This work presents a review of development of the theory of plasmon-polariton structures and nanoantennas based on them. It shows the method for solving the problem of excitation of impedance structures, modulated by multiple periodic sequences of impulse functions by an external source of electromagnetic field. The algorithm and the recurrence formula are proposed for the construction of mathematical models of a wide class of elements of infocommunication systems based on structures with N-fold periodicity. A comparative analysis is provided of the influence of the form of impulse sequences on the formation of spatial distribution of radiation field. Parameters for the design of nanoantennas, spatial filters, interferometers, commutators, superlenses and supercollimators have been calculated.