Principles of the plane-wave transfer-matrix method for photonic crystals

We introduce the principle of the plane-wave transfer-matrix method, a theoretical tool that we have recently developed systematically to solve optical problems of photonic crystals (PCs). 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. We briefly discuss the standard application of the TMM to solution of transmission, reflection and absorption spectra for a finite PC slab and photonic band structures for an infinite PC. Then we push the formulation further to handle wave propagation in semi-infinite PC crystal structures. The three-dimensional wood-pile PC is taken as an example to show the power of the theory.