Simulations of Realizable Photonic Bandgap Structures with High Refractive Contrast
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Simulations of Realizable Photonic Bandgap Structures with High Refractive Contrast Bonnie Gersten and Jennifer Synowczynski Weapons and Materials Research Directorate, Army Research Laboratory Aberdeen Proving Grounds, MD 21005-5069 ABSTRACT The transfer matrix method (TMM) software (Translight, A. Reynolds [1]) was used to evaluate the photonic band gap (PBG) properties of the periodic arrangement of high permittivity ferroelectric composite (40 wt% Ba0.45Sr0.55TiO3 /60 wt% MgO composite, εR = 80, tanδ = 0.0041 at 10 GHz) in air (or Styrofoam, εR ~ 1) matrix compared to a lower permittivity material (Al2O3, εR = 11.54, tanδ = 0.00003 at 10 GHz) in air. The periodic structures investigated included a one-dimensional (1D) stack and a three-dimensional (3D) face centered cubic (FCC) opal structure. The transmission spectrum was calculated for the normalized frequency for all incident angles for each structure. The results show that the bandgaps frequency increased and the bandgap width increased with increased permittivity. The effects of orientation of defects in the opal crystal were investigated. It was found by introducing defects propagation bands were introduced. It was concluded that a full PBG is possible with the high permittivity material. INTRODUCTION Photonic crystals (PCs) are periodic dielectric structures that exhibit frequency ranges over which an electromagnetic waves cannot propagate (called a bandgap). They are composites that are artificially engineered to have a periodic variation in the dielectric constant with a period that is on the order of the electromagnetic (EM) wavelength. When the phases have a strong refractive contrast (>3), a bandgap is created in the frequency spectrum due to the Bragg-like reflection at the interface between the two phases. PCs have many applications in optical devices including waveguides, lasers, light-emitting diodes, couplers, and filters [2]. They have also been used in microwave devices for high efficiency antenna substrates and reflectors [3] as well as waveguides, filters and delay lines. Typically, silicon has been the material of choice. It has both a high dielectric contrast (εR = 12.0:1) and is compatible with fabrication methods in microelectronic and optical components. However, in this paper we propose using an even higher dielectric material, 40 wt% Ba0.45Sr0.55TiO3 / 60 wt% MgO composite (εR = 80, tanδ = 0.0041 at 10 GHz [4]). Because Ba0.45Sr0.55TiO3 is also a ferroelectric material whose permittivity changes under an applied electric field, it is also possible to electronically tune the position and width of the bandgap. In order to prepare a PC, the material must be periodic within less than 5% deviation. Therefore in order to obtain the correct length-scale for the desired bandgap, a model of the structure and simulation of the EM propagation must first be made. Many numerical approaches are described in the literature [5] including the plane wave method, transfer matrix method (TMM) and finite difference time domain (FDTD) method. The plane wav
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