Chapter 36 Analytical Computation of Band Structure of 1D Photonic Crystal Under Normal Incidence of Electromagnetic Wave

摘要

Band structure of one-dimensional photonic crystal is analytically computed under the normal incidence of electromagnetic wave inside first Brillouin zone. Plane wave expansion method is applied on Maxwell's equations, and set of eigenvalues are computed for different momentum values. Helmholtz theorem is used along with Fourier transform method to obtain the direction of wave propagation inside the lattice, and size of the Hamiltonian is reduced due to the identical behaviour of TE and TM modes. Result is computed for AlGaN/GaN composition, and is compared with conventional SiO_2/air material system. Result will be helpful to determine the dispersion relation of 1D photonic crystal, allowing us to design periodic photonic structures with required photonic bandgap. Knowledge may be utilized to design photonic crystal-based bandpass filter for use in photonic integrated circuit.