Propagation of high-frequency current waves along periodical thin-wire structures

The homogeneous problem of propagation of current along a thin wire of arbitrary geometric form near the ground by the using of the Full-wave Transmission Line Theory [1-3] is reduced to a Shrodinger-like differential equation with a "potential" depending on the geometry of the wire and on frequency. This "potential" is a complex - valued quantity that corresponds to radiation losses in the initial electrodynamics problems or corresponds to absorption of the particles in the quantum mechanic analogy. If the wire structure is quasi periodical (i.e., it consists from a finite number of identical sections), the "potential" can be approximately represented as a set of periodically arranged identical potentials. We use a formalism of transfer matrix and find an analytical expression for the transmission coefficient of the finite number of periodically located non-uniformities which also contains the scattering data for one non-uniformity. The obtained result gives the possibility to investigate forbidden and allowed frequency zones which are typical for periodic structure.