Singular characteristics of one-dimensional Fibonacci optical waveguide networks composed of PT-symmetric elements

Abstract

In this paper, the singular optical properties of the interesting one-dimensional (1D) Fibonacci optical waveguide networks composed of parity-time-symmetric ( PT -symmetric) elements (FCOWNCPTSEs) are studied. It is found that there are three types of systematic phases defined by the modulus of the eigenvalues of the scattering matrix, eleven types of unidirectional transparency, and an approximate bidirectional transparency in the FCOWNCPTSEs, which have not been reported in PT -symmetric periodic optical systems and aperiodic Thue–Morse multilayers composed of PT -symmetric elements. It can be seen that the types of systematic phases and transparencies in FCOWNCPTSEs are more abundant than those of periodic systems and Thue–Morse systems. It further shows that with the decrease of symmetry the properties of the optical systems composed of PT -symmetric elements will be more abundant, which deepens people’s understanding of the relationship between symmetries and optical properties. In addition, we also find three sets of interesting Fibonacci numbers in transmitted and reflected spectra and an interesting quasiconstant in scattering spectra. Our results may be useful for the designing of novel structures with singular optical properties, e.g., invisible cloak and stealth aircraft, etc.