Cavity solitons in semiconductor microcavities - PowerPoint PPT Presentation

Cavity solitons in semiconductor

microcavities

Luigi A. Lugiato

INFM, Dipartimento di Scienze, Università dell'Insubria, Como, Italy

luigi.lugiato@uninsubria.it

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

Temporal Solitons: no dispersion broadening

“Temporal” NLSE:

z

propagation

dispersion

Spatial Solitons: no diffraction broadening

x

1D

“Spatial” NLSE:

diffraction

z

2D

y

Solitons in propagation problems

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

Nonlinear media in cavities

Diffraction in the paraxial

approximation:

Nonlinear Medium

Nonlinear Medium

c

c

nl

nl

Input

Cavity

Output

Kerr medium in cavity

)

)

Pattern

(

Plane Wave

(

.Lugiato Lefever, PRL 58, 2209 (1987).

Hexagons

Honeycomb

Rolls

“Dissipative” NLSE:

dissipation

diffraction

Optical Pattern Formation

1

1

0

0

0

1

1

1

0

Encoding a binary number in a 2D pattern??

Problem: different peaks of the pattern are strongly correlated

1D case

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

Localised Structures

Tlidi, Mandel, Lefever

Writing

pulses

Possible applications:

realisation of reconfigurable

soliton matrices, serial/parallel

converters, etc

Phase profile

CAVITY SOLITONS

Holding beam

Output field

Nonlinear medium

cnl

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

Dissipation

Non-propagative problem:

CS profiles

Intensity

y

x

y

x

Cavity Solitons

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

Mean field limit: field is assumed

uniform along the cavity (along z)

CS as Optical Bullet Holes (OBH):

the pulselocally 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

What are the mechanisms responsible for CS formation?

Absorption

Refractive effects

Interplay between cavity

detuning and diffraction

Long-Term Research ProjectPIANOS

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 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

E In

E R

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

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)

Above threshold,

no injection (FRL)

Below threshold,

injected field

x

x

Intensity (a.u.)

Intensity (a.u.)

Frequency (GHz)

Frequency (GHz)

x (m)

x (m)

Observationof different

structures (symmetry and

spatial wavelength)

in different spatial regions

Experimental results

Interaction disappears on the right side

of the device due to cavity resonance

gradient (400 GHz/150 mm, imposed

by construction)

In the homogeneous region:

formation of a single spot of about

10 mm diameter

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

Control of two independent spots

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 = 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.

x (m)

0 37.5 75 112.5 150

Patterns (rolls, filaments)

Cavity Solitons

-2.25 -2.00 -1.75 -1.50 -1.25



Theoretical interpretation

The vertical line corresponds to the MI boundary

CS form close to the MI boundary, on the red side

Experiment

Numerics

 (x,y)

Broad beam only

Add local perturbation

Cavity Solitons

appear close to the MI boundary,

Final Position is imposed by roughness

of the cavity resonance frequency

Broad beam only

Pinning by inhomogeneities

Courtesy of Luca Furfaro e Xavier Hacier

7Solitons: a more recent achievement

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

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

Output intensity profile

By reducing the input intensity, the system passes from the pattern

branch (filaments) to CS

There is by now a solid experimental demonstration of CS

in semiconductor microresonators

Conclusions

Cavity solitons look like very interesting objects

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