This paper presents an application of the constained interpolation profile basis set (CIP-BS) method to electromagnetic fields analyses. Electromagnetic fields can be expanded in terms of multi-dimensional CIP basis functions, and the Galerkin method can then be applied to obtain a system of linear equations. In the present study, we focus on a two-dimensional problem with TMz polarization. In order to examine the precision of the CIP-BS method, TE202 resonant mode in a rectangular cavity is analyzed. The numerical results show that CIP-BS method has better performance than the finite-difference time-domain (FDTD) method when the time step is small. Then an absorbing boundary condition based on the perfectly matched layer (PML) is formulated, and the absorption performance is demonstrated. Finally, the propagation in an inhomogeneous medium is computed by using the proposed method, and it is observed that in the CIP-BS method, smooth variation of material constants is effectively formulated without additional computational costs, and that accurate results are obtained in comparison with the FDTD method even if the permittivity is high.

A rigorous analysis for a TM010 mode cylindrical cavity with insertion holes is presented on the basis of the Ritz-Galerkin method to realize accurate measurements of the complex permittivity of liquid. The effects of sample insertion holes, a dielectric tube, and air-gaps between a dielectric tube and sample insertion holes are taken into account in this analysis. The validity of this method is verified from measured results of some kinds of liquid.

Effects of the sample insertion holes of the TM010 mode cylindrical cavity are analyzed on the basis of rigorous analysis by the Ritz-Galerkin method. The measurement accuracy of complex permittivity is examined by comparing the values by the perturbation method with ones by the rigorous analysis. Charts of relative errors Δ ε/εp and Δ tan δ/tan δp are presented, which are useful to measure the complex permittivity accurately by the perturbation method. The present analysis extends the validity of the conventional perturbation method.

A beam adaptive frame for finite-element beam-propagation analysis is proposed. The width of the frame can be adapted itself to either the guiding structure or the propagating beam in optical circuits, so the size of the computational window can be reduced.