Tuesday, August 26, 2008

Simplified Calculation of Guided Nonlinear Boundary-Wave Parameters Using Optimization Procedure

A guided wave excited along the boundary between linear and nonlinear media known as initial inspiration for developing devices based on Kerr nonlinear optics, such as the nonlinear directional coupler, etc. Two important parameters for such structure are respectively the minimum amplitude of light required for the excitation, and the location of the peak of guided nonlinear boundary wave. Analytical procedure of derivation the two parameters commonly involved the Jacobi’s elliptic functions based on the numerical integration. In order to simplify the calculation procedure, in this paper we introduce optimization procedure based on applying the solitary wave solution for guided field inside the nonlinear media. The simulation of guided wave excitation at the interface between linear and nonlinear media is also presented

1. Introduction

In integrated optics, all of optical devices have been made in waveguide structures, based on both linear and nonlinear optics materials. The simpliest structure of optical waveguides made of linear materials whose all of refractive indices independently to the propagating light intensity requires three layers that known as slab optical guide or slab waveguide [1]. Hence, an advanced devices such as directional-coupler that commonly applicable for optical power transfer and/or optical switching, beside in complicated structure, but also it requires applying of external treatments, because all devices made of linear materials only can operate as passive components [2]. On the other hand, due to the dependency to the propagating light intensity, recently the nonlinear materials especially for the Kerr optics materials much be applied for fabricating active-optical waveguides, that have been commonly used in many application branches, for examples, all devices of X-junction, Mach-zender interferometer, feedback grating, optical bistability, etc [3]. In addition, because of self focusing of the nonlinear Kerr optics materials, the number layer of slab waveguide reduces from three into two layers, while optical wave that propagates over the waveguide is commonly called as the boundary wave. Important to be stressed here, that the two-layer slab waveguide consists of a nonlinear Kerr optics material as the guiding layer is deposited on top a substrate of linear optics material [4].
The main problem in designing the two layers slab waveguide that are determination of the minimum amplitude of light required for the excitation, and the location of the peak of guided nonlinear boundary wave. The two parameters are depend on the effective refractive index of the slab waveguide. This paper introduces optimization procedure for obtaining all parameters of the two layer slab waveguide. The procedure of optimization was primarly applied to maximize the peak of electric field guided boundary wave in the nonlinear guiding layer.

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