HERMITIAN FINITE ELEMENT METHOD FOR THE DISPERSION CHARACTERISTICS OF AN OPTICAL WAVEGUIDE

Abstract

In the designing of a waveguide device, it is helpful to know the complete eigenvalue spectrum and the corresponding field solutions. To find these, finite element method is the most appropriate method and has been considered in this dissertation. The first order polynomial finite element method is a broadly used method but is uneconomical for accurate field computation. In contrast the higher order Lagrangian polynomials finite element method for triangular elements leads to considerable saving in computer storage and time but at sharp corners they exhibit field singularities because they do not converge rapidly. The Hermitian polynomials are more efficient because the continuity requirement is not only on the function Ez or Hz as in the case of Lagrangian case but also on the first and possibility second order derivatives also. The use of a fifth degree Hermitian polynomial has an additional advantage that it is possible to find approximate solution belonging to C1 continuity. Chapter 1 of the dissertation gives a general introduction to terms and concepts. Chapter 2 gives a general review of the numerical methods. In chapter 3 the fifth. degree Hermitian polynomial is used to find the eigenvalue. In chapter 4 results obtained from computer programme are discussed.