Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals

Chapter 10: Discrete Light Propagation in Arrays of Liquid Crystalline Waveguides

Katarzyna A. Rutkowska

Warsaw University of Technology, Warsaw, Poland

Gaetano Assanto

Nonlinear Optics and OptoElectronics Lab, University ROMA TRE, Rome, Italy

Miroslaw A. Karpierz

Warsaw University of Technology, Warsaw, Poland

10.1 Introduction

In the past two decades, linear and nonlinear effects in discrete systems, in the form of photonic structures with a periodic modulation of refractive index (along one or more spatial directions), have become the subject of growing interest. The latter mainly stems from both the inherent physics and the variety of potential applications [1–3]. The unique properties of discrete structures originate from the discretization of light–matter interactions (both in linear and nonlinear regimes) taking place over a finite number of unit elements in a photonic lattice. The relevance of discrete systems has been supported by a wealth of materials and nonlinear mechanisms to be employed, including semiconductors [4–6], glasses [7, 8], polymers [9], photorefractives [10, 11], ferroelectrics [12], with a cubic and a quadratic nonlinear response, respectively. This has resulted in a wide range of novel and fascinating phenomena such as discrete blockers and routers [13], discrete diffraction and solitons [1, 14–21], gap solitons [22], discrete breathers [23], multiband solitons and their interactions [24, 25], linear and nonlinear Bloch oscillations (BO) [26–30], Landau–Zener ...