Computing Photonic Bandgap from Dispersion Relation for TM Mode Propagation Inside Metamaterial-Based 1D PhC

Abstract

Aim: Calculation of dispersion profile and photonic bandgap for negative refractive index based onedimensional photonic crystal structure. Objective: Determine mathematically the variation of first and second photonic bandgaps under angular incidence variation for the metamaterial-based 1D PhC structure for both TE and TM mode of propagations. Methods: Two lowermost photonic bandgap widths of metamaterial-based one-dimensional photonic crystal are analytically computed from the dispersion relation under the propagation of transverse electromagnetic wave along the direction of confinement. Three practically realizable double negative index materials are considered for computation of bandgaps, where air-gaps are considered along with the artificially made materials as the composite grating structure. This is a combination of negative positive indices materials, where incident angles are tailored within practical limit to calculate the variation of bandgaps, which may be quasi or complete depending on the material composition and angle of incidence. Results: Results are compared with that obtained for TE mode propagation, and are highly important for design of the all-optical filter with DNG materials.