Analysis of Photonic crystal (original) (raw)
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Effects of filling rates on the photonic band gaps in the photonic crystal
Nucleation and Atmospheric Aerosols, 2022
The plane wave expansion method was implemented in modeling and simulating the band structures of 2D photonic crystals (PhCs) with square, triangular and honeycomb lattices. Two types of PhCs are presented, the first is circular air holes in dielectric and the second is circular GaAs rods in air, respectively. The eigenvalue equations of TE and TM modes will solved using Matlab environment. The results shown that the first type of PhCs is more flexible than the second type in controlling the band widths and the achieved frequency positions, and the triangular lattice showed the greatest flexibility. On the other hand, the work showed the significant effect of the filling ratio and the lattice constant on the achieved bandwidth.
Effects of Lattice Types on the Frequency Band Widths in Photonic Crystals
University of Thi-Qar Journal of Science, 2022
The plane wave expansion method was implemented in modeling and simulating the band structures of two dimensional photonic crystals (PhCs) with square, triangular and honeycomb lattices with circular air holes in dielectric or circular GaAs rods in air. The eigen value equation of TE and TM modes will presented. The Fourier transform of dielectric constant will analyzed and the effects of lattice type will discussed. The eigenvalue equations of TE and TM modes will solved using Matlab environment. Our results show that the first type of PhCs is more flexible than the second type in controlling the band widths and the achieved frequency positions, and the triangular lattice showed the greatest flexibility. On the other hand, this work showed the significant effect of the dielectric constant and the lattice constant on the achieved bandwidth.
Band gap studies of triangular 2D photonic crystals with varying pore roundness
Solid State Communications, 2000
Photonic crystals (PCs) are theoretically studied in order to correlate the structural parameters with the resulting electromagnetic behaviour. Two-dimensional (2D) PCs of dielectric media are routinely assumed to be formed by circular rods or pores, respectively. Main topics of the paper are band gap modi®cations (TM-and TE-polarization) for pores of deteriorating roundness, approximated by ellipses of varying eccentricity. On the basis of Maxwell's equations and a`plane wave expansion', band structures are computed for triangular 2D lattices of air columns in silicon. The results are compared with calculations for circular air columns of varying ®lling factors. q
Body Centered Photonic Crystals
The photonic energy bands of body centered cubic photonic crystals formed from SiO 2 , GaP, Si, InAs, GaAs, InP, Ge and BaSrTiO 3 dielectric spheres drilled in air and air holes drilled in these dielectric mediums were calculated using the plane wave expansion method. The filling factor for each dielectric material was changed until a complete energy gap was obtained and then the density of states was calculated. There were no complete band gaps for air spheres drilled in these eight dielectric mediums. The lattice constants were determined by using wavelengths in the region 1550 nm -1nm . The variation of the band gap widths with the filling factor and the variation of gap width to midgap frequency ratios with dielectric contrast were investigated. The largest band gap width of 0.021 for normalized frequency was obtained for GaP for the filling factor of 0.0736. The mode filed distributions were obtained by guiding a telecommunication wave with 1.55µm wavelength through a 3 3 3 × × photonic cell formed from GaP spheres in air with a filling factor of 0.0736 for transverse electric and magnetic modes.
Analysis of photonic band gap structure for the design of photonic devices
Comptes Rendus Physique, 2004
A detailed analysis, based on Kronig-Penney model and finite-difference time-domain (FDTD) method, is used to explain the air-filling factor effect on the optical properties of defect-free photonic crystals. By the use of the Kronig-Penney model, we calculated the photonic band structure for electromagnetic waves in a structure consisting of a periodic square array of dielectric rods of lattice constant a separated by air holes. Gaps in the resulting band structures are found for waves of both polarisations. We analysed the air-filling factor effect on both polarisations in low and high frequency regions. It is shown that the frequency of the lower TE (transverse-electric) band edge is independent of the air-filling factor in the low frequency region. The opposite behaviour holds for the upper band edge, growing rapidly with the air-filling factor. Using the FDTD we simulated the electric field as the pulse propagates through the structure. The results of both approaches are compared, and the operation characteristics of the measuring air-filling factor device are described. We investigate the optical properties of a single and two defects incorporated in the PC, which can be potentially applied to ultra small surface-emitting-type channel drop filter. It is shown that the frequency and polarisation of the dropped light can be controlled by changing the size and/or shape of the defect. The electric field distribution calculations show that the electric field for a given frequency is located only at the defect, which means that each defect can detect only its corresponding wavelength. To cite this article: F.
Two Classes of Photonic Crystals with Simultaneous Band Gaps
Japanese Journal of Applied Physics, 2004
In this study, we consider band structures of two classes of photonic crystals with two geometric parameters. The first class has a square lattice and is studied for dielectric contrast, centered at "=" 0 ¼ 11:4 (GaAs-air). The second class has a hexagonal lattice and is studied for dielectric contrast, centered at "=" 0 ¼ 13 (silicon-air). These examples have the following feature: the optimal (and largest) full band gap is obtained when both band gaps for E and H polarizations have the same (simultaneous) band edges. In addition, photonic crystals with two geometric parameters typically have much larger optimal band gaps than their counterparts with one geometric parameter.
Photonic band gap engineering in 2D photonic crystals
Pramana, 2006
The polarization-dependent photonic band gaps (TM and TE polarizations) in two-dimensional photonic crystals with square lattices composed of air holes in dielectric and vice versa i.e., dielectric rods in air, using the plane-wave expansion method are investigated. We then study, how the photonic band gap size is affected by the changing ellipticity of the constituent air holes/dielectric rods. It is observed that the size of the photonic band gap changes with changing ellipticity of the constituent air holes/dielectric rods. Further, it is reported, how the photonic band gap size is affected by the change in the orientation of the constituent elliptical air holes/dielectric rods in 2D photonic crystals.
An emerging element in optical fiber communication, 2D Photonic Crystal is an artificial periodic structure having a bandgap which shows a prohibition of a range of wavelengths to pass away through it. Various design parameters which affect the bandgap of 2D photonic crystal structure such as lattice structure, shape of rods, r/a ratio, dielectric constant etc. are studied in this paper. The Plane Wave Expansion (PWE) method is used to calculate the bandgap structure of two dimensional photonic crystals.