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

Localised Structures Tlidi, Mandel, Lefever

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

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

nsity

x y x

y

Cavity Solitons are individual entities, independent from one another

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

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

Nature 419, 699 (2002)

The experiment at INLN (Nice) and its theoretical interpretation

was published in

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

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

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)

Freq

uenc

y (G

Hz)

x

Above threshold,no injection (FRL)

Intensity (a.u.)

x (m)

Freq

uenc

y (G

Hz)

x

Below threshold,injected field

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

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 2EaiENiyxEEyxitE

I

NdyxIENNtN 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)

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

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)

7 Solitons: a more recent achievement

Courtesy of Luca Furfaro e Xavier Hacier

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

Intensity profile Temperature profile

Thermal effects induce on CS a spontaneous translational motion,originated by a Hopf instability with k 0

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

The thermal motion of CS can be guided on a ring, created by means of an input amplitude modulation

Output intensity profileInput amplitude modulation

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

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

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