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

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