The cavity resonator design: stochastic optimization of the transmission line method

Abstract

Stable cavity resonators provide an ideal solution for high quality applications in telecommunications, laser sources, sensors, oscillators and filters, instrumentation and other large area of applications. For the determination of the electromagnetic field (EMF) properties in a cavity resonator several numerical methods are widely used. In our approach we used the transmission line modeling method (TLM). It is a wide-band time-domain numerical method suitable for solution of the electromagnetic field in a studied region. TLM method is based on the isomorphism between the theory of passive electrical network and the wave equation describing the properties of the EMF. TLM method offers two important advantages over the time-domain techniques such as the finite-difference time domain methods. The electric and magnetic field are resolved synchronously in time and space and TLM in implicitly stable method due to the mapping to electrical circuits. The EMF in the rectangular cavity is in our approach determined by the TLM method and the frequency spectrum is computed by the Fourier transform of the time signal. The theoretical model of the cavity EMF power spectral density function contains information about the geometrical configuration of the resonator. In our work we use the genetic algorithm for the determination of optimal dimensions of the cavity resonator expected for the proposed output resonant frequency. The stochastic modification of the theoretical model parameters is controlled by the genetic operators of mutation, crossover and selection, leading to overall improvement of the theoretical model estimation during the optimization process.