We calculated propagation constants of supermodes for two-dimensional two-slab waveguides, with small core gap, using second-order perturbation expansion from gapless slab waveguide system, and compared our results with the existing works. In the perturbation calculation, we used trapezoidal method to calculate the integral over the transverse direction in space and obtained second-order expansion of (core gap)/(core width) for propagation constants. Our result can explain the qualitative relationship between the propagation constants and the gap distance in the neighbor of (core gap)/(core width) being zero.

In this paper we present eigenmode analysis of the propagation constant for a microstrip line with dummy fills on a Si CMOS substrate. The effect of dummy fills is not negligible, particularly in the millimeter-wave band, although it has been ignored below frequencies of a few GHz. The propagation constant of a microstrip line with a periodic structure on a Si CMOS substrate is analyzed by eigenmode analysis for one period of the line. The calculated propagation constant and characteristic impedance were compared with measured values for a chip fabricated by the 0.18 µm CMOS process. The agreement between the analysis and measurement was very good. The dependence of loss on the arrangement of dummy fills was also investigated by eigenmode analysis. It was found that the transmission loss becomes large when dummy fills are arranged at places where the electromagnetic field is strong.

A rigorous semi-analytical approach for the scalar field in a microstructured optical fiber, which is formed of layered cylindrical arrays of circular rods symmetrically distributed on each concentric cylindrical layer, is presented. The method uses the T-matrix of a circular rod in isolation and the generalized reflection and transmission matrices of cylindrical arrays. Numerical examples of the mode index for three-layered hexagonal structure of circular air holes are demonstrated and compared with those obtained by a variational method.

An exact solution of the propagation constant of a cylindrical waveguide has been obtained in the event of the conductivity of the waveguide-composing conductor being finite. The said analysis has been reduced to a problem to solve a transcendental equation concerning an eigenvalue of the individual modes of the in-guide electromagnetic wave, and calculation of Jn-1(z)/Jn(z) by using of Bessel function becomes necessary. With a large conductivity the absolute value of the complex number z becomes excessively large, and none of calculation method with high accuracy has been found with the aid of a computer. This paper has solved the problem by using a continued fraction for the calculation with regard to which a recurrence formula is utilized. With the TE01 wave that has conventionally been used as a millimeter-wave guide, it is cleared that it is sufficient to select the number of the calculation terms of the continued fraction to the extent of approximately 1000 in the accuracy in accordance with this calculation method. It is also cleared that the approximation solution obtained by a method of perturbation coincides with the exact solution for the conductivity σ 102 [S/m].