Photonic band gap engineering in 2D photonic crystals (original) (raw)
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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
Modelling and design of complete photonic band gaps in two-dimensional photonic crystals
Pramana, 2008
In this paper, we investigate the existence and variation of complete photonic band gap size with the introduction of asymmetry in the constituent dielectric rods with honeycomb lattices in two-dimensional photonic crystals (PhC) using the plane-wave expansion (PWE) method. Two examples, one consisting of elliptical rods and the other comprising of rectangular rods in honeycomb lattices are considered with a view to estimate the design parameters for maximizing the complete photonic band gap. Further, it has been shown that complete photonic band gap size changes with the variation in the orientation angle of the constituent dielectric rods.
Photonic bandgap of two-dimensional dielectric crystals
Solid-State Electronics, 1994
The existence of an absolute photonic bandgap in the near-infrared for two-dimensional periodic dielectric structures is discussed for photons propagating in the plane of such 2D crystals. A special emphasis is put on the influence of the shape and size of the filling pattern on the absolute bandgap formation. A very large absolute photonic bandgap is predicted for 2D crystals formed by etching into a semiconductor slab a periodic array of large vertical cylindric voids of circular cross-section arranged in a triangular lattice. The technological feasibility of such "optimum" air/GaAs 2D crystals by standard processing techniques (electron beam lithography and reactive ion etching) is demonstrated.
Band Gap Properties of Two-Dimensional Photonic Crystal Structures with Rectangular Lattice
Journal of Optical Communications, 2015
In this paper we proposed a new structure of two-dimensional photonic crystals with rectangular lattice. After deducing the primitive lattice vectors and first Brillouin zone of the structures, we studied the band gap properties of horizontal and vertical rectangular lattice structures and compared them with conventional square lattice structure. The most excellent characteristic of these structures is their joint band gap regions, which make them suitable for designing polarization-independent devices. The other advantage of these structures is having band gaps at higher normalized frequencies.
Simulation of Two Dimensional Photonic Band Gaps
International Letters of Chemistry, Physics and Astronomy, 2013
The plane wave expansion method was implemented in modelling and simulating the band structures of two dimensional photonic crystals with square, triangular and honeycomb lattices with circular, square and hexagonal dielectric rods and air holes. Complete band gaps were obtained for square lattice of square GaAs rods and honeycomb lattice of circular and hexagonal GaAs rods as well as triangular lattice of circular and hexagonal air holes in GaAs whereas square lattice of square or circular air holes in a dielectric medium ε = 18 gave complete band gaps. The variation of these band gaps with dielectric contrast and filling factor gave the largest gaps for all configurations for a filling fraction around 0.1.The gap maps presented indicated that TM gaps are more favoured by dielectric rods while TE gaps are favoured by air holes. The geometrical gap maps operating at telecommunication wavelength λ = 1.55 μm showed that a complete band gap can be achieved for triangular lattice with c...
Optics Express, 2008
Photonic crystals exhibiting a photonic band gap in both TE and TM polarizations are particularly interesting for a better control of light confinement. The simultaneous achievement of large band gaps in both polarizations requires to reduce the symmetry properties of the photonic crystal lattice. In this letter, we propose two different designs of two-dimensional photonic crystals patterned in high refractive index thin silicon slabs. These slabs are known to limit the opening of photonic band gaps for both polarizations. The proposed designs exhibit large complete photonic band gaps : the first photonic crystal structure is based on the honeycomb lattice with two different hole radii and the second structure is based on a "tri-ellipse" pattern in a triangular lattice. Photonic band gap calculations show that these structures offer large complete photonic band gaps Δω ω larger than 10 % between first and second photonic bands. This figure of merit is obtained with single-mode slab waveguides and is not restricted to modes below light cone.
Design and Optimization of 2D Photonic Crystals for the Best Absolute Band Gap
2011
The existence and properties of photonic band gaps was investigated for a square lattice of dielectric cylinders in air. Band structure calculations were performed using the transfer matrix method as function of the dielectric constant of the cylinders and the cylinder radius-to-pitch ratio r/a. It was found that band gaps exist only for transverse magnetic polarization for a dielectric contrast larger then 3.8 (index contrast >1.95). The optimum r/a ratio is 0.25 for the smallest index contrast. For silicon cylinders (n = 3.45) the widest gap is observed for r/a = 0.18. Band structure calculations as function of r/a show that up to four gaps open for the silicon structure. The effective index was obtained from the band structure calculations and compared with Maxwell-Garnett effective medium theory. Using the band structure calculations we obtained design parameters for silicon based photonic crystal waveguides. The possibility and limitations of amorphous silicon, silicon germanium and silicon-on-insulator structures to achieve index guiding in the third dimension is discussed.
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.
Effect of doping on defect modes of 2D photonic band gap crystals
INTERNATIONAL CONFERENCE ON MULTIFUNCTIONAL MATERIALS (ICMM-2019), 2020
Here we report numerical simulation results obtained by performing photonic band structure calculations for a 2D periodic array of dielectric cylinders, having square symmetry with a lattice constant of 600nm. We have performed electromagnetic calculations using finite element method by employing COMSOL Multiphysics software. The band structure of the infinite crystal is calculated using plane wave method using MIT Photonic Band gap Package software. The calculated reflectance spectra showed three photonic bands spanning over visible and Infra-red regions a for refractive index contrast of 2.98. In order to study the property of a resonator, a point defect is introduced by replacing the dielectric cylinder with an air-cylinder. A sharp dip within the band gap of the reflectance spectra is observed and is attributed to the localized mode associated with the defect. Q-factor associated with the localized mode is calculated. The effect of refractive index of the defect on the localized mode frequency have been investigated and results are reported here.