Optical Waveguide Modelling Based on Scalar Finite Difference Scheme

Abstract

Pemodelan pandu gelombang optik telah dilakukan dengan kaedah berangka berasaskan pembezaan skalar terhingga menggunakan peraturcaraan MATLAB®. Perbandingan dengan kaedah-kaedah lain telah dijalankan bagi menilai kebolehupayaannya dalam pemodelan tersebut. Keputusan perbandingan menunjukkan ciri-ciri kualitatif yang sama antara kaedah-kaedah tersebut. Prestasi kaedah ini juga telah dinilai berdasarkan kepada kerumitan pengiraan, saiz jaring dan kesan faktor cepatan. Kerumitan pengiraan boleh dikurangkan dengan menambahkan saiz jaring tetapi ini akan menambahkan ralat pengiraan. Masalah ini boleh diatasi dengan memperkenalkan faktor cepatan iaitu parameter SOR. Ditunjukkan bahawa julat SOR di antara 1.3 dan 1.7 akan menghasilkan masa pengiraan yang lebih singkat dan keputusan simulasi yang lebih konsisten. Kata kunci: Gelombang optik, pemodelan pandu gelombang, kaedah berangka berasaskan pembezaan skalar A numerical method based on scalar finite difference scheme was adopted and programmed on MATLAB® platform for optical waveguide modeling purpose. Comparisons with other established methods in terms of normalized propagation constant were included to verify its applicability. The comparison results obtained were proven to have the same qualitative behaviour. Furthermore, the performances were evaluated in terms of computation complexity, mesh size, and effect of acceleration factor. Computation complexity can be reduced by increasing the mesh size which will then produce more error. The problem can be rectified by introducing the acceleration factor, Successive Over Relaxation (SOR) parameter. It shows that SOR range between 1.3 and 1.7 can give shorter computation time, while producing constant value of simulation results. Key words: Optical waveguide, waveguide modelling, finite difference technique, successive over relaxation