TRANSMISSION THROUGH ONE-DIMENSIONAL PERIODIC MEDIA

The transmission through a one-dimensional periodic system is studied, using the transfer matrix method. The connection of the transmission coefficient with the Chebyshev polynomials of the second kind is shown, emphasizing that this result is valid only for particular ranges of values of the wave number. The position and the width of these Chebyshev-ranges are independent from the number of periods. The conditions for perfect transmission, which are related to the roots of these polynomials, have been analysed. These results may be applied to electromagnetic wave propagation in dielectric films, to electron scattering in quantum wells and to phonon transmission in superlattices.