Алгоритмический метод расчета отражения и прохождения волны через многослойную структуру. Часть 1. Матричный алгоритм

Abstract

The matrix algorithm for calculation of single-dimension wave through multi-layer structure is proposed. The case of simultaneous incidence on structure two waves in opposite directions is investigated. The structure is presented as successive uniform layers having different parameters. In the basis of method is established the analogy between propagation of wave in multi-layer wave-conducting structure and chain which consist of successive connected four-pole blocks of propagation and connection. The results received on the model of four-pole blocks are generalized to the case of propagation of one-dimension waves in multi-layer structure. It is found the resulting matrix which is formatted by successive product of propagation and connection matrix for structure in a whole. On the basis of calculation scheme receiving elements of last matrix from the elements of previous matrix is proposed the algorithm which allows by recurrent way to find the resulting matrix for arbitrary number of medium. On the basis of proposed algorithm, the amplitudes of leaving out structure waves through the amplitude of coming waves may be calculated. Also, the coefficients of reflection and passing by energy for the structure as a whole may be calculated. For the convenience of machine programming, it is proposed the block-scheme of program which realizes the algorithm. This program includes the under-program which calculates the elements of last matrix from the elements of previous matrix. The proposed the recurrent formulas which allows to generalize proposed algorithm to the propagation of electromagnetic waves. It is proposed the recommendations which allow to generalize proposed algorithm to the waves which do not have the harmonic character.