The following two papers outline Professor Wang's recent research achievement on waveguide optics. Both have been published in the world's outstanding journal , IEEE Journal of Quantum Electronics. Keep-going works have addressed the issues of two- and three-dimensional waveguides. The methods derived by Professor Wang ( Lkwang@ee.nthu.edu.tw ) are strongly believed to be quite efficient ones in terms of computer time, especially in the problem of two- and three-dimensional waveguides, where CPU time can be one or two orders of magnitude less than required by any existing methods. The methods are commercializable.



A NEW NUMERICAL METHOD FOR SOLVING PLANAR WAVEGUIDE PROBLEMS WITH ARBITRARY INDEX PROFILES : TE MODE SOLUTIONS

Likarn Wang and N. Huang
Department of Electrical Engineering
National Tsing Hua University
Hsinchu, Taiwan 300, R.O.C.
Tel: +886-3-5742580
Fax: +886-3-5715971 Email: Lkwang@ee.nthu.edu.tw

Abstract

A new method is employed to study one-dimensional waveguide problems in which the profiles of refractive index are arbitrary. In this method, both distributions of refractive index and electric field are expanded into finite-term Fourier cosine series,respectively. A particular matrix is then formed by the Fourier spectral amplitudes corresponding to the refractive-index distribution.The eigenvalues and the eigenvectors of such a matrix correspond to, respectively, the mode indices and the electric field distribution in the waveguide considered. TE mode solutions are found for the cases of step-index structure, inhomogeneous structure and absorbing structure. A solution method based on the proposed matrix method for the wave propagation in a directional coupler is also presented. It is found that quite accurate results can be obtained by this proposed method.

A Novel Matrix Method for Studying TM Modes of Planar Waveguides with Arbitrary Index Profiles

Likarn Wang and C. S.Hsiao
Department of Electrical Engineering
National Tsing Hua University
Hsinchu, Taiwan 300,R.O.C.
Fax: +886-3-5715971
Tel: +886-3-5742580
Email: Lkwang@ee.nthu.edu.tw

Abstract

Application of a previously proposed matrix method (which can only be used for TE mode solutions) is extended to study wave characteristics of TM modes. To derive the matrix equation for TM mode solutions of slab waveguides, the gradient of a continuous field is defined as a sum of a continuous function and stepwise function so that boundary conditions are satisfied . By expanding both the index profile and mode field distribution into truncated Fourier series, a particular matrix equation for determining mode indices and mode field distributions is obtained. Such a matrix equation can be generalized as B·X=β2X, where B is a constant matrix,β is the propagation constant and the vector X accounts for the mode field distribution. Wave characteristics of TM modes of slab waveguides with arbitrary index profiles can thus be obtained following the solution of a linear algebra problem in a way similar to that for studying TE modes. The matrix B here, however, as indicated by this work, is different from that for TE mode solutions. Also, It is pointed out in this paper that the matrix B for TM mode solutions has a different form as a different kind of waveguide is considered. Numerical results presented herein show that a sufficiently good accuracy can be obtained by using the proposed method.