Transform techniques for optical wave guides.

Abstract

Practical applications of integrated optics require understanding of light propagation in dielectric waveguides of various geometries and call for elegant and quick methods of analysis. The aim of the thesis is to analyse a few practical integrated?optic structures such as bent waveguides, coupled waveguides, and branching waveguides using the Beam Propagation Method (BPM) and a new transform technique. In the first chapter, optical communication and the role of integrated optics in optical communication are discussed. In the second chapter, various analytical and numerical techniques for analysing dielectric waveguides are reviewed. This chapter provides the necessary background. In the third chapter, the beam propagation method is discussed. One of the contributions of the present study, viz., improvements over BPM and extensions to cylindrical coordinates, is explained. To solve the homogeneous wave equation, Simpson抯 1/3 rule is combined with the FFT so that the speed of FFT and the accuracy of Simpson抯 1/3 rule are simultaneously achieved. Also, a modification to the beam propagation algorithm is suggested so that one integral has to be evaluated instead of two for every iteration. This reduces a lot of computational time. The modified BPM algorithm is applied to the combination of a taper and a circular lens. A second important contribution is the suggestion of a new transform technique for optical waveguides. With this technique, the partial differential equation is converted into a set of algebraic equations which can be easily solved on a computer. The theory and practical applications of this new method are presented in Chapter 4.