Optical transmission through generalized third-order Fibonacci multilayers

In this paper, by means of three kinds of methods we study the transmission properties of the light through the quasiperiodic multilayers vertically following the generalized third-order Fibonacci (GTOF) sequences. By means of the decomposition–substitution (DS) method we predict that the GTOF systems possess an interesting four-cycle transmissive characteristic at the central wavelength. Based on the electromagnetic wave theory, we then deduce the formulae of propagation matrices and transmission coefficients analytically at the central wavelength and obtain the numerical simulation results at the same time. The results obtained by three kinds of methods accord with each other and three kinds of methods are complementary. The cyclic transmissive characteristics may be useful for the designing of some optical memories, optical logical gates, and other optical controlling devices.