Band Structure Of Photonic Crystals Research Articles

A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions

A finite-difference time-domain scheme in a nonorthogonal coordinate system is presented to calculate the band structure of a two-dimensional photonic crystal consisting of a skew lattice. The method can be used for a photonic crystal of complicated configuration, such as a photonic crystal with both dielectric and metallic inclusions. The method is verified by comparing with the results obtained by other methods for some special cases. The band structure of a photonic crystal with a dielectric layer coated on a metallic cylinder as an inclusion is studied. For such a case, it is noticed that both the dielectric and metallic characteristics of the band structure are inherited.

Obtaining the Band Structure of a Two-Dimensional Photonic Crystal by an Averaged Field Approach

An averaged field approach is suggested for obtaining the band structure of a photonic crystal when the dimension of the inclusions is much smaller compared with the longest period of the rectangular lattice of the photonic crystal. The method is illustrated for the H-polarization of the 2-dimensional case. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wave expansion method.

Direct visualization of photonic band structure for three-dimensional photonic crystals

We propose a method to experimentally determine the full photonic band structure of photonic crystals by monitoring the beam propagation, and we demonstrate the experimental results of the band-structure measurement in the near-infrared regime for ${\mathrm{S}\mathrm{i}/\mathrm{S}\mathrm{i}\mathrm{O}}_{2}$ three-dimensional hexagonal photonic crystals fabricated by autocloning bias-sputtering process.

Modelling of 3D photonic crystals based on opals

The construction of 3D photonic crystals with gaps in the visible or the near-infrared frequency range requires engineering of complex microstructures which are very difficult to realize by etching and micro-fabrication. Consequently, self-ordered systems such as synthetic opals are very promising. Synthetic bare opals are constituted by SiO2 spheres that organize themselves by a sedimentation process in a face centered cubic (fcc) arrangement. Using the plane wave method, we examine the photonic band structures of close-packed opal-based photonic crystals with an SiO2 (n = 1.5) matrix. The incomplete photonic band gaps at the X- and L-points have been studied which correspond to normally incident plane waves onto the (100) and (111) crystal planes. With the transfer matrix method, we model the transmission properties. We find that the incomplete gap at the L-point fully inhibits the transmission of waves propagating in the [111] direction for opal sample thicknesses that are easily obtainable. This property shows that bare opals could be good candidates for complete inhibition of transmission in the near-infrared and visible frequency range for given orientations.

An averaged-field approach for obtaining the band structure of a dielectric photonic crystal

An averaged-field approach is suggested for obtaining the explicit form of the dispersion equation for electromagnetic waves propagating in a three- or two-dimensional dielectric photonic crystal when the dimension of the inclusions is small compared with the longest period of the rectangular lattice of the photonic crystal. The band structure is obtained in an explicit and simple way. The method is verified numerically by comparing with the conventional plane-wave expansion method for a special case.

Near-field scanning optical microscopy as a simultaneous probe of fields and band structure of photonic crystals: A computational study

We demonstrate the feasibility of employing near-field scanning optical microscopy (NSOM) imaging to simultaneously obtain both the eigenfield distribution and the band-structure information of a photonic crystal. We introduce the NSOM measurement configuration required and simulate the imaging process, with both the tip and the sample included, using three-dimensional finite-difference time-domain calculations. Both the field-pattern and the frequency–wave-vector relations of photonic crystal eigenmodes are revealed by analyzing simulated images.

Enhancement of Nonlinear Optical Effect in One-Dimensional Photonic Crystal Structures

We observed the photonic band structure of one-dimensional photonic crystals using a white-light Michelson interferometer. In one-dimensional photonic crystals with a structural defect, there is a localized mode where the field is localized around the position of the defect. If the defect is made of nonlinear optical material, the effective nonlinearity of the photonic crystal is largely enhanced by the enhanced light intensity at the defect. In a one-dimensional photonic crystal with a defect, we observed a large enhancement of degenerate four-wave mixing efficiency. Since the total thickness of the whole structure is only a few micrometers, it was successfully used to form an optical phase-conjugated image.

Existence of Photonic Band Gaps in Two-Dimensional Metallodielectric Photonic Crystals

ABSTRACT Using the method of projection operators based on plane wave expansion, we theoretically investigate photonic band structures in two-dimensional metallodielectric photonic crystals, especially, square arrays of dielectric and perfectly conducting cylinders. Existence of photonic band gaps in metallodielectric photonic crystals and validity of the proposed numerical method are demonstrated.

Far-field emission pattern and photonic band structure in one-dimensional photonic crystals made from semiconductor microcavities

One-dimensional ~1D! photonic crystals have been investigated by angle-resolved photoluminescence measurements. The crystals have been fabricated out of a semiconductor microcavity by lateral etching of photonic wires with a 1D lattice of small holes in the top mirror stack along the wire axis. The photonic band structure of such photonic crystals has been shown to demonstrate very small photonic gaps and can be regarded as a set of modes with the dispersion curves being replicas of the photonic wire modes periodically shifted with an integer number of the Brillouin zone periods. The replicas are well observed only for the even photonic wire modes which have the antinodes at the hole locations. The far-field emission pattern of the replicas demonstrates a much wider angle distribution than that of the main modes having the energy minima at k50.

Finely resolved transmission spectra and band structure of two-dimensional photonic crystals using emission from InAs quantum dots

Reference LOEQ-ARTICLE-1999-025doi:10.1103/PhysRevB.59.1649View record in Web of Science Record created on 2007-08-31, modified on 2017-05-12

Effective properties and band structures of lamellar subwavelength crystals: Plane-wave method revisited

The plane-wave method used to compute the band structure of photonic crystals is revisited in light of recent mathematical results about the Fourier factorization of products of discontinuous functions. Highly accurate numerical predictions for the effective index and for the band structure are obtained for two- and three-dimensional dielectric lamellar crystals with high dielectric contrasts. At the same time, we clarify some aspects related to the effective properties of multidimensional crystals by establishing clear links between their band structures and their effective indices.

Heterostructures of photonic crystals: frequency bands and transmission coefficients

We present a program for the calculation of the frequency band structure of an infinite photonic crystal, and of the transmission, reflection and absorption coefficients of light by a slab of this crystal. The crystal consists of a stack of identical slices parallel to a given surface; a slice may consist of a number of different components, each of which can be either a homogeneous plate or a multilayer of spherical particles of given periodicity parallel to the surface.

Boundary-element calculations of electromagnetic band-structure of photonic crystals

A boundary element method is developed for calculating the photon modes of periodic structures whose unit cells consist of piecewise homogeneous dielectric materials of arbitrary shapes. Green’s function techniques are used to derive integral equations for these structures. These equations involve integrals over the boundaries between the regions, which are discretized and solved numerically. Thus the full set of Maxwell’s equations with boundary conditions in d independent variables is changed into an integral equation in d−1 variables. This allows for the calculation of mode frequencies and field patterns for wave vectors throughout the Brillouin zone, thus allowing the determination of photonic band gaps. An illustrative example is given here for a two-dimensional system.

Photonic-band-structure calculation of material possessing Kerr nonlinearity.

The Finite Difference Time Domain (FDTD) technique dates back to 1966 when it was first developed by Yee [1]. Since then it has been widely used to calculate the radar cross section of objects as well as normal modes of wave guides. Chan et al. [2] recently applied this technique to calculate the band structure of photonic crystal with excellent results. The motivation for their use of this technique is the fact this technique scales linearly with system size. Systems having random defects, which destroy any periodicity, are often studied using the “super cell” method where the system is assumed to be periodic with a very large period. In such a case, it is important the technique for band structure calculation scales favorably with system size. The plane wave expansion technique, for example, is impractical since it scales as N3 where N is the system size. In this paper I show how the FDTD technique can be extended to calculate the band structure of nonlinear photonic crystals, in particular, those which possess Kerr nonlinearity.