Air waveguide in a hybrid 1D and 2D photonic crystal hetero-structure

An air waveguide in hybrid one-dimensional photonic crystal and two-dimensional photonic crystal slab hetero-structure is designed. Light propagating in air waveguide can be confined by two-dimensional photonic crystal slab in x-y plane and one-dimensional photonic crystal films in z direction. Theoretical calculations show that air waveguide in the hetero-structure can achieve some functions as 3D PhCs but could be made more easily than 3D PhCs.     

Observation of multiple higher-order stopgaps from three-dimensional chalcogenide glass photonic crystals

For the first time to our knowledge the observation of near-IR multiple higher-order stopgaps in three-dimensional photonic crystals (PhCs) fabricated using the direct-laser-writing method in thick chalcogenide glass films is reported. The fabrication and etching conditions necessary to realize well-defined structures are presented. The fabricated PhCs exhibit higher-order stopgaps, which are only evident in high-quality structures. The higher-order stopgaps observed permit these high-refractive-index and high-nonlinear PhCs to be used directly as functional photonic devices operating at telecommunication wavelengths without further miniaturizing structural dimensions.     

Improved combined wave number eigenvalue equations method for band structure calculations of metal photonic crystal

We provide the combined wave number eigenvalue equations (CWNEE) method based upon the plane-wave expansion (PWE) method to calculate and optimize the band structures of the two-dimension (2D) photonic crystals (PhCs). Compared with the traditional PWE methods for the metal PhCs, the band structures can be obtained directly using the CWNEE method, and not any extra procedures are needed to handle the folded band structures. The comparison between the CWNEE method and FDTD method in accuracy and time-consuming has been analyzed, and the results show that the CWNEE method is reliable and accurate. With the CWNEE method and the Bisection-Particle Swarm Optimization method, we optimize the large gap–midgap ratio of the 2D square lattice of square metal rods and circular metal rods. Unlike many traditional PWE method, the CWNEE method can directly calculate the band structure in the arbitrary given frequency range, and it is quite useful for calculating the defect mode of photonic crystal cavity.     

Fabrication of Two-Dimensional Photonic Crystals with Controlled Defects by Combination of Holographic Lithography and Two-Photon Polymerization

A new ternary photopolymer system is used in fabricating photonic crystals （PhCs） with controlled defects by combination of single-photon and two-photon photopolymerization. The former process can produce PhCs in one-step recording with a low-power （tens mW） continuous-wave laser at 532nm, while the latter can create desired defects. The preparation of the material, the optical setup and the preliminary experimental results are given. Compared with other methods, this approach is much more accessible and convenient for use of visible light and has advantages of making PhCs in a large scale quickly and economicaJly and introducing any defects exactly, especially for three-dimensional structures.     

Holographic design of hexagonal photonic crystals of irregular columns with large full band gap

The shape and size of the dielectric columns or particles (“atoms”) of photonic crystals (PhCs) formed by holographic lithography are determined by the isointensity surfaces of the interference field; consequently the PhCs’ photonic band gap (PBG) properties are closely related to their fabrication design. Here we have proposed a new structure of two-dimensional (2-D) hexagonal lattice with irregular columns, which can yield a 2-D complete relative band gap of 24.0% in case of the dielectric columns of ε = 13.6 in air, about 27% increase compared with that of the same lattice with regular triangular columns. This band gap size is among the largest for all the possible 2-D PhCs reported until now. The relationship between band gap properties of resultant structure and the specific fabrication conditions such as structure design and the choice of optimum intensity threshold and filling ratio are systematically discussed. The optical design for making this structure by two exposures is explained. 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.     

Various photonic crystal structures fabricated by using a top-cut hexagonal prism

We demonstrate a holographic approach for the fabrication of large-area photonic crystal (PhC) microstructures by applying a single top-cut hexagonal prism (TCHP). The interference patterns of the beams from the TCHP are calculated. Various two-dimensional PhC structures are fabricated in photo-resist films. They include symmetrical hexagonal structures, the honey-comb structure and the hexagonal structure with skewed elliptical rods. The first structures come from six-beam and symmetrical three-beam interfering. The second structure appears when the beam is incident on the TCHP obliquely. The third structure is obtained when adjacent three beams or four beams are interfered. The period can be decreased to 285 nm. SPM observations of the PhCs provide the basis for measurement of their structural parameters. A good agreement is obtained for the measured structural parameters and calculated results for the PhCs. The photonic band gaps of the hexagonal symmetrical and honeycomb structures are derived by using the plane wave method. These results reveal that, by varying the number of split beams and the incident angle, using the single TCHP PhCs, different band gaps can be achieved.     

Modeling photonic crystals by boundary integral equations and Dirichlet-to-Neumann maps

Efficient numerical methods for analyzing photonic crystals (PhCs) can be developed using the Dirichlet-to-Neumann (DtN) maps of the unit cells. The DtN map is an operator that takes the wave field on the boundary of a unit cell to its normal derivative. In frequency domain calculations for band structures and transmission spectra of finite PhCs, the DtN maps allow us to reduce the computation to the boundaries of the unit cells. For two-dimensional (2D) PhCs with unit cells containing circular cylinders, the DtN maps can be constructed from analytic solutions (the cylindrical waves). In this paper, we develop a boundary integral equation method for computing DtN maps of general unit cells containing cylinders with arbitrary cross sections. The DtN map method is used to analyze band structures for 2D PhCs with elliptic and other cylinders.     

Cluster coherent potential approximation for disordered photonic crystals using photonic Wannier functions

We present an investigation of disordered photonic crystals (PhCs) based on the combination of photonic Wannier functions with the concept of the coherent potential approximation (CPA). In particular, we provide the theoretical foundation of a real-space cluster CPA that is causal, enforces the proper symmetries of the effective medium, and includes effects of multiple scattering of the same and nearby defects, which is essential for strong defects. Based on this, we present results for the density of states of disordered PhCs for different types of disorder. Our results are thus relevant to such diverse areas as random lasing and the analysis of fabricational imperfections in PhCs.     

Photonic Band Gap Properties of Three-Dimensional SiO2 Photonic Crystals

Three-dimensional SiO2 photonic crystals （PhCs） are fabricated on quartz substrates by the vertical deposition method. Scanning electron microscopy measurement reveals that the samples exhibit an ordered close-packed arrangement of SiO2 spheres. It is found that the position of the [111] photonie band gap （PBG） shifts to a long wavelength （red shift） with increasing sphere size. Gap broadening effects are observed due to the presence of defects in the samples. Moreover, the optical properties of the PBG are very sensitive to the annealing temperature. Our results indicate that the optical properties of the PBG can be easily tuned in the visible region by appropriate experimental parameters, which will be useful for practical applications of PhC optical devices.     

FDTD analysis of 2D triangular-lattice photonic crystals with arbitrary-shape inclusions based on unit cell transformation

A finite-difference time-domain method based on Yee’s orthogonal cell is utilized to calculate the band structures of 2D triangular-lattice-based photonic crystals through a simple modification to properly shifting the boundaries of the original unit cell. A strategy is proposed for transforming the triangular unit cell into an orthogonal one, which can be used to calculate the band structures of 2D PhCs with various shapes of inclusions, such as triangular, quadrangular, and hexagonal shapes, to overcome the shortage of plane-wave expansion method for circular one. The band structures of 2D triangular-lattice-based PhCs with hexagonal air-holes are calculated and discussed for different values of its radius and rotation angle. The obtained results provide an insight to manipulate the band structures of PhCs.     

Properties, applications and fabrication of photonic crystals with ring-shaped holes in silicon-on-insulator

We show that photonic crystals with ring-shaped holes (RPhCs) exhibit superior properties compared to conventional photonic crystals (PhCs). At low air-fill factors RPhCs can have a larger bandgap than conventional PhCs. Moreover, RPhC waveguides with both high group index and small group velocity dispersion can be designed. RPhC waveguides are also more sensitive to external refractive index changes, which is attractive for sensor applications. Finally we set up a procedure to pattern RPhCs in silicon-on-insulator.     

Negative refraction in photonic crystals

We demonstrate that light propagation in strongly modulated 2D/3D photonic crystals (PhCs) becomes refraction-like in the vicinity of the photonic bandgap, which is contrary to the fact that light propagation in weakly modulated PhCs is very different from refraction and thus the definition of refraction index becomes meaningless. Such a crystal behaves like a material having an effective refractive index controllable by the band structure. This situation is analogous to the effective-mass approximation in electron-band theory. The propagation states having a negative effective index exhibit unusual properties, such as mirror-like imaging effect, image-transfer effect. These properties are confirmed by finite-difference time-domain simulations.     

Relationship between group velocity and symmetry of photonic crystals

Group velocity (GV) of eigenmode is a crucial parameter to explain the extraordinary phenomena about light propagation in photonic crystals (PhCs). To study relationships between group velocity and symmetry of PhCs, a new general expression of GV in PhCs made up of non-dispersive material is introduced. Based on this, the GVs of eigenmodes of PhCs, especially those of degenerate eigenmodes at highly symmetric points in the first Brillouin zone, are discussed. Some interesting results are obtained. For example, the summation of degenerate eigenmodes' GVs is invariant under the operations of wave vector ${{\bm K}}$-group $M_{{\bm K}} $. In addition, some numerical results are presented to verify them.     

Enhancement of the light output of light-emitting diode with double photonic crystals

A light-emitting diode (LED) with double photonic crystals (PhCs) is designed to enhance the light output. Based on the configuration of the PhC assisted LED with a single PhC (SPC-LED), a second PhC is added on the bottom surface of the active layer to improve the light output. The optical properties of this double PhCs assisted LED are simulated using the three-dimensional (3D) finite-difference time-domain (FDTD) method. The calculation results show that its light output can be 3.2 times higher than that of LED without PhC, and 1.39 times higher than that of SPC-LED.     

Nearly Perfect Spin Conversion Based on Topological Singularity in 1D Anisotropic Photonic Crystals

Although the spin-controlled vortex generation and photonic spin-Hall effect of spin-flipped abnormal mode have been widely studied recently, the traditional method based on the metasurface is difficult to fabricate, and the efficiency of the spin-flipped abnormal mode is rather low due to process errors and intrinsic material loss. Here, a new method is proposed based on the insights into the topological singularity and special Bragger reflections resonant (BRR) mode of one-dimensional (1D) finite photonic crystals (PhCs) with anisotropic material to realize nearly perfect (100%) spin-conversion efficiency. For a finite 1D PhC with cell number N, there are 3N complete spin-conversion (CSC) and complete spin-maintained (CSM) channels. Two mechanisms of these CSC and CSM channels are revealed. The working bandwidths and the angular ranges of these CSC and CSM are also studied. Based on these theoretical findings, multi-angles and multi-frequencies perfect spin-conversion (-maintained) devices can be designed. At last, these theoretical results are confirmed by the numerical experiments based on finite-difference time-domain (FDTD) methods. This work paves the way to exploring the topological properties and polarization control of PhCs made of anisotropic dielectrics and provides a prospective method for the design of multi-channels spin optical devices.     

Extremely low optical transmittance in the stopbands of photonic crystals

We demonstrate extremely low transmittance characteristics of photonic crystals (PhCs) with a finite thickness in specific photonic bandgaps (PBGs) through numerical simulation, and clarify its origin. Some of the PhCs support decaying Bloch eigenmodes, whose propagation constant (real part of the Bloch wavenumber) as well as their decay constant (imaginary part) changes with frequency inside the bandgap. Such a class of modes can interfere destructively at the exit end of the crystal depending on their round-trip phase change, which creates comb-like valleys in their transmission spectra.     

High Efficiency One-Way Transmission by One-Dimensional Photonic Crystals with Gratings on One Side

We propose a scheme of optical one-way transmission by using one-dimensional photonic crystals （PhCs） with diffraction gratings on one side. The one-way transmission is realized by making the PhC opaque to the zeroth diffraction order and transparent to another propagating （in air） diffraction order. For such a structure with 10-period PhC, 93% of the incident energy passes through when an electromagnetic wave impinges from one side, and the transmittance decreases to the order of 0.001% as the electromagnetic wave illuminates from the other side.     

2D and 3D electrically switchable hexagonal photonic crystal in the ultraviolet range

Two holographic lithography systems are demonstrated for easy and large-area fabrication of 2D and 3D photonic crystal (PhC) microstructures in a polymer dispersed liquid crystal (PDLC) by applying a single top-cut hexagon prism. A six-beam system has been used to produce 2D hexagonal PhCs. By adding an additional mirror, a twelve-beam system is demonstrated to fabricate 3D PhCs with ultraviolet (UV) band-gap along the z direction. A good agreement is obtained for measured PhCs structure and theoretical results. Far-field diffraction patterns and electrical switching characteristics of the 2D and 3D PhC HPDLC films have been investigated. PACS 42.15.Eq; 42.40.Eq     

Compact RBF meshless methods for photonic crystal modelling

Meshless methods based on compact radial basis functions (RBFs) are proposed for modelling photonic crystals (PhCs). When modelling two-dimensional PhCs two generalised eigenvalue problems are formed, one for the transverse-electric (TE) mode and the other for the transverse-magnetic (TM) mode. Conventionally, the Band Diagrams for two-dimensional PhCs are calculated by either the plane wave expansion method (PWEM) or the finite element method (FEM). Here, the eigenvalue equations for the two-dimensional PhCs are solved using RBFs based meshless methods. For the TM mode a meshless local strong form method (RBF collocation) is used, while for the tricker TE mode a meshless local weak form method (RBF Galerkin) is used (so that the discontinuity of the dielectric function ?(x)$?(x)$ can naturally be modelled). The results obtained from the meshless methods are found to be in good agreement with the standard PWEM. Thus, the meshless methods are proved to be a promising scheme for predicting photonic band gaps.     

Photonic crystal surface mode microcavities

Our recent research on surface mode optical microcavities based on two-dimensional photonic crystals (PhCs) was reviewed in this paper. We presented the design, fabrication and characterization of high quality (Q) factor surface mode microcavities. Realizations of these PhCs were based on both amorphous silicon-on-insulator (SOI) structures and crystalline SOI structures.