Dispersion relation of 1-D photonic crystal

Photonic crystal is a periodic dielectric material that affect the propagation of light. That produces a photonic bandgap. Photonic bandgap is a structure where a range of frequency cannot propagate through the structure. The characteristics can bee seen from the dispersion relation of the light propagate in the structure. In this paper, we use two different methods to simulate the dispersion relation; firstly we use a Plane wave method and secondly we use a transfer matrix method. Both methods use a different approach to describe the periodic dielectric structures. In the simulation we try to compare both results and show them in graph of wavevector k vs frequency, with unit cell consisting GaAS as material of the dielectric and air as the gap. The width of GaAS is 0.8 micron and width of the air gap is 0.2 micron. We also rescaling both normalized frequency to be the similar. In the process we examine the normalised frequency values using both methods as well as the difference results appears on the calculations.