Large Complete Band Gaps Research Articles

Complete band gaps in two-dimensional piezoelectric phononic crystals with {1–3} connectivity family

In this paper, we present results of full band structures for two-dimensional piezoelectric phononic crystals with {1–3} connectivity family. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes: a transverse polarization mode and a mixed (longitudinal-transverse) polarization mode. And the band structures of the two modes for both the case of piezoelectric rods embedded in a polymer matrix and the case of polymer rods embedded in a piezoelectric matrix are calculated for two different cross-sections of the rods, i.e., circular and square, considering the practical fabrication of phononic crystals. We reveal the existence of several very large complete band gaps in a material of practical interest such as PZT rods reinforced polythene composite. The effects of shapes and filling fraction of the rods on band gaps are discussed in detail. The existence of these gaps in relation to the physical parameters of the constituent materials involved is studied. Understanding the band structures of piezoelectric phononic crystals can give some information for improvements in the design of acoustic transducers.

Large complete bandgaps in a two-dimensional square photonic crystal with isolatedsingle-atom dielectric rods in air

It is well known that the square lattice of isolated single-atom dielectric rods in air does notgive rise to complete bandgaps even when asymmetry is introduced to lift some degeneracy.However, in this paper, a new kind of two-dimensional square photonic crystal with isolatedsingle-atom dielectric rods in air formed by holographic lithography is proposed, and therelation between their photonic bandgap properties and their specific holographic designare systematically analyzed. In addition to the large complete relative bandgap,namely 9.68% gap/midgap ratio for the dielectric constant contrast of 13.6:1,this structure has very large tolerance on the system parameters and fabricationconditions. This fact can greatly relax the experimental requirements. This work maydemonstrate the unique feature and advantages of photonic crystals made by theholographic method and provide a guideline for their design and fabrication.

Optimal design based on a two-dimensional photonic crystal of hexagonal lattice with a large complete band gap

Optimal design based on a two-dimensional photonic crystal of hexagonal lattice with a large complete band gap

Controlling the photonic bandgap structures via manipulation of refractive index of electromagnetically induced transparency vapor

A new application of coherent manipulation of EIT (electromagnetically induced transparency) medium is suggested. A two-dimensional photonic cystal with a triangle lattice of elliptic air cylinders, which are filled with the EIT atomic vapor, in the KAs backgroud material is designed. By manipulating the refractive index of the EIT vapor via the external control field, one can obtain the controllable bandgap structure that is sensitive to the variations of external conditions (e.g. the intensity of the control field). It is shown that a large complete bandgap of about 0.0503ωe in the region of high normalized frequency could be achieved by choosing the specific parameters such as the spontaneous decay rate, dephasing rate, Rabi frequency of control light, atomic number density as well as elliptic geometric parameters.

Holographic design of a two-dimensional photonic crystal of square lattice with a large two-dimensional complete bandgap

Theoretical analysis has shown that a two-dimensional (2D) lattice with circular columns connected by veins can produce a large complete bandgap when the radius of the columns and the width of the veins are properly chosen. We propose a holographic method to fabricate a similar 2D structure of irregular columns that can yield a 2D complete bandgap for a wide range of dielectric contrasts and a bandgap as large as 15.0% for ε=11.4 and 15.8% for ε=13.6. The specific problems of interference beam design, intensity threshold selection, and the effect of the shape and size of the unit cells on the final bandgap are discussed. This analysis demonstrates the unique features and advantages of the holographic method in bandgap engineering and gives a guideline for practical fabrication.

Photonic crystal with diamondlike structure fabricated by holographic lithography

In this letter, we report a diamondlike structure. Our theoretical analysis reveals that a large complete band gap exists between the second and third bands with only a very low refractive index is needed (n⩾2.05) to open the complete band gap for this inverse structure. Large-scale and high-quality three-dimensional structures with this diamondlike symmetry are fabricated by a holographic lithography method using four laser beams incident from the same half-space. The beam geometry is similar to that for the face-centered cubic (fcc) structure except that the central beam is circularly polarized and the polarizations of the three outer beams must be optimized, which is critical to construct this diamondlike interference pattern.

Theoretical study of a modulated pore approach to a photonic crystal of inverted diamond type

In this paper a photonic crystal sPCd approach to an inverted diamondlike structure with a large complete bandgap is introduced. We theoretically study the dispersion behavior of PCs being fabricated by modulating macroporous silicon. The widening of single narrow pores to air bulges of spherical or ellipsoidal shape follows the lattice sites in the diamond cell. We compile band structure calculations as a function of sid the radius of the air spheres, siid the radius of the connecting pores, and siiid of the shape ssphere/ellipsoidd of the air bulges. The degradation of the bandgap, caused by the remaining air pores, can be partially compensated by nonspherical air bulges of adapted size and eccentricity.

Holographic design of a two-dimensional photonic crystal of square lattice with pincushion columns and large complete band gaps

In holographic fabrication of photonic crystals the shape and size of the dielectric columns or particles ("atoms") are determined by the isointensity surfaces of the interference field. Therefore their photonic band gap (PBG) properties are closely related to their fabrication design. As an example, we have investigated the PBGs of a kind of holographically formed two-dimensional (2-D) square lattice with pincushion columns rotated by 45 degrees , and shown that this structure has complete PBGs in a wide range of dielectric contrast comparable to or even larger than those of the same lattice with square columns reported before. The optical design for making this structure is also given. This work may demonstrate the unique feature and advantages of photonic crystals made by holographic method and provide a guideline for their design and experimental fabrication.

Scaling properties of a tetragonal photonic crystal design having a large complete bandgap

Photonic crystal structures (PCs) of tetragonal lattice type are introduced and studied. They feature complete three-dimensional (3D) photonic bandgaps (PBGs). The PC design is based on two systems of ordered, parallel pores being perpendicular to each other. For increasing pore radii, the pore systems interpenetrate and an inverted woodpile geometry arises. The size of the 3D bandgaps depends on the ratio of the cell parameters L x , L y , and L z , the pore radii and the refractive index of the dielectric material. If realized as a silicon/air structure, the maximum 3D gap is larger than 25%. A possible fabrication route for the near-infrared is based on 2D macroporous silicon where perpendicular pores are drilled, e.g., by focused-ion-beam etching. The dispersion behaviour of the PCs is theoretically analysed (band structures, density-of-states), systematically varying all relevant parameters. The optimization of the PBG sizes as well as a possible tunability of the PBG energies are discussed.

Large two-dimensional band gaps in three-component phononic crystals

By using of the plane wave expansion method, we present the large complete elastic wave band gap in the two-dimensional three-component phononic crystals consisting of coating cylinders embedded in a glass host. Based on the localized resonance structure, the optimum gap is obtained by tuning the thickness ratio of the coating layer. The calculations also demonstrate that the acoustic band gaps varied with the filling fraction of the coating cylinders display a different character from the two-component system at the high filling fraction.

Macroporous-silicon-based three-dimensional photonic crystal with a large complete band gap

A photonic crystal (PC) structure is described revealing a complete three-dimensional (3D) photonic band gap of about 25% if realized as a silicon/air structure. It is based on two systems of parallel circular pores being orthogonal to each other. The gap size depends on the degree of mutual penetration of the pore systems. A possible fabrication route is based on macroporous silicon (lattice constant a=0.5 μm), into which orthogonal pores are drilled, e.g., by focused-ion-beam etching. This yields a 3D photonic crystal with a complete band gap in the near infrared. The dispersion behavior of the PC is theoretically analyzed (band structure, density of states), varying the pore radii. We discuss the influence of pore shape variations and topological modifications on the size of the gap.

A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal

A plane-wave expansion method based on the effective medium theory for calculating the band structure of a two-dimensional photonic crystal is presented. Compared to two other plane-wave expansion methods, the present method has a faster convergence and advantage to calculate the band structure for complicated structures. Using the present fast method, a photonic crystal with a large complete bandgap Δ ω=0.1111(2 πc/ a) ( a is the lattice constant) is found. The designed photonic crystal is formed by a triangular array of elliptic air holes in GaAs medium.

A two-dimensional photonic crystal with six large bandgaps formed by a hexagonal lattice of anisotropic cylinders

The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a hexagonal structure of anisotropic cylinders. Two cylindrical inclusions in the unit cell have two different radii, R1 and R2 (R1<R2). By reducing the symmetry of the structure and choosing appropriately parameters R2 and s = R1/R2 (s<1), we obtain six large complete bandgaps, among which three are over 0.05 ωe (where ωe = (2πc)/a) in the high region of the normalized frequency (however, one of these over 0.065 ωe is not stable). There are two other stable complete bandgaps in the low-frequency region.

Optimal design of a two-dimensional photonic crystal of square lattice with a large complete two-dimensional bandgap

Optimal design of a two-dimensional photonic crystal with a square lattice of air holes in GaAs is considered. It is shown how a maximum complete two-dimensional band gap is obtained by optimally connecting the dielectric rods with veins. The complete two-dimensional bandgap of our optimal design reaches Δω=0.0762(2πc/a) (a is the lattice constant).

Large complete band gap in two-dimensional photonic crystals with elliptic air holes

It is shown that elliptic air holes can be used effectively as inclusions to obtain a large complete band gap for two-dimensional photonic crystals. An instructive procedure of how one quickly finds the optimal configuration which gives the maximum complete band gap is described.

Complete acoustic band gaps in periodic fibre reinforced composite materials: the carbon/epoxy composite and some metallic systems

We present results of elastic band structure for two-dimensional composite materials, composed of periodical square arrays of parallel cylinders in a background. We reveal, for the first time, the existence of several very large complete band gaps in the band structure of a material of practical interest such as a C fibre reinforced epoxy composite. Within these gaps the propagation of acoustic waves is forbidden. The influence of the geometry of the cylinders and the effect of the composition of the composite material on the band structure are studied. We also compare these results with those obtained for metallic composites such as W (Al) cylinders in an Al (W) matrix. The complete band gaps are observed in the cases of C cylinders in epoxy or W cylinders in Al, but not in the opposite situations. We discuss the existence of these gaps in relation to the physical parameters of the materials involved.