Representation of frequency responses of open resonator by polylogarithm

As frequency-selective devices for millimeter and submillimeter waves, open resonators are widely used. Selective properties of open resonators are defined by their frequency response. In many cases it is convenient to use model for representation of the frequency response of the open resonator. For example, utilization of model considerably simplifies search of complex natural frequencies of the resonator in experimental data. In some cases the transient process of transformation of exciting field in the resonator eigenmode can be delayed. At certain relations between resonator Q factor and exciting field parameters the small number of initial rereflections of unformed field can become apparent on background of large number of rereflections of the shaped field and by that exert influence on form of the resonator frequency response. In this case use of pole model for representation of the frequency response of the open resonator will lead to poor-quality approximation of experimental data and, as a result, to errors of estimates of parameters of the resonator. There are also other causes complicating approximation of resonator frequency response obtained as experimental results. First of all, it is intrinsic frequency response of coupled port of the resonator. Therefore modification of the model of representation of the frequency response of the open resonator is of interest for the purpose of reducing the approximation error. The present paper is devoted to consideration of this problem.