A novel variable source impedance technique for emulating unperturbed eigenmodes in the FD-TD method

The finite-difference time-domain method (FD-TD) is a tool for the solution of EM problems. When applied to eigenproblems, the method comprises two steps: identification of resonant frequencies of the structure and evaluation of modal patterns. While the first step is well covered in the literature, the latter one has hardly gained any attention. Gwarek and Celuch-Marcysiak (1993) (G and C-M) have noticed that exciting a particular mode by directly imposing one of the field components at a chosen point of space does not lead to pure distribution of the mode in space, even if the excitation at the resonant frequency is continued for a very long time. The reason is that when starting the excitation, we introduce a certain spectrum of frequencies rather than a single frequency. Thus except for the desired mode, a mixture of many modes is also excited. In a lossless circuit the undesired modes do not vanish and the desired mode distribution is permanently contaminated by them. G and C-M have proposed to introduce excitation of the mode from a source of finite output impedance allowing attenuation of the undesired modes through the source. This concept is further developed in the present paper. It is shown that only by using sources of variable input impedance we can produce the mode distribution unperturbed either by undesired physical modes or by a spurious mode of non-zero divergence appearing near the excitation point. Furthermore in the new approach the backward integration scheme is introduced in the source´s circuit as the only one allowing a stable algorithm in a very wide range of source impedances