Transmission characteristics of one-dimensional periodic optical waveguide networks

Abstract

In this study, the transmission characteristics of one-dimensional (1D) periodic optical waveguide networks (POWNs) composed of simple or complex unit cells are systematically studied with the transfer matrix method. Using this method, the general transmission formula is analytically derived for any 1D POWNs. Due to the periodicity, three types of transmission resonance peaks can be produced, one of which shows an interesting missing order effect. The conditions for producing these phenomena are analytically obtained from the transmission formula. Moreover, it is found that transmission valleys in the passbands can be described by a simple envelope function. A greater number of waveguides in a simple unit cell or more nodes in a complex unit cell result in smaller minima of the passband transmission valley. Finally, the formula for the depth of photonic band gaps (PBGs) is analytically determined. We find that the depth of PBGs exponentially increases with the cell number and the width of PBGs becomes wider with the increase of the node in unit cells. Our work enhances people's understanding of the optical characteristics of periodic waveguide networks, and may be useful for designing all-optical devices, such as dense wavelength division multiplexers, high-efficiency optical switches, and wideband and/or narrowband optical filters.