Band Gap Structures Of Photonic Crystals Research Articles

Calculating the Band Structure of Photonic Crystals Through the Meshless Local Petrov-Galerkin (MLPG) Method and Periodic Shape Functions

This paper illustrates how to determine the bandgap structure of photonic crystals through MLPG. This method is akin to the Finite Element Method (FEM), as it also deals with the discretization of weak forms and produces sparse global matrices. The major difference is the complete absence of any kind of mesh. We concentrate in a particular version of it, the MLPG4, also known as Local Boundary Integral Equation Method (LBIE). Since the boundary conditions governing the electromagnetic field are periodic in a unit cell, we develop a special scheme to embed this feature on the shape functions used in the discretization process. As a result, boundary conditions do not need to be imposed on the unit cell. Index Terms—Electromagnetic wave propagation, finite element methods, integral equations, photonic crystals.

Band gap studies of 2D photonic crystals with hybrid scatterers

Two-dimensional (2D) photonic crystals (PCs) of a square lattice with dielectric hybrid rods in air are proposed; these PCs consist of a square rod at the center of the unit cell and additional circular rods with their outermost edges against the middle of each side of the lattice unit cell. The band gap structures of PCs can be tailored and optimized by rotating the square rods and adding circular rods to the lattice unit cell. The variation of bands near the complete photonic band gap boundaries, due to some specific modes, is sensitive to certain structural parameters of the system. The results can be understood by analyzing the spatial energy distribution of the electromagnetic fields. Based on such a field analysis, a novel interpretative model is proposed. The PC can be fabricated easily and operated in the microwave region and, hence, should be suitable for applications in new microwave devices.

Investigation of patch antennas based on crossed idiosyncratic PBG structure

The method of finite difference time domain (FDTD) was used, and characteristics of the patch antenna based on drilling periodic air holes in the substrate were studied, the results indicate that the surface waves which propagate along the surface of the substrate can be suppressed by the crossed idiosyncratic PBG (photonic crystal band-gap) structure because of its effect of forbidden-band, that it can radiate most of electromagnetic waves’ energy in the substrate significantly, and that it has lower return loss (S11) compared to the conventional patch antennas, thus, a high gain is attained, its performance is improved. Due to these advantages, the use of photonic crystal patch antennas will be extended in areas such as mobile communication, satellite communication, aviation, etc.

Investigation of patch antennas based on drilled PBG structure

The method of finite-difference-time domain (FDTD) was used to study the characteristics of the patch antenna based on drilling air holes in the PBG substrate. The results obtained show that the waves propagating along the substrate surface can be suppressed by the drilled photonic crystal band gap (PBG) structure due to the influence of its forbidden band. The energy of the electromagnetic waves is concentrated mainly in the substrate. As a result, patch antennas based on drilling air holes in the PBG substrate have lower return losses (S11) in comparison with the conventional patch antennas; thus, a high gain is reached and the performance is improved. Due to such the advantages, the use of patch antennas can be extended to such fields as mobile communication, satellite communication, aviation, etc.

Omnidirectional two-dimensional photonic crystal band gap structures

Omnidirectional (3D) band gaps can evolve in $2\frac{1}{2}$ honeycomb and squared photonic crystal lattices and also in hexagonal crystals [Li and Xia, Phys. Rev. B 64, 153 (2001)]. This study presents a study of the according full parameter space. The calculation of omnidirectional photonic bands is based on the plane wave method for a two-dimensional photonic crystal with an off-plane wave vector ${k}_{z}={k}_{0}\phantom{\rule{0.2em}{0ex}}\mathrm{sin}(\ensuremath{\theta})$. The results are fully respecting the parameters index of refraction, the angle of incidence, as well as the structure radii. Omnidirectional band gaps are found for radii between $R=0.34$ and $R=0.5$, starting with index values from $3.0$ and show maximum relative band gap sizes ranging from $2.7%$ up to $10%$.