1. 1 « Control of pattern formation in a single feedback system by photonic bandgap structures » Nicolas Marsal, Germano Montemezzani, Delphine Wolfersberger, Marc Sciamanna Lab. Matériaux Optiques, Photonique et Systèmes (CNRS - UMR 7132) Université Paul Verlaine - Metz and SUPELEC France Dragomir Neshev Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australia

2. 2 1.Introduction to pattern and photonic lattice 2. Our experimental setup 3. Results 4. Conclusions Outline

3. 3  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

4. 4  Pattern : properties Light structures spatially modulated and correlated Generated thanks to noise and modulation instability Disordered or ordered geometry GoalControl of pattern 1. Patterns / photonic lattice 2. Setup 3. Results 4. Conclusions

5. 5  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

6. 6  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 Properties n1n1 n0n0 real space 1 st and 2 nd BZ a w = kc / n Constant refractive index Periodic refractive index Bandgap effect 2π / a k space

7. 7  Experimental setup 1. Patterns / photonic lattice 2. Setup 3. Results 4. Conclusions Goal Pattern control by a photonic lattice Mirror Photorefractive BaTiO 3 crystal Far field (k space) External periodic illumination

8. 8 ff2f2 f2f2 f BSP BS Lattice HWP L1SF LA PC 2f LASER Far Field M L2 L3 L4 Horizontal polarization Vertical polarization 4f system M : Mirror : Feedback loop VM BS : Beam Splitter HWP : Half Wave Plate BSP : 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

9. 9 = 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 Mirror Photorefractive crystal

10. 10  Results 1. Patterns / photonic lattice 2. Setup 3. Results 4. Conclusions 1. Pattern beam intensity above threshold and fixed lattice periodicity ( k L = 2 k P ) 2. Pattern beam intensity below threshold with fixed lattice intensity (arbitrary lattice periodicity) 1D lattice 2D lattice Forcing ? Bragg / bandgap effect ?

11. 11  Results 1. Patterns / photonic lattice 2. Setup 3. Results 4. Conclusions I in I hex 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

12. 12  Conclusions We have experimentally studied the possibility to control a pattern by an optically induced photonic lattice Pattern Photonic lattice Photorefractive BaTiO 3 in single feedback configuration External periodic illumination to create a virtual photonic crystal inside the BaTiO 3 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

13. 13 Thank you for your attention !