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GENERAL ASPECTS OF OPTICAL PATTERNSGENERAL ASPECTS OF OPTICAL PATTERNS

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Laser Light

Nonlinear medium in optical cavity

Single feedback mirror configuration

E0

MIRRORCELL SCREEN

T. Ackemann et al. PRL 75, 3450(1995)

Na cell

LASER

LASER

LASER

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S. Residori et al, PRL 76, 1063 (1996)

P. L. Ramazza et al, Physica D 96, 259 (1996)

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H. Li et al Chaos, Solitons and Fractals 4, 1619 (1994)

H. Li et al Chaos, Solitons and Fractals 4, 1619 (1994)

x

ytime

Sub-nanosecond electric excitation

time

J. Mulet et al, IEEE J. Quantum Electron. 38, 291 (2002 )

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0º90º

L L ∼∼ 11µµmm

VCSEL

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DIFFRACTION, TIME SCALES, CLEAN SYSTEMS…DIFFRACTION, TIME SCALES, CLEAN SYSTEMS…

INFORMATION PROCESSING: INFORMATION PROCESSING:

Localized Structures /Cavity Solitons

All-optical image processing

POLARIZATION OF LIGHT: POLARIZATION OF LIGHT: Vectorial Spatio-Temporal Phenomena

Correlated Patterns, Phase separation, Symmetry TuningQUANTUM ASPECTS:QUANTUM ASPECTS:

Macroscopic quantum correlations in patterns.

PARALLEL Quantum Information

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ndiffractio ofstrength :1 Laplacian, transverse:

fieldinput : detuning,cavity :1 2

0

=∇

=

aEθ

L. A. Lugiato & R. Lefever, Phys. Rev. Lett. 58, 2209, (1987).

Self-focusing Kerr medium in a ring cavity

Time evolution of field envelope

( )3χx

y

z

field envelope

output field

input field E0

( ) ( ) ( )

( )y,xx

twzkiet,xEt,z,xE=

−=r

vrvr00

( ) EEiEEiaEitE 2

02 21 ++∇+θ+−=

∂∂

Hopf

4. 2f-oscillating hexagons 6. Spatio-temporal

chaos

Spatio - Temporal Regimes of Self-Focusing Kerr

3. Oscillating hexagons

2. Static hexagons

1. Homogeneous

max

(|E|2 )

-Is

Is0.450 0.470 0.500 ∼∼∼∼ 0.6200.525

5. Chaotic hexagons

Hopf

0.53

D. Gomila and P. Colet

Photorefractive CrystalsPhotorefractive Crystals

Arecchi et al. PRL 67, 3751 (1991)

Optical vortex and phase spiral

Vortices and shocks

Vortex lattice

Staliunas et al.

PRL 79, 265 (1997)

BroadBroad Area LaserArea Laser Optical Parametric OscillatorOptical Parametric Oscillator

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OPTICAL PROCESSING WITH CAVITY SOLITONSOPTICAL PROCESSING WITH CAVITY SOLITONSOPTICAL PROCESSING WITH CAVITY SOLITONS

Write and erase Write and erase solitons solitons

in an optical cavityin an optical cavity

Switching of Spatial Solitons, Ackemann-Lange (Munster)

LS0067

intensity of the 2nd beam time

background SS moves due to noise and intensity gradient

SS erased minimum unstable

SS ignited

• Adressing: focused second beam (approximately the same size as soliton)

• Ignition: circular polarization parallel to holding beam

• Erasure: circular polarization orthogonal to holding beam

• Polarization properties provide phase insensitive way of control (!)

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Control of localized states in Control of localized states in broad area broad area VCSELsVCSELs (150 (150 µµµµµµµµm)m)

Homogeneous beam + Local addressing perturbation

Switch ON-OFF of LS

J. Scheuer, M. Orenstein, Science 285, 230 (99)

T. Ackemann et al., IMEDEA-INLN (1999)

Patterns and Localized States in VCSELS

J. Scheuer, M. Orenstein, Science 285, 230 (99)

E0LASER

MIRRORCELL SCREEN

LASER

E+ E-

Rb cell

Grynberg et al, PRL 72,2379 (1994)

Na cell |E+|2 |E-|2

E0

96º

90º

84º Aumann et al, Phys. Rev. A 56, R1709 (1997)

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Degenerate OPTICAL PARAMETRIC OSCILLATOR:

( )[ ] ( )( )[ ] ( )tAAiKAiaAiA

tAiKAiaEAiA

t

t

,1

,21

110*101

211111

002100

2000000

r

r

ξεγ

ξεγ

++∇+∆+−=∂

++∇++∆+−=∂

( ) ( ) arbitrary fixed, , 01 ψφ ∆=∆ ⊥kMq

FLUCTUATIONS:FLUCTUATIONS:nsfluctuatio large ψ

( )2 small ±±−+ =− AIII QUANTUM COMPLEMENTARITYQUANTUM COMPLEMENTARITY

Squeezing in photon number differenceSqueezing in photon number difference

ω2ω

ω

( )⊥k,zk

( )⊥−k,zk

( ) ( )ψφ +=+= −−+ xqeReAeAtA M

ixiqxiq MM cos,1 r

PARAMETRIC DOWN CONVERSION:

)2(χTWIN PHOTON EMISSIONTWIN PHOTON EMISSION

Optical Cavity

ω2 :Pump 0 ⇒A

ω⇒1 :Signal A

Stripe patterns

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