A novel approach to the synthesis of the electromagnetic field distribution in a chain of coupled resonators

TL;DR

This paper introduces a new matrix-based method for synthesizing electromagnetic field distributions in chains of coupled resonators, utilizing solutions of difference and Riccati equations to determine resonator characteristics.

Contribution

The paper presents a novel matrix approach for electromagnetic field synthesis in coupled resonator chains, linking difference equations with Riccati solutions for design.

Findings

New matrix form of solutions for second-order difference equations

Method to determine resonator parameters for desired field distribution

Analysis of non-uniqueness in field component separation

Abstract

A novel approach to the synthesis of the electromagnetic field distribution in a chain of coupled resonators has been developed. This approach is based on the new matrix form of the solutions of the second-order difference equations. If a chain of coupled resonators can be described by the second-order difference equation for amplitudes of expansion of the electromagnetic field, two linearly independent solutions can be constructed on the basis of the solutions of nonlinear Riccaty equation. Setting the structure of one solution, from the Riccaty equation we can find the electrodynamical characteristics of resonators and coupling holes, at which the desired distribution of amplitudes is realized. On the base of this approach we considered the problem of separation of the electromagnetic field into forward and backward components in the inhomogeneous chain of resonators. It was shown that in the frame of considered model such separation is not defined uniquely.