Transfer matrix approach to study light scattering in complex layered media

Many useful and interesting optical applications of thin films make use of multilayer stacks of films, or layered media. To evaporate multiple layers while maintaining control over both refractive index and individual layer thickness has become a matured technology today. In recent years, light scattering with nano-structures has received much attention due to the advancement of modern crystal-growth techniques such as MBE and CVD. In nano-scales, in which quantum mechanical principles play an essential role, material properties are different from that we observe in macroscopic world. Due to the size effect, the optical constants of nano-structures become much more complex than that of bulk material. In this work, light scattering in complex layered media is investigated. A transfer matrix approach is employed to discretize the dielectric function profile of the complex layered media and the transmission coefficient is calculated by matching the boundary conditions at each interface. The polarization effects and geometry-dependent characteristics are considered in our simulation model. The formulation and program are tested by comparing with some standard examples in the textbooks as limiting cases, ε(z) and μ(z) can be arbitrary complex functions in our calculations. Photonic band gaps (PBGs) have been studied. PBGs are affected seriously by the complexity of materials and the polarization. Field enhancement along with ATR is investigated. Left-handed materials are also considered. Detailed analysis is presented.