Development of a full-Vector beam-propagation method for optical waveguide analysis and its application to radiation problems

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The method of simulating a full-vectorial propagating beam in dielectric waveguides has been developed, and its application to radiation problems has been discussed.First, consideration is given to the improvement of the accuracy of a finite difference formula. The so-called Douglas scheme has been extended to a non-uniform grid, while maintaining the fourth-order truncation error. Furthermore, the boundary conditions at the dielectric interface are introduced, which allows the analysis of a step-index waveguide with high-index contrast. The eigenmode and the coupling length are calculated and compared with previously published results.Before, studying the radiation problems, we investigate the performance of the boundary conditions at the edge of the computational window. The perfectly matched layer achieves high absorption when the number of layers is more than 20, but it requires considerable memories. The concurrent complementary operators method gives the performance comparable to the PML with 16 layers. The most efficient calculation can be made using Higdon-type boundary condition, although the application is limited to particular problems.The radiation problems of a dielectric rod antenna are investigated using the FDTD method. The propagating beam is decomposed into surface and unguided waves. The effects of the length of the dielectric rod on the gain have been explained qualitatively and quantitatively. It is found that the gain becomes maximal, when the surface wave interferes with the unguided wave in such a way that the resultant field at the plane containing the edge of the rod extends toward the air region with the equiphase condition. The theoretical results agree well with the experimental results.