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« Control of pattern formation in a single feedback system by photonic bandgap

structures »

Nicolas Marsal, Germano Montemezzani, Delphine Wolfersberger, Marc SciamannaLab. Matériaux Optiques, Photonique et Systèmes (CNRS - UMR 7132)

Université Paul Verlaine - Metzand SUPELEC France

Dragomir NeshevNonlinear Physics Centre, Research School of Physical Sciences and Engineering,

Australian National University, Canberra, Australia

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1. Introduction to pattern and photonic lattice

2. Our experimental setup

3. Results

4. Conclusions

Outline

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Pattern

Nonlinear medium

Free propagation

Single feedback

Linear cavity

Mirror

Photorefractive crystal, Kerr…

Liquid-crystal light valves (LCLV), Photorefractive crystal, Na vapors…

Lasers…

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

Active medium

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Pattern : properties

• Light structures spatially modulated and correlated

• Generated thanks to noise and modulation instability

• Disordered or ordered geometry

Goal Control of pattern

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

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Pattern : control

C. Denz, Ann. Phys. (Leipzig) 13, 391 (2004)

A.V. Mamaev, M. Saffman, Europhys. Lett. 34, 669 (1996)

C. Denz, Phys. Rev. Let. 81, 1614 (1998)

And with a photonic lattice … ?

R. Neubecker and A. Zimmermann, Phys. Rev. E 65, 035205 (2002)

E

Fourier Filter

External illumination

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

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Photonic lattice

Light induced

photonic crystal

photonic crystal

Periodic illumination ( lattices or light

interferences )

Light sensitive medium ( photorefractive crystal )

Periodic variation of the refractive index inside the

medium

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

Propertiesn1

n0

real space 1st and 2nd BZ

a

w = kc / n

Constant refractive index Periodic refractive index

Bandgap effect

2π / a

k space

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Experimental setup

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

Goal Pattern control by a photonic lattice

MirrorPhotorefractive BaTiO3 crystal

Far field (k space)

External periodic illumination

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ff2

f2

f

BSP BS

Lattice

HWP

L1SF

LA

PC

2f 2f

LASER

FarField

M

L2

L3 L4

Horizontal polarization

Vertical polarization

4f system

M : Mirror

: Feedback loop

VM

BS : Beam SplitterHWP : Half Wave PlateBSP : Polarizing Beam Splitter L : Lens SF : Spatial Filter LA : Linear Atenuator PC : Photorefractive Crystal VM : Virtual Mirror

: Pattern beam: Lattice beam

λ = 532

Experimental setup

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

CAM

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=

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

Results

1D Lattice Beam

Pattern Beam

Lattice k vector

+Pattern

k vector

k space

Lattice Bragg plane

MirrorPhotorefractive

crystal

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Results

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

1. Pattern beam intensity above threshold and fixed lattice periodicity ( kL = 2 kP )

2. Pattern beam intensity below threshold with fixed lattice intensity (arbitrary lattice periodicity)

1D lattice 2D lattice

Forcing ?

Bragg / bandgap effect ?

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Results

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

Iin

Ihex

Hexagonal pattern threshold

Pattern formation with and without lattice

(lattice intensity fixed)

Hexagonal pattern

formation without lattice

Hexagonal pattern

formation with 1D lattice

Bragg effect

Forcing

k L =

2 k P

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Conclusions

We have experimentally studied the possibility to control

a pattern by an optically induced photonic lattice

• Pattern

• Photonic lattice

• Photorefractive BaTiO3 in single feedback configuration

• External periodic illumination to create a virtual photonic crystal inside the BaTiO3

We have provided a rapid survey of different concepts

We have observed 2 different behaviors which may be

due to :

1. Patterns / photonic lattice

2. Setup

3. Results

4. Conclusions

• Bandgap effect

• Forcing

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Thank you for your attention !