Absolute Band Gap Research Articles

Large absolute band gaps in two-dimensional photonic crystals formed by large dielectric pixels

Large absolute band gaps are searched among photonic crystals whose unit cells are formed by large dielectric pixels. To speed up the computation, a fast plane-wave expansion method is introduced for calculating the band structures for such special photonic crystals. Two structures are found to have absolute band gaps of $0.1158(2\ensuremath{\pi}c/a)$ and $0.11(2\ensuremath{\pi}c/a)$ $(a$ is the period of the square lattice) at the low- and high-frequency regions, respectively. Both structures are stable and convenient for fabrication.

Analytically solvable model of photonic crystal structures and novel phenomena

The purpose of this work is twofold. First, we present a new simple model of photonic crystal structures that can be treated analytically. Second, from the rigorous analysis of propagation and resonance of the models, we point out two novel properties of waves in the structure. The first is that there is a waveguide in which a leakage-free guided mode can have the same propagation constant (wavenumber) as that of continuum waves. The second novel property is that there is a resonator in which the wave can be localized, even in the absence of a "full bandgap." These facts disprove some "common beliefs" about photonic crystal structures: many people believe that (1) in a photonic crystal waveguide, a radiation-free guided mode cannot have the same wavenumber as that of continuum modes and (2) in a photonic crystal resonator, lossless localization can take place only if the host photonic crystal has an absolute bandgap. Our examples show that such beliefs are overstatements.

Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range: a theoretical and experimental study.

The propagation of acoustic waves in a two-dimensional composite medium constituted of a square array of parallel copper cylinders in air is investigated both theoretically and experimentally. The band structure is calculated with the plane wave expansion (PWE) method by imposing the condition of elastic rigidity to the solid inclusions. The PWE results are then compared to the transmission coefficients computed with the finite difference time domain (FDTD) method for finite thickness composite samples. In the low frequency regime, the band structure calculations agree with the FDTD results indicating that the assumption of infinitely rigid inclusion retains the validity of the PWE results to this frequency domain. These calculations predict that this composite material possesses a large absolute forbidden band in the domain of the audible frequencies. The FDTD spectra reveal also that hollow and filled cylinders produce very similar sound transmission suggesting the possibility of realizing light, effective sonic insulators. Experimental measurements show that the transmission through an array of hollow Cu cylinders drops to noise level throughout frequency interval in good agreement with the calculated forbidden band.

Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes

Despite the considerable amount of research undertaken on various lattice structures, the photonic band gap (PBG) for a triangular lattice remains the largest both in the transverse magnetic (TM) and transverse electric (TE) modes. The PBG for a square lattice can be doubled by using square air holes rather than air cylinders. Reducing the symmetry was effective in terms of a honeycomb lattice in that the PBG can be increased 40% by deforming the lattice and using oval dielectric rods instead of cylindrical rods. The PBGs for all the examined structures increase monotonously as the refractive index is increased. The overlap PBG between the TM and TE gaps (polarization-independent PBG) is the largest for a triangular lattice of circular air rods. The overlap PBG for a hybrid square lattice of air rods is the next largest, and is twice as large as that for the well-known honeycomb lattice consisting of dielectric cylinders. When the refractive index of a dielectric material is increased to more than 3.50, the magnitude of the overlap PBG for almost all the photonic crystals that exhibit an overlap PBG saturates or decreases, except for the largest and next largest overlap PBG’s mentioned above.

Large Absolute Photonic Bandgap at High Frequencies in a Two-DimensionalPhotonic Crystal with a Hexagonal Structure

A new large absolute photonic bandgap at high normalizedfrequencies can be obtained in a two-dimensional hexagonalstructure with alumina cylinders in air by reducing the symmetryof the structure. An instructive procedure is described forfinding the optimal configuration which gives the maximum absolutebandgap Δω = 0.091(2πc/a).

Effects of shapes and orientations of scatterers and lattice symmetries on the photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional photonic crystals consisting of lattices with different symmetries and scatterers of various shapes, orientations, and sizes are studied numerically. Specifically, four types of lattices (triangular, hexagonal, square, and rectangular) and five different shapes of scatterers (hexagon, circle, square, rectangle, and ellipse) are considered. The scatterers are either dielectric rods in air, or air rods in dielectric media. The lattice symmetry and all these properties of the scatterers can affect the band gap size. Given a lattice symmetry, the largest absolute photonic band gap is achieved by selecting a scatterer of the same symmetry; e.g., hexagonal rods in triangular or honeycomb lattices, square rods in square lattices, and rectangular rods in rectangular lattices. The band gap can be further maximized by adjusting the orientation and size of the scatterers; but no simple, systematic rules can be drawn.

Omnidirectional absolute band gaps in two-dimensional photonic crystals

A plane-wave expansion method has been developed to investigate the off-plane propagation of electromagnetic waves in a two-dimensional (2D) photonic crystal. Photonic band-structure calculations indicate that some 2D crystal structures can support a common band gap for both polarizations and for all off-plane angles from $0\ifmmode^\circ\else\textdegree\fi{}$ up to $90\ifmmode^\circ\else\textdegree\fi{}.$ The presence of such an omnidirectional absolute band gap implies that a 2D photonic crystal can exhibit some of the functionalities of a three-dimensional crystal with a complete band gap.

Strain-tunable photonic band gap crystals

We have designed a two-dimensional strain-tunable photonic band gap crystal by distorting the symmetry of the crystal from a regular hexagonal to a quasihexagonal lattice by means of field driven strain using a piezoelectric material. Calculations predict that the original high symmetry energy bands split up into several strained energy bands depending on the magnitude and direction of the strain. In the proposed structures, we show that 2% (3%) shear strain can be used to tune ∼52% (73%) of the original undistorted absolute band gap of a two-dimensional photonic band gap crystal. These device structures can be used for optical switching and modulation.

Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals.

Experimental measurements of acoustic transmission through a solid-solid two-dimensional binary-composite medium constituted of a triangular array of parallel circular steel cylinders in an epoxy matrix are reported. Attention is restricted to propagation of elastic waves perpendicular to the cylinders. Measured transmitted spectra demonstrate the existence of absolute stop bands, i.e., band gaps independent of the direction of propagation in the plane perpendicular to the cylinders. Theoretical calculations of the band structure and transmission spectra using the plane wave expansion and the finite difference time domain methods support unambiguously the absolute nature of the observed band gaps.

Absolute photonic band gaps in 12-fold symmetric photonic quasicrystals

A recent publication [Nature (London) 404, 740 (2000)] claimed that absolute photonic gaps can be realized in 12-fold quasicrystalline arrangement of small airholes in a matrix of silicon nitride or glass. The result is rather surprising since silicon nitride $(n=2.02)$ and in particular, glass $(n=1.45)$ have rather low refractive index. In this work, we have studied the transmission properties of the same systems by using the multiple-scattering method. We found that the 12-fold triangle-square tiling is indeed very good for the realization of photonic gaps and we found absolute gaps in systems with airholes in dielectric, dielectric cylinders in air, and metal cylinders in air. However, for the case of air-holes in a dielectric background, absolute gaps appear only when the dielectric contrast is sufficiently high, and both silicon nitride and glass have refractive indices below the threshold.

Complete three-dimensional photonic bandgap in a simple cubic structure

The creation of a three-dimensional (3D) photonic crystal with simple cubic (sc) symmetry is important for applications in the signal routing and 3D waveguiding of light. With a simple stacking scheme and advanced silicon processing, a 3D sc structure was constructed from a 6-in. silicon wafer. The sc structure is experimentally shown to have a complete 3D photonic bandgap in the infrared wavelength. The finite size effect is also observed, accounting for a larger absolute photonic bandgap.

The photonic band structure of macro-`ionic' crystal

The photonic band structures depend on both the crystal symmetry and composing elements of the primary cell, the opening up of photonic gap is determined by the dielectric modulation in space. Since the high-dielectric medium acts as attractive centers while the metallic medium acts as repulsive centers for the field, the photonic crystals composed of a periodic arrangement of both high-dielectric and metallic spheres will have the highest dielectric contrast. The field distribution in such crystals is expected to resemble the electron distribution in ionic crystals, thus it should favor the formation of the absolute band gap. We show as an example that in GaAs-type photonic crystals this does prove to be the case and three large absolute gaps are found.

The photonicband structures of body-centred-tetragonal crystals composed of ionic ormetal spheres

The photonic band structures of body-centred-tetragonal (BCT)crystals composed of ionic or metal spheres are computed using thehighly efficient vector-wave Korringa-Kohn-Rostoker (KKR) method;an absolute band gap is found for the photonic crystals with highfilling ratio. The band gap is smaller in the crystals composed ofionic spheres than in those composed of metal spheres. The particularBCT structure was chosen since such structure can be easily realizedin an electrorheological fluid in the presence of an electric field.

Complete and absolute photonic bandgaps in highly symmetric photonic quasicrystals embedded in low refractive index materials

It is firmly established that periodic lattice structures can support photonic bandgaps (PBG). However, complete and absolute photonic bandgaps (CAPBG) have only been achieved in high dielectric constant mediums such as GaAs ( ε=13.6). An artificial quasiperiodic photonic crystal based on the random square-triangle tiling system was designed and fabricated. The photonic quasicrystal possesses 12-fold symmetry and was analysed using a finite difference time domain (FDTD) approach. High orders of symmetry in photonic quasicrystals have been shown to provide isotropic bandgaps across all the directions of propagation of light. As an outcome of these properties, this new class of photonic quasicrystal has been shown, for the first time, to possess a secondary non-directional CAPBG for a relatively low index material, silicon nitride ( ε=4.08). These materials are compatible with integrated optical technologies. This allows the fabrication of efficient integrated optical PBG devices such as WDM filters and multiplexers to become a real possibility.

Photonic band gaps in anisotropic photonic crystals

Photonic band gaps can be improved in photonic crystals fabricated from anisotropic materials. In three-dimensional photonic crystals, the anisotropy can open partial band gaps in simple lattices such as face-centered-cubic, body-centered-cubic, and simple-cubic lattices of dielectric spheres in air, where no absolute band gap exists. Yet, this anisotropy will reduce originally existing band gap. Such an anisotropy can substantially improve the absolute band gap in two-dimensional photonic crystals due to the quasi-independent adjustment of the refractive indices for the E- and H-polarization modes in anisotropic materials.

Large two-dimensional sonic band gaps.

We show that absolute sonic band gaps produced by two-dimensional square and triangular lattices of rigid cylinders in air can be increased by reducing the structure symmetry. In the case of square lattices, symmetry reduction is achieved by a smaller diameter cylinder placed at the center of each unit cell. For triangular lattices the reduction is achieved by decreasing the diameter of the cylinder at the center of the hexagons in the lattice. Theoretical predictions are also demonstrated experimentally: starting from a honeycomb lattice (using cylinders of 4 cm of diameter size and 6.35 cm nearest-neighbor distance) we have studied the transition to a triangular symmetry by putting rods with increasing diameter (in the range 0.6-4 cm) at the center. The greatest enhancement of the attenuation strength observed in transmission experiments has been obtained in the high frequency region for diameter ratios in the range 0.1-0.3.

Large absolute photonic band gaps created by rotating noncircular rods in two-dimensional lattices

Absolute photonic band gaps (PBG's) can be substantially improved in two-dimensional (2D) lattices by rotating noncircular air rods in dielectric background, in which the configuration of high-dielectric regions that are both practically isolated and linked by narrow veins can be freely adjusted to create large absolute PBG's. For square lattice, the largest absolute PBG's in the single-square-rod and double-hybrid-rods structures are 315 and 150 % sizes of those in the corresponding single-circular-rod and double-circular-rods structures, respectively. Furthermore, the large absolute PBG's persist in a wide range of filling fractions and reach their maxima far away from the close-packed conditions, and this is in vast favor of preparation of crystals. Such an approach is also applicable to other 2D lattices. It may open up a scope for engineering PBG's.

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal

In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements. @S0163-1829~99!07419-6#

Absolute three-dimensional photonic band gap in the infrared regime in woven structures

We closely study the formation of a three-dimensional (3D) photonic band gap in a system composed of dielectric fibers. The fibers are woven into layers that are then stacked up to form 3D lattices of different structures. The woven systems have the advantage of easy fabrication and, with the cross sections of fibers in microns, the band gap can be made in the infrared regime. We employ the transfer-matrix method to study the photonic band structures. The optimized gap-formation condition is found in a quasi-body-centered-cubic structure. A 3D full gap is identified in the middle infared regime with the use of fibers of moderate dielectric constants $(\ensuremath{\epsilon}<~16)$. Our studies strongly suggest the possibility of employing such woven structures in various photonic insulator-related applications.