One-dimensional Photonic Band Gap Structure Numerical Methods

In the 21th century, with the fast development of science and technology, the global world's demands for new energy and resources are keep on growing. Massive kinds of new materials are developed to meet the requirements of the information boost. Among those materials photonic crystals is one of the most promising materials. More than twenty years have passed since Yablonovitch and John brought forward the concept of photonic crystals in 1987. Lots of studies have been made to understand this new material which is considered to be much more advanced than the semiconductor material, and thanks to the fast development of manufacturing industry, photonic crystals now can be prepared in all dimensions, from simply 1D structure to more complicated 3D structure. The wide applications of photonic crystals materials in the modern photoelectron industry have stimulated great interests in analyzing their properties both in theory and in experiment. The study of photonic crystals unveils its unique "photon band gap" property of which photons propagating in a periodic dielectric structure, the process is similar to the electron energy band gap phenomena, one of the major reason people consider photonic crystals have a bright future. To date, numerous methods have been proposed to calculate the energy band structures of photonic crystals with different geometric structures, such as the plane wave method (PWM), the transfer matrix method (TMM), and the finite-different time domain (FDTD) method. However, the differences of these approaches are lack of detailed analysis and comparison, and hard to be tested by precise experiments.In this work, we designed multiple models of 1D photonic crystals structure, using the TMM, PWM and FDTD methods to simulate the band gap structure of these photonic crystals, along with the transmission, dispersion and refraction properties. Then we discussed the origin of the differences between each methods based on the consideration of boundary conditions and their physics foundations. We also did an experiment to compare the theory result and the experiment result, proofed that TMM is a more precise method in simulating 1D photonic crystals photon bang gaps under different situations, the results can be used to help us better understanding the process of photons interacting with the periodic dielectric materials and the characters of photonic crystals, extending their applications.