A Compact 2-D Finite-Difference Frequency-Domain Method Combined With Implicitly Restarted Arnoldi Technique

A compact 2-D finite-difference frequency-domain (FDFD) method is proposed to analyze the propagation characteristics of arbitrary guiding structures. Unlike other FDFD methods, which calculate the propagation constant for a given frequency, this method adopts the technique that is usually used in the compact 2-D finite-difference time-domain method, i.e., extracting the eigenfrequency based on an initial phase constant. Similar with other FDFD methods, this method will lead to a standard eigenvalue problem. However, the difference equations of this method are much simpler compared to the previous methods. When being combined with the implicitly restarted Arnoldi technique, this method can be used to simulate large-scale guided-wave problems due to the significantly increased speed of calculation and the greatly decreased memory requirement. Besides, by means of the concept of an equivalent resonator, the method can also be used to calculate the attenuation constant of arbitrary guiding structures.