Partial Band Gaps Research Articles

Dispersion characteristics of negative refraction sonic crystals

Dispersion characteristics of negative refraction sonic crystals are investigated. The plane wave expansion method is used to calculate the equifrequency surface; the dependences of refractive direction on frequencies and incident angles for triangular lattices are shown. There exist the positive and negative refractive waves which include k· V g⩾0 and k· V g⩽0 in the second band for the triangular system. We also use the finite element method to demonstrate that the relative intensity of the transmitted acoustic waves is dependent on incident frequencies and angles. The positions of the partial band gaps obtained by the plane wave expansion method are in good agreement with those obtained by the finite element method. The sonic crystals with negative effective index are shown to have higher transmission intensities. By using the negative refraction behavior, we can design a sonic crystal plane lens to focus a sonic wave.

Local observation of modes from three-dimensional woodpile photonic crystals with near-field microspectroscopy under supercontinuum illumination

A near-field microscope coupled with a near-infrared (NIR) supercontinuum source is developed and applied to characterize optical modes in a three-dimensional (3D) woodpile photonic crystal (PC) possessing a NIR partial bandgap. Spatially resolved near-field intensity distributions under different illumination wavelengths demonstrate that the electric fields preferentially dwell in the polymer rods or in the gaps between rods, respectively, for frequencies below or above the stop gap, as predicted by the 3D finite-difference time-domain modeling. Near-field microspectroscopy further reveals that the position-dependent band-edge effect plays an important role in PC-based all-optical integrated devices.

Partial frequency band gap in one-dimensional magnonic crystals

Collective spin wave modes propagating in an array of magnetic stripes coupled by dynamic dipole interaction are investigated by Brillouin light scattering. It is demonstrated that this structure supports propagation of discrete spin waves at any angle with respect to the stripes length. The data are interpreted using a theoretical model based on the Bloch wave approach. It is shown that, due to the one-dimensional artificial periodicity of the medium, the gaps in the spin wave spectrum are partial: the frequency passbands for propagation along the direction of periodicity overlap with the stop bands for propagation along the stripes.

Analyses of negative refraction in the partial bandgap of photonic crystals

We consider the conditions for negative refraction in the partial bandgap of photonic crystals and show that, in contrast to previously published studies, anisotropy is not a necessary condition for negative refraction, and that unrestricted imaging is possible. This analysis is made possible by the introduction of a negative local wavevector. In addition, we analyze the origins of the previously reported restricted and adjacent imaging properties and extend negative refraction to higher bands.

Tuning coherent radiative thermal conductance in multilayer photonic crystals

We consider coherent radiative thermal conductance of a multilayer photonic crystal. The crystal consists of alternating layers of lossless dielectric slabs and vacuum, where heat is conducted only through photons. We show that such a structure can have thermal conductance below vacuum over the entire high temperature range due to the presence of partial band gap in most of the frequency range, as well as the suppression of evanescent tunneling between slabs at higher frequencies. The thermal conductance of this structure is highly tunable by varying the thickness of the vacuum layers.

Self-collimated waveguide bends and partial bandgap reflection of photonic crystals with parallelogram lattice

The photonic crystal structure with parallelogram lattice, capable of bending a self-collimated wave with free angles and partial bandgap reflection, is presented. The equifrequency contours show that the direction of the collimation wave can be turned by tuning the angle between the two basic vectors of the lattice. Acute, right, and obtuse angles of collimating waveguide bends have been realized by arc lattices of parallelogram photonic crystals. Moreover, partial bandgap reflection of the parallelogram lattice photonic crystals is validated from the equifrequency contours and the projected band structures. A waveguide taper based on this partial bandgap reflection is also designed and proved to have above 85% transmittance over a very wide operating bandwidth of 180 nm.

Electrical tuning of photonic crystals infilled with liquid crystals

In this paper we perform a complete study of electrical tuning in liquid crystal-infilled two-dimensional (2D) photonic crystals (PCs). The nematic liquid crystal (NLC) is characterized by a full range of bulk and surface elastic parameters. An essentially DC tuning field is applied in the axial direction. By minimizing the total (elastic plus electromagnetic) free energy, the configuration of the NLC directors, as a function of radial distance, is obtained. Three possible configurations are considered: escaped radial, planar radial, and axial. It is found that, in general, the escaped radial configuration is the preferred one. However, for sufficiently large applied fields, a phase transition occurs to the axial configuration. For example, in the case of the NLC 5CB, this transition is realized at about 14V/μm provided that the cylinder radius is greater than about 50nm. The configuration of the NLC directors determines the dielectric tensor as function of radial distance and this, in turn, leads to the eigenvalue equation for the PC. We present two such equations: one exact and the other approximate. The exact eigenvalue equation is based on the full anisotropy of the dielectric tensor and does not result in the usual separation of normal modes in a 2D PC. The approximate eigenvalue equation is derived from the average (over the cylinder cross-section) dielectric tensor and leads to modes that are polarized in the directions either parallel (E-mode) or perpendicular (H-mode) to the cylinders. Our calculations of the photonic band structure, by both methods, show that the approximate calculation works very well for the 5CB NLC cylinders in a silicon oxide (silica) host. This allows us to introduce the terminology quasi-E and quasi-H polarizations. We show how the partial photonic band gap in the [100] direction for these polarizations can be tuned and even completely closed. This behavior could be applied to the design of versatile, tunable polarization filters.

Fabrication of silica/zinc oxide core–shell colloidal photonic crystals

We have fabricated three-dimensional ZnO photonic crystals by the self-assembly of SiO2/ZnO core–shell microspheres of diameter 180–220 nm by means of a vertical deposition method. The organized crystals adopt a uniform close-packed hexagonal structure with long-range order and a high filling fraction. They exhibit strong partial photonic band gaps at 565–688 nm in the transmission spectrum and a broadened band edge emission at 383 nm in the photoluminescence spectrum. For comparison with these ZnO photonic crystals, we have also prepared pure silica crystals of the same dimensions. The photonic band gaps of the former have been found to be shifted to a longer wavelength by about 200 nm compared to those of the latter as a result of the higher refractive index of ZnO. This approach provides an efficient, economical alternative means of obtaining other, more complicated photonic crystals.

Thermal radiation in photonic crystals

We analyze the properties of thermal radiation in photonic crystals and show that the spectral energy density, the spectral intensity, and the spectral hemispherical power are only limited by the total number of available photonic states and their propagation characteristics. In addition, we show that the central quantity that determines these thermal radiation characteristics is the area of the isofrequency surfaces and not the photonic density of states as it is generally assumed. Through the presence of partial or complete photonic band gaps and the associated spectral and angular redistribution of photonic states, it is possible to have spectral regions over which the thermal radiation intensity is enhanced relative to the free space blackbody limit and propagation directions along which thermal photon focusing effects appear.

Optical properties of porous silicon Thue‐Morse structures

AbstractDielectric aperiodic Thue‐Morse structures up to 128 layers have been realized by the porous silicon technology. Normal incidence reflectivity measurements have been performed to investigate the photonic properties of the devices. A partial photonic band gap region, centered at 1100 nm and 70 nm wide has been observed for the S6 and S7 Thue‐Morse structures. The S6 multilayer has been studied as sensor device on exposure to several chemical substances. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Properties of metallo-dielectric opals and metallic inverse opal photonic crystals

Colloidal silica spheres with 290 nm diameters were self-assembled with single crystal crystallites 4–5 mm wide and 10–15 mm long. Larger spheres with diameters between 1000 and 2300 nm were self-assembled with single crystal crystallites up to 1.5 mm wide and 2 mm long. The silica opals self-assembled vertically along the [100] direction of the face centered cubic lattice resulting in self-templated opals. Inverse opal photonic crystals with a partial band gap possessing a maximum in the near infrared at 3.8 μm were constructed from opal templates composed of 2300 nm diameter spheres with chalcogenide Ge33As12Se55 (AMTIR-1). Inverse gold photonic crystals were fabricated from synthetic opal templates composed of 290 nm silica spheres.

Optical properties of a square-lattice photonic crystal within the partial bandgap

Optical properties of a two-dimensional square-lattice photonic crystal are systematically investigated within the partial bandgap through anisotropic characteristics analysis and numerical simulation of field pattern. Using the plane-wave expansion method and Hellmann-Feynman theorem, the relationships between the incident and refracted angles for both phase and group velocities are calculated to analyze light propagation from air to photonic crystals. Three kinds of flat slab focusing are summarized and demonstrated by numerical simulations using the multiple scattering method.

Optical switches based on partial band gap and anomalous refraction in photonic crystals modulated by liquid crystals

Optical switches using two transmission properties in triangular photonic crystals infiltrated with liquid crystals (LCs) are investigated for incorporation in wave-guided structures for planar lightwave circuits. The two devices employ partial band gap and anomalous refraction, which are based on the anisotropic characteristics of LC reorientation under applied fields. These switches have been designed and their parameters have been analyzed by the plane wave and finite-difference time-domain calculations. In the on/off switching system, the partial band gap can be controlled when the normalized operation frequency is 0.27. The anomalous refraction can be modulated to deflect a light beam with a maximum deflection angle ~57 degrees when the frequency is 0.3. The tunability induced by LCs can create a sharp switching in the photonic devices.

Creation of tunable bandgaps in a three-dimensional anisotropic photonic crystal modulated by a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the tunable bandgap in a three-dimensional anisotropic photonic crystal structures modulated by a nematic liquid crystal. The PC structure composed of an anisotropic dielectric sphere in the liquid crystal medium is studied by solving Maxwell's equations using the plane wave expansion method. The photonic band structures are found to exhibit partial bandgaps for the simple-cubic lattices. Numerical simulations show that the bandgaps can be continuously tuned in simple-cubic lattices consisting of anisotropic dielectric spheres by infiltrating nematic liquid crystals. We analyzed the variations of bandgap by considering various modulation of electric field. Such a mechanism of bandgap adjustment should open up a new application for designing components in photonic integrated circuits.

Manipulation of spontaneous emission in a tapered photonic crystal fibre

We characterize the spontaneous emission of dye that is introduced into the central core of a tapered photonic crystal fiber. Since the photonic crystal period in the fibre cladding varies along the taper, the transmission and spontaneous emission spectra over a wide range of relative frequencies can be observed. The spontaneous emission spectra of the fibre transverse to the fiber axis show suppression due to partial band-gaps of the structure, and also enhancement of spontaneous emission near the band edges. We associate these with van Hove features, as well as finite cluster size effects.

Tunable pseudogaps in electrochromic WO3 inverted opal photonic crystals

The numerical investigation of the optical properties of electrochromic WO3 inverted opal structure has been carried out with the help of plane wave expansion and finite difference time domain simulation methods. Electrochromic effect is incorporated through the tunable parameters of the frequency-dependent Drude dielectric function. Dependence of photonic bands on free electron density and radius of air spheres is investigated. Five kinds of partial band gaps in (111) direction are found to appear with the change of the sphere radius. The photonic band gaps tend to be upshifted in frequency with insertion of free electrons or with increase of the sphere radius.

Modulation of photonic band structures with dielectric anisotropy

By the multiple scattering method and the extended Mie theory, we have calculated the photonic band structure of the photonic crystals consisting of the dielectric spheres with uniaxial/biaxial anisotropy. The results demonstrate that for fcc lattice structure there exist two partial photonic band gaps which does not appear in the isotropic case. Among them, the lower one, lying between the second and the third bands, exists in one third of the first Brillouin zone, while the upper one, opening between the fourth and fifth bands, can appear simultaneously in the rest two thirds of the first Brillouin zone. The effects of anisotropy on the band structures are studied as well, which suggests the biaxial anisotropy are much more flexible than the uniaxial anisotropy in modulating the band structures.

Light collimator made of photonic crystal by partial band gap

Basing on finite-difference time-domain method and partial band gap effect of photonic crystal, we obtain collimated light beams from point optical source and two-dimensional photonic crystal structure. The diffusive light with some special frequencies can be collimated and propagate along a special direction within photonic crystal structure. Our study presents a new method to make light collimator.

Engineering the bandgap of a two-dimensional anisotropic photonic crystal

The photonic band structures of two-dimensional square lattice photonic crystals made of anisotropic materials with one of the principal axes oriented along the extension direction of cylinders are studied. The band structure of the photonic crystal can be substantially engineered to achieve large bandgaps by reorienting the other two principal axes of the anisotropy media in the periodic plane of the photonic crystal. In particular, it is shown that large full bandgap for H polarization can be created for a photonic crystal with circular holes in an anisotropic matrix medium. For pillar-type photonic crystals, we show that large partial bandgaps for H polarization can be created in half of the irreducible Brillouin zone. With the use of anisotropic materials and the flexibility of arranging the principal axes, the requirement on the filling ratio, refractive index and anisotropy to achieve the largest bandgap is greatly alleviated.

A new kind of light splitter made of a photonic crystal using the effect of a partial bandgap

We present finite-difference time-domain studies for light propagation in a two-dimensional photonic crystal. For a specific configuration, the two-dimensional photonic crystal allows the light mainly to propagate in two ΓX directions, which makes it a good light splitter.