  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.
