Modal Analysis Of Optical Waveguide Using Finite Element Method Mr. R. P. Nagarkar / Prof. M. M. Pawar Student of ME (E & TC) Assistant Professor Dept. of Electronics & Telecommunication Engg. Dept. of Electronics & Telecommunication Engg. S.V.E.R.I.s COE, Pandharpur, Maharashtra, India S.V.E.R.I.s COE, Pandharpur, Maharashtra, India nagarkarraviraj@gmail.com minakshee2000@gmail.com Abstract — The optimization of the performance of optical waveguides requires the knowledge of the propagation characteristics, field distribution and their dependence on the fabrication parameters. As the range of guiding structures and the depending parameters becomes more intricate, the need for computer analysis becomes greater and more demanding. Therefore, there is a great deal of interest in theoretical methods of waveguide analysis. The Finite Element Method (FEM) gives the elaborate and in depth analysis of the waveguide problems in all dimensions. This project presents a method for computing the propagation modes of an optical fiber. Finite element Method Analysis reduces Maxwell’s equation to standard eigen value equation involving symmetric tri-diagonal matrices. Routines compute their eigen values and eigenvectors, and from these the waveforms, propagation constants, and delays (per unit length) of the modes are obtained. The method is reliable, economical, and comprehensive, applying to both single and multimode fibers with different refractive index profiles. Index Terms— Eigenvalue, Eigenvector, FEM, Field distribution, Open boundary problem I. INTRODUCTION Recently, a method employing finite element analysis to investigate the propagation characteristics of circular waveguide with arbitrary refractive index profile has attracted the attention of many researchers. The finite element method reduces Maxwell’s equation to standard eigen value equation involving symmetric tri-diagonal matrices. Routines compute their eigen values and eigenvectors, and from these the waveforms, propagation constants, and delays (per unit length) of the modes are obtained. The method becomes a powerful tool throughout engineering [9]. Generally, Optical fiber is dielectric waveguide that operates at optical frequencies. It confines electromagnetic energy in the form of light. Optical fiber Guides the light in a direction parallel to its axis. II. TYPES OF ANALYSIS Analysis of optical waveguide is divided into following two types. a. Analytical method b. Numerical method a. Analytical method The analytical method of analysis gives the exact solution of the analysis. In this method, the scalar wave equation is obtained from Maxwell’s equations. The mode field distribution in optical fiber can be solved using Maxwell’s equation. Even though the method gives exact solution, the method is somewhat complicated as compare to numerical method. b. Numerical method The numerical method is another method used for the same purpose. The Finite Element Method is one type of this method. Recently, a method employing finite element analysis to investigate the propagation characteristics of circular waveguide with arbitrary refractive index profile has attracted the attention of many researchers. The finite element method reduces Maxwell’s equation to standard eigen value equation involving symmetric tri-diagonal matrices. Routines compute their eigen values and eigenvectors, and from these the waveforms, propagation constants, and delays (per unit length) of the modes are obtained. The method becomes a powerful tool throughout engineering. Finite element method (FEM) is a numerical method for solving a differential or integral equation. It has been applied to a number of physical problems, where the governing differential equations are available. The method essentially consists of assuming the piecewise continuous function for the solution and obtaining the parameters of the functions in a manner that reduces the error in the solution. In this article, a brief introduction to finite element method is provided. The method is illustrated with the help of the plane stress and plane strain formulation. III. BRIEF HISTORY OF FEM The term finite element was first coined by Clough in 1960. In the early 1960s, engineers used the method for approximate solutions of problems in stress analysis, fluid flow, heat transfer, and other areas. The first book on the FEM by Zienkiewicz and Chung was published in 1967. In the late 1960s and early 1970s, the FEM was applied to a wide variety of engineering problems.