Optical transmission through generalized Thue-Morse superlattices

Abstract

In this paper we study the transmission properties of light through generalized Thue-Morse (GTM (m, n)) aperiodic superlattices and obtain the formulae of the transmission coefficients (TCs) analytically at the central wavelength, which are confirmed by numerical simulations. It is found that: (1) all of the 1st generation systems are transparent to the substrates medium B; (2) GTM (m, 2 j) systems are transparent to the substrates medium B; (3) GTM (2i, 2j + 1) systems are translucent to the substrates medium B except the 1st generation; and (4) when i not equal j, transmission through GTM (2i + 1, 2j + 1) systems attenuates rapidly with the increase of generation number l and sequence parameters m, n. On the other hand, the positional correlations between the constituents of GTM (m, n) aperiodic superlattices responsible for the resonant states are also discussed. Based on the conclusions we study the properties of the amplitude of the electric field vector and find that they are different from those of periodic lattices and chaotic systems.