Finite difference method

Abstract: Summary. A new method is presented for computing the complete elastic response of a vertically heterogeneous half-space. The method utilizes a discrete wavenumber decomposition for the horizontal dependence of the wave motion in terms of a Fourier-Bessel series. The series representation is exact if summed to infinity and consequently eliminates the need to integrate a continuous Bessel transform numerically. In practice, a band-limited solution is obtained by truncating the series at large wavenumbers. The vertical and time dependence of the wave motion is obtained as the solution to a system of partial differential equations. These equations are solved numerically by a combination of finite element and finite difference methods which accommodate arbitrary vertical heterogeneities. By using a reciprocity relation, the wave motion is computed simultaneously for all source-observer combinations of interest so that the differential equations need only be solved once. A comparison is made, for layered media, between the solutions obtained by discrete wavenumber/finite element, wavenumber integration, axisymmetric finite element, and generalized rays.

Abstract: Mode multiplexing and demultiplexing devices by using multimode interference couplers are proposed. Mode separating as well as superposing based on single and multiple self-imaging are utilised. Simulation results of wave propagation by the finite difference beam propagation method demonstrate the validity of the synthesis method.

Abstract: An approach is presented for the direct modeling of electromagnetic penetration problems which involves a hybrid technique combining the frequency-domain method of moments (MM) and the finite-difference time-domain (FD-TD) method. The hybriding is based upon a novel use of a field equivalence theorem due to Schelkunoff, which permits a field penetration problem to be analyzed in steps by treating the relatively simple external region and the relatively complex internal region separately. The method involves first, determination of an equivalent short-circuit current excitation in the aperture regions of the structure using MM for a given external illumination. This equivalent current excitation over the aperture is next used to excite the complex loaded interior region, and the penetrating fields and induced currents are computed by the FD-TD method. A significant advantage of this frequency domain/time domain hybriding is that no Green's function need be calculated for the interior region. This hybrid approach takes advantage of the ability of MM to solve exterior problems using patch models and also takes advantage of the ability of FD-TD to model in great detail localized space regions containing metal structures, dielectrics, permeable media, anisotropic or nonlinear media, as well as wires.