Analysis of multimode planar graded index optical waveguides

An algorithm is developed for analyzing the propagation characteristics of multimode planar graded-index optical waveguides. The algorithm is based on a modified impedance boundary method of moments. The algorithm is used to calculate the field dispersion and the field distribution of multimode planar graded-graded index optical waveguides. The technique is based on Galerkin's procedure and the exact boundary conditions at the interfaces between the graded index guiding region and step index cover and substrate regions. Legendre polynomials are used as basis functions. The efficiency of the algorithm is tested with waveguides having various index profiles such as step, linear, parabolic, exponential, Gaussian, and complementary error functions. The convergence behavior of the technique is also examined. With this algorithm a minimum number of basis functions is used to provide accurate results. The obtained results show good agreement with other data available in the literature. Moreover, the algorithm can be easily developed to study the propagation and coupling characteristics of planar graded-index optical waveguides directional couplers.