The Energy Band Structure And Band Gap Of The Photonic Crystal Design

Photonic crystals are periodically structured electromagnetic media, generally possessing photonic band gaps: ranges of frequency in which light cannot propagate through the structure. This periodicity, whose length scale is proportional to the wavelength of light in the band gap, is the electromagnetic analogue of a crystalline atomic lattice, where the latter acts on the electron wave function to produce the familiar band gaps, semiconductors, and so on, of solid-state physics.Photonic band structure calculations are performed for several two dimensional and three dimensional photonic crystal geometries. Using a plane wave expansion method, Maxwell equations are solved numerically with a frequency-domain computational method that takes the vector nature of the electromagnetic field into account.It is found that photonic band gaps exist in both two dimensional and three dimensional photonic crystal geometries. Specifically, we study the photonic band structure of the two dimensional triangular lattice and analyze qualitatively the influences of the structure parameters of photonic crystal lattice on its TM polarization band gap. Then the complete photonic band gaps of the two dimensional triangular lattice photonic crystal with air columns in dielectric materials are investigated and the maximum gap ratio is found to be 16.19% when the dielectric constant is 12. The influencing factors of the lattice are also summarized. In the last section of the chapter on two dimensional situation a new model composed of square rods in two rectangular lattices nested each other with large complete band gap is proposed and some other new models with large complete band gaps are also mentioned. In the new model with dielectric constant being 12 a complete band gap with 15.86% gap ratio is found and it is also found that to a certain extent the model has good stability. Moreover the complete photonic band gaps of the anisotropic triangular lattice photonic crystal are computed and much larger gaps than that of isotropic photonic crystals are found.In Chapter four photonic band structures of three dimensional face-centered...