# Control of pattern formation in a single feedback system by photonic lattices

Nicolas Marsal, Germano Montemezzani, Delphine Wolfersberger, Marc

Sciamanna, Dragomir N. Neshev

► To cite this version:

Nicolas Marsal, Germano Montemezzani, Delphine Wolfersberger, Marc Sciamanna, Dragomir N. Neshev. Control of pattern formation in a single feedback system by photonic lattices. International Commission of Optics, Jul 2008, Sidney, Australia. [hal-00334515](https://hal.science/hal-00334515v1)

HAL Id: hal-00334515

https://hal.science/hal-00334515v1

Submitted on 11 May 2022

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Control of pattern formation in a single feedback system by photonic lattices

N. Marsal¹, D. Wolfersberger¹, M. Sciamanna¹, G. Montemezzani¹, D.N. Neshev²

¹Laboratoire Matériaux Optiques, Photoniques et Systmes (LMOPS), CNRS UMR 7132, Unité de recherche commune à Supelec et Université Paul Verlaine de Metz, France.

²Nonlinear Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra, Australia.

email: nicolas.marsal@supelec.fr

## Summary

We investigate experimentally the possibility to control the pattern formation in a non-linear photorefractive single feedback system by using a periodic photonic lattice. By varying the lattice strength and periodicity, we can induce patterns of particular symmetry, suppress the modulational instability or spatially control the pattern.

## Introduction

Periodic photonic structures enable novel possibilities for manipulation of the fundamental aspects of wave propagation including enhancement of optical nonlinearity and control of light emission and radiation. The interplay between nonlinearity, optical gain, and photonic bandgap structures gives rise to new physical phenomena on control of nonlinear dynamics and spatial pattern formation. This has inspired recent interest in dissipative discrete systems leading to the prediction of localized structures or bandgap manipulation of modulational instability [1]. Despite the strong theoretical activities, experimental studies of such phenomena are lacking. In this work, we present the experimental observation of manipulation of modulational instability in a periodic nonlinear dissipative system.

<figure><img src="image_2.png" /><figcaption>Fig 1. a) Observation in the far field of an hexagonal pattern in presence of a lattice inside the photorefractive crystal. b) Hexagonal pattern switching to a diagonal one for a well defined intensity ratio between the pattern beam and the lattice beam. c) Suppression of the modulational instability in the bandgap area of the photonic lattice.</figcaption></figure>

## Experiments

We use a setup based on a photorefractive BaTiO₃ crystal in a single feedback mirror configuration giving rise to hexagonal pattern formation [2] (Center of Fig: 1a). Additionally, we impose an optical lattice to induce a photonic bandgap structure with variable parameters (see the two outer spots in Fig 1a, corresponding to the linear diffraction of the pattern beam on the lattice created inside the crystal). By varying the
lattice strength and periodicity, we can induce patterns of different symmetry. Figure 1b
shows how the far field hexagonal pattern switches to a “diagonal pattern” after the ad-
dition of the optical lattice. Additionally, the modulational instability can be suppressed
when the position of the lattice bandgap coincides with the instability gain region (Fig:
1c). Finally, for a well-defined lattice periodicity, we can rotationally control the pat-
tern in its transverse plan depending on the lattice orientation. We also study how the
threshold for modulational instability depends on the lattice strength and periodicity.

Conclusions

In conclusion, we have experimentally demonstrated a new optical method for con-
trolling the pattern formation in a photorefractive single feedback system that takes
advantage of the presence of a periodic optical lattice. It is shown that the creation
of new patterns, the suppression of the modulational instability and the control of the
pattern orientation is all possible by an all-optical addressing. To our knowledge, this
work shows for the first time how a (weak) photonic lattice can influence the pattern
formation in several fashions.

References

[1] D. Gomila and G-L Oppo, Phys. Rev. E **72**, 016614 (2005)

[2] C. Denz, Ph. Jander, M. Schwab, Ann. Phys. (Leipzig) **13**, 391-402 (2004).