In this paper, outlines of the derivation of two recently developed finite difference beam propagation methods based on the higher-order Pad approximations are given to simulate the optical field propagation of tilted and turning waveguides. In order to investigate the accuracy and limitation for a propagation angle of these approaches, numerical results are presented for two benchmark tests. The present algorithms will offer, to our knowledge, the new beam propagation methods in optics.

A detailed investigation of the electromagnetic field distributions inside waveguide circuits is useful for physical understanding, studies of electromagnetic coupling effects for EMC and EMI and for optimization of waveguide circuit designs. In this paper, we describe how to calculate and measure the two-dimensional electromagnetic field distributions inside waveguide-type planar circuits, making use of an analogy between H-plane waveguide- and trough-type surface-wave planar circuits. The measurement results are in good agreement with the results of the numerical analysis based on the normal mode expansion method.

A detailed investigation of the electromagnetic field distributions in high frequency printed circuits and high-speed interconnects is very useful for physical understanding, studies of electromagnetic coupling effects for EMC and EMI and for optimization of electromagnetic circuit designs. The aim of this paper is to show how to measure the electric field distributions in electromagnetic circuits. An electromagnetic analysis for microstrip-line circuits is carried out by using a finite-difference time domain technique and its measurement is carried out by using a small probe antenna. The measurement results are in fairly good agreement with those of the numerical analysis using the FDTD method. Thus, the measurement system offers a valid means for predictions in the theoretical analysis of more complicated discontinuity problems.