Investigating Fill Factor Effect on Brillouin Zone of Metamaterial-Based 2D Photonic Crystal

Abstract

: Fill factor in the negative permittivity materials are tailored within the physically permissible limits to characterize the Brillouin zone for two-dimensional crystal under the propagation of both s and p-polarized waves. Two lowermost band-gaps are computed along with corresponding mid-band frequencies, where the plane wave expansion method is invoked for computational purposes. The rectangular geometrical shape is considered for the simulation, and all the results are calculated inside the ‘Γ’ point and ‘X’ point of the first Brillouin zone. Simulated findings depict monotonous variations of both band-gap width as well as mid-band frequency for higher negative permittivity materials, when the magnitude of fill factor is comparatively low, for both TE (Transverse Electric) and TM (Transverse Magnetic) mode of propagations. Lower negative permittivity leads to random fluctuations, which makes it unsuitable for photonic component design. Multiple forbidden regions may be observed for some specific artificial materials which can be utilized in the antenna or multi-channel filter design in higher THz region. Aims: The present paper aims to compute the shape of the first Brillouin zone from the fill factor for a two-dimensional photonic crystal structure. Background: EBG (Electromagnetic Bandgap) of a photonic crystal plays a major role in determining its candidature for optical applications, which is critically controlled by the fill factor. Therefore, it is significant to investigate the effect of F.F on the wave propagation characteristics of 2D PhC(Twodimensional photonic crystal). Objective: Investigation of metamaterial-based photonic crystal structure for electromagnetic band-gap analysis in the desired spectrum of interest as a function of fill factor inside the first Brillouin zone. Methods: Maxwell’s equations are solved using the plane wave propagation method to solve the problem, and simulation is carried out in MATLAB® software. Result: Both the first and second photonic band-gaps are simultaneously computed with a variation of refractive index differences of the constituent materials as well as with the fill factors. Results are extremely significant about the formation of narrowband and wideband filters on certain material combinations and structural designs. Conclusion: Better tenability is observed for metamaterial structure compared to conventional positive index materials, and fill factor has a great role in shaping the Brillouin zone and corresponding bandgap width.