Controlled switching of discrete solitons in arrays of cubic and quadratic nonlinear optical waveguides Rodrigo A. Vicencio and Mario I. Molina Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile rodrigov@fisica.ciencias.uchile.cl Yuri S. Kivshar Nonlinear Physics Group and Centre for Ultra-high bandwidth Devices for Optical Systems (CUDOS), Research School of Physical Sciences and Engineering, The Australian National University, Canberra ACT 0200, Australia Abstract: We suggest a simple and effective method for controlling the multi-port switching of discrete solitons in arrays of nonlinear optical waveguides. We demonstrate the digitized switching of a narrow input beam in both cubic and quadratic nonlinear waveguide arrays. 2003 Optical Society of America OCIS codes: (190.4770) Nonlinear Optics, Fibers; (190.5530) Pulse propagation and solitons 1. Introduction During last decade many studies have been conducted on the propagation and steering of discrete solitons in nonlinear arrays of optical waveguides. For example, Królikowski et al. [1] showed that steering of discrete localized modes is possible in a homogeneous array of cubic waveguides, by applying an initial phase tilt in the excited waveguide. In another method [2], a linear coupling waveguide impurity embedded in a homogeneous nonlinear array was employed to trap, reflect, and refract an incoming discrete soliton. A somewhat different approach was suggested by Bang and Miller [3] who used the property of a discrete system to trap an initial strongly-localized mode on a single lattice site. They proposed achieving the soliton switching by means of a controlled perturbation that can displace a self-trapped beam in the transverse direction. The resulting switching was observed to be chaotic, especially for the switching beyond the nearest-neighbor waveguides. For quadratic nonlinear arrays, Pertsch et al. [4] suggested a multi-port switching mechanism where a low-power diffractionless beam parametrically coupled to a pump results in a steerable strong idler beam. Other studies [3,5,6] demonstrated that in homogeneous arrays, a sweep of the final beam output as a function of the beam intensity or input beam angle results in chaotic beam output positions. In contrast, here we show a simple and effective solution to the problem of the steerable switching employing an optimized waveguide coupling, and demonstrate a digitized selection of the output waveguide. 2. Model and Concept We consider a cubic (or quadratic) array of weakly coupled nonlinear optical waveguides. In the framework of a standard coupled-mode theory, the waveguide array is described by a system of coupled discrete equations which for the cubic case takes the form of the discrete nonlinear Schrödinger equation (DNLSE): , 0 2 1 1 1 1 1 = + + + - - + + n n n n n n n u u u V u V dz du i γ (1) where u n is the amplitude of the normalized electric field, z is the coordinate along the propagation direction, V n describes coupling between two neighboring sites, γ 1 is the coefficient proportional to the Kerr coefficient n 2 . For a quadratic array, we have the modified discrete nonlinear Schrödinger equation (DNLSE-m): 0 2 * 2 1 1 , 1 1 , = + + + - - + + n n n n u n n u n u v u C u C dz du i γ (2a) . 0 2 2 1 1 , 1 1 , = + + + + - - + + n n n n v n n v n u v v C v C dz dv i γ β (2b) Here u n (v n ) represent the amplitudes of the first (second) harmonic fields, C u,n (C v,n ) represent the first (second) harmonic coupling coefficients at site n, γ 2 represents the normalized second-order nonlinear coefficient, proportional to the second-order dielectric susceptibility, and β is the normalized mismatch between the modes. MC1 MC33 MC34 MC35 MC36 MC37 © 2004 OSA/NLGW 2004