Plane-wave-based transfer-matrix method for photonic crystal functional elements

Abstract

In this paper, we introduce a plane-wave-based transfer-matrix method (TMM) in application to photonic crystal (PC) functional elements and integrated circuits. In this formulation, the electromagnetic fields are expanded into superposition of plane waves associated with the crystal lattice, which facilitates access to many advanced Fourier analysis techniques. In addition to the standard solution of transmission, reflection and absorption spectra for a finite PC slab and photonic band structures for an infinite PC, the TMM can be used to handle wave propagation in semi-infinite photonic crystals and related waveguide structures. This capability is particularly useful for accurate solution of the intrinsic optical properties of a variety of functional elements comprising a PC integrated circuit. The TMM possesses a great advantage over the popular finite-different time-domain approach in handling these structures that are embedded in an environment of periodic geometries. We have discussed several prominent examples to demonstrate the power and capability of the TMM in this new frontier of applications. These include 2D PC filters based on resonant waveguide-cavity coupling, analysis of 2D channel add-drop filters that exhibit wideband continuous tunability, and discussion of the performance feature and radiation loss in resonant waveguide-cavity coupling based filters which are built on 2D slab PC platforms.