Analytical solutions for multi-wave transfer matrices in layered structures

The matrix approach to the calculation of n-beam diffraction in a periodic structure is discussed. The possibility of representing N-layered transfer matrix T^N through the principal minors of the matrix T is investigated. The method of computing integer powers of a matrix by means of symmetric polynomials of the latter is developed. New analytic formulas for integer powers of matrices are represented. These solutions are demonstrated using examples of matrices of the sixth order. (paper)