Index profiles: TE mode solutions

This letter presents a novel method to study one-dimensional waveguide problems in which the profiles of the refractive index are arbitrary. In the proposed method, distributions of both the refractive index and electric field are expanded into finite-term Fourier cosine series. A particular matrix is then formed by the Fourier spectral amplitudes that correspond to the refractive-index distribution. The eigenvalues and the eigenvectors of such a matrix correspond to the mode indices and the electric field distribution, respectively, in the waveguide considered herein. TE mode solutions are obtained for a step-index structure and an inhomogeneous structure. It is found that quite accurate results can be obtained by this proposed method.