cavity solitons : the semiconductor experimentalist's point of view

Laboratoirede Photonique et de Nanostructures

Spring School on Solitons in Optical Cavities, Cargèse May 8-12 2006

Cavity Solitons : the semiconductor experimentalist's

point of view

Robert KuszelewiczLaboratoire de Photonique et de Nanostructures

LPN-CNRS/UPR20, Marcoussis, France



What is at stake ?

Cavity solitons have a double concern :● Fundamental :

Phenomena, concepts and theoretical approaches of non linear pattern formation

● Applied :Original Functions, all-optical signal processing.

III-V Semiconductor materials are at the crossroad of two streams of interest.

• Strong intensity-dependent nonlinear optical properties near the band gap edge

• Integrability and ability to realise a large variety of optical devices with a complete crystal compatibility (compacity)



Purpose of the lecture

● Show how theoretical concepts pertaining to TNO can be implemented into physical systems

● Draw a short history of the most striking advances with various materials :

● Na-vapor, LCLV, III-V semiconductors

● Concentrate on semiconductor systems :

● State of the art

● Advantages, limitations, drawbacks

● Capabilities and expectations



Outlines

Materials : • Na-vapour, LCLV and III-V semiconductors

Mechanisms for Transverse Nonlinear Optics:• Nonlinearity• Competition mechanisms• Transverse mechanisms

Phenomena : • From bistability to spatial pattern formation

... Transverse Nonlinear Optics

Description of various systems :• Passively injected systems • Amplifying injected systems • Laser systems : injected or saturable absorber

Limitations :• Uniformity : thickness, current, defects• Thermal effects : Production, dependance and dissipation

What to do with ?• Functions, processing



Material systems and related optical models

Liquid Crystal Light Valves

Kerr-like dispersive medium

Sodium Vapor :

Two-level system : saturable dielectric function

III-V semiconductors

Electronic bands : Dynamical responseMany-body interactionsDielectric function



LCLV : the Pure Kerr-model

0 2n I n n I

Residori et al., J. Opt. B: Quantum Semiclass. Opt. 6 (2004) S169–S176



The two level system : optical response

'0

I

'

0I

● Positive or negative nonlinear dispersion

● Inversion of properties above transparency



The bulk semiconductor model

Parabolic model

+ Exciton

Many-body effects

+ Band filling

+ Coulomb interactionsElectron screening, Band gap renormalisationExchange interaction

Direct gap semiconductors



Recombination mechanisms

Radiative

Stimulated

Spontaneous

Auger

phonon-assisted

Non radiative

Recombinations on defects

Electron-phonon

nrnr

nn

t

3

Auger

nCn

t

2

rad

nBn

t

2,

stim

nn E

t

Direct Indirect



Dynamical regimes

Dynamical regimes : ultra short pulses.

Coherent transients : photons écho, superradiance, self-induced transparency.. Dynamical Stark Effect : : Dynamic nonlinearities. Polarization quasi-steady state vs Electric field. NL response ruled by the evolution of excited populations : intraband relaxation

: quasi-stationnary situation : adiabatic elimination of the carriers

Characteristic timescales Dephasing time

Time after which phase relation is lost between the polarisation and the exciting field

Populations lifetimeRelaxation time of excited populations (probabilities)

In general For III-V materials ,

Excitation duration pT

2 1pT T T

2 1 pT T T

1T

2T

2 1T T 2 200T fs 1 1 10T ns

2pT T



Carrier dynamics

Excitation of optically coupled states

Intraband dynamics of carriers



The direct gap semiconductor dielectric function

The Carrier density-dependant susceptibility with and without many-body effects (Koch model)

Real and imaginary part are connected by the Kramers-Kronig transform :

-factor derives as so that Re nN NIm gN Nc

i

220

cn d

'0

I

'

0I



QD susceptibility

Energy

WL

TEd

γrad

QD γNR

QD

Energy

WL

TEd

γrad

QD γNR

QD

InAlAs/GaAlAs QD

Dynamic model of QD

Density ~ 1011 cm-3

Inhomogeneous broadening

Inhomogeneously broadened optical response



Observations

The properties of the susceptibility in III-V semiconductor are multifactorial :

● High background index n~3.5,

● Strong NL in the vivinity of the band gap,

● In the passive case, the NL dispersion is defocusing

● Above transparency, focusing NL appear

● III-V semiconductor are highly temperature-sensitive

via the shift of the band gap

● Quantum dots seem quite a promising alternative for focusing NL

0gE

T



Mechanisms of TNO

Transverse Nonlinear Optical phenomena require :

• Kerr-like or saturable intensity-dependent susceptibility

• Positive feedback : Fabry-Perot resonance or feedback mirrorenforces light-matter interaction duration yielding a “catastrophy”. Mechanism with threshold :

NL + feedback PW bistability

• Transverse effects : diffraction, diffusionCreate the conditions of non locality.

Mechanism with threshold : MI

The conjunction of these three mechanisms generate the spatio-temporal dynamics.



Phenomena

From bistability to spatial pattern formation ... Transverse Nonlinear Optics

• PW bistability : thermal / electronic NL

• Switching waves

BISTABILITY + LARGE FRESNEL NUMBER

• Pattern formation

• Localised states



Devices

Description of various classes :

• Passive injected systems : Na vapours and III-V semiconductors

• Injected amplifying systems : optically- and electrically- pumped VCSEL

• Laser systems : injected or saturable absorber systems



Passive injected systems



Na-vapor feedback mirror systems (Muenster univ.)

Drift in a gradient

Modulated landscape



LCLV in a feedback loop

Non local interactions

Patterns and localised states



Semiconductor systems

Experimental system (LPN, PTB)



Switching waves

Iinc

0 I0 I

downI

up

Iref

Outward front

Inward front

Maxwell point



Patterns and dressed solitons



Injected semiconductor amplifiers



Injected semiconductor amplifiers

Arguments on the interest for over transparency operation

● Positive : dispersive confinement

● Amplification : cascadability

Two similar approaches :

● Electrical pumping

INLN

● Optical pumping

LPN

Discussion on the respective interest of each

( )

N



Electrical vs Optical pumpingPump

I

Advantages Disadvantages

Electrical

Optical

Pumping

- High current densities- Integration

- Joule heating- Technological steps- Spatial inhomogeneities at the borders

- Few technological steps- No Joule heating- Choosing the pump spatial profile

- External laser source- Coupling to the cavity- Thermal management due to the substrate (850 nm)



Theoretical model for field and carriers

[M. Brambilla, L. Lugiato, F. Prati, L. Spinelli, W. Firth, PRL 79, 2042 (1997)]

C : bistability parameter: pumpHenry factor

2

22 2

1 2 1

1

i

Ei E E i i N E i E

tN

N N N E D Nt

C

= 1 transparency = 1+1/2C laser threshold

Good compromise : C ≈ 0.5high finesse cavity

C large small excursion range in terms of

small

C small large excursion range in terms of

large



Electrically injected VCSELs

Bottom emitting laser (ULM)



Patterns and localised states (INLN)



The initial demonstration : independance of 2CS

Writing Erasure sequence of 2 CS (Barland et al., Nature 419, 699(2002)



Interplay with non uniformity

80 m

The thickness gradient scans the state space through the detuning parameter

Seven CS



Cavity design for optical pumping

[S. Barbay, Y. Ménesguen, I. Sagnes, R. Kuszelewicz, APL 86, 151119 (2005)]

Active layer

Absorbing spacers

Aperiodic back mirror Front mirror

Pump window

Cavity resonance

[Y. Ménesguen, R. Kuszelewicz, to appear IEEE-JQE 41,N°7 (2005)]

Optical pump fewer technological steps, less heating



Experimental setup

Large-area semiconductor amplifier in AlGaAs/GaAs



Results / pattern formation

890.98 nm 889.95 nm 889.27 nm

888.23 nm

888.62 nm

Decreasing



Spontaneous formation of CS

Pump

120 m Increasing Pumping

Pump + injection 888.38nm



Independance and multiplicity of CSs

Y. Ménesguen, S. Barbay, X. Hachair, L. Leroy, I. Sagnes and R. Kuszelewicz, submitted PRA (2006)

Independence of 2 CSW/E in the vicinity of 3 other CS


Hysteresis

HB power

Loca

l re

flect

ed

in

ten

sity

Field Carriers



Fast incoherent writing/erasure : 60ps pulses

CS off

CS on~2nsCS on

CS off

~5 ns

60 ps writing 60 ps writing pulsepulse

Repeated writing and reset

writing erasure



Semiconductor Laser devices



Laser systems

Why going above threshold ?

Cascadability

Diversification of the bistable mechanisms

Injection or feedback lasers : mode competition

Saturable absorber (SA): gain loss competition

With SA, no holding beam is necessary

Incoherent switching

Optically pumped monolithic active cavity with SA



Injected lasers above Threshold (INLN)



Bistability of CS above threshold



Feedback Lasers (USTRAT)



Feedback laser

80m Laser (ULM) spatially filtered feedback,appear spontaneously at

preferential locations

With 200 m, LS can be written without spatial filtering

Bistable localised states(Y. Tanguy, T. Ackemann, USTRAT)

Frequency tuning dependence



Saturable Absorber Semiconductor lasers (LPN)

Need a cavity with special requirements

Very good cavity finesse around lasing wavelength (use QW)

pump window (OP) + optimized pumping

Saturable absorber section

no pump field but laser field

Gain section

pump field & laser field

Optically pumped monolithic active cavity with SAOP-VCSELSA

QW gain medium(/QD?)

QW or QD saturable absorber

Pump field

Laser field



OP-VCSELSA cavity design

Simplex optimization procedure on layer thicknesses :front and back mirror R,Tfront and back mirror j

R, j

T

overall cavity A

Front mirrorBack mirror

SA sectionSA section Gain sectionGain section

Laser field~980 nm

Pump fields795-805 nm

1 InGaAs/AlGaAs QW2 InAs/GaAs QW

Experiment :Optically pumped monolithic active

cavity with SA

Theory : Laser with SA (coll. INFM/Como) QD model (coll. INFM/Bari)



Laser L(P) curve



External cavity Laser with SA



Stability analysis vs Fresnel number



Transverse mode mapping



Nearly self-imaging cavity



Limitations

Semiconductor structures are subject to very stringent requirementsWith respect to :

• Uniformity : ~ (0.1nm)l/(10m)t

• thickness, • current, • defects

• Thermal management : • production, • dependance on temperature• dissipation



Thickness Uniformity

~40 GHz/100 m

885 nm

Ti:Sa injection @ 883.93nm

12 mm

~400 GHz/150 m

-> 40GHz/200 m

MBE grown (Ulm)

MOVPE grown (LPN)



Pump uniformity

Optical pumping

Use flat top incoherent beams

Electrical pumping :

bottom emitting structure (Ulm)

metallic grids

Indium Titanium Oxide (ITO) (cf. LAAS)



Thermal management

Substrate transfer on SiC, or C

Sub. GaAs

Ti deposition SiC + AuIn2

Mechanical polishing

Chemical etching

Heat source Heat dissipation



General Conclusion

Semiconductors are indeed promising candidates for the exploitation towards applications of the rich panel of NL dynamical properties.

High NL response

Integrability and compacity for devices

Number of limitations presently arisen such as those pertaining to

Uniformity, purity, thermal management

must be circumvented but solutions exist from other domains of semiconductor physics.

Hope that this school will have convinced at least some of you to contribute to this very exciting development.

cavity solitons : the semiconductor experimentalist's point of view

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