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.     

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.     

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.     

Wavelet method for computing band diagrams of 2D photonic crystals

A wavelet method is applied for the first time to the computation of band diagrams of photonic crystals (PhCs). The wavelet algorithm is described. Its numerical implementation is validated in the case of emblematic two-dimensional triangular and square lattice PhCs. Although these examples do not emphasize the full power of wavelet methods, the number of wavelets needed to achieve a prescribed accuracy is already shown to be orders of magnitude smaller than the number of waves used in the traditional plane wave method. Further extension to more complex photonic structures is discussed.     

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.     

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.     

Photonic crystal LEDs – designing light extraction

Photonic crystals (PhCs) have attracted much attention during the last decade as a solution to overcome the low extraction efficiency of as‐grown light‐emitting diodes (LEDs). In this review we describe the underlying physics and summarize recent results obtained with PhC LEDs. Here, the main focus is on diffracting PhC. In order to quantify the benefit from the incorporation of PhCs for diffracting light a comparison by simulations between a PhC LED and a standard state‐of‐the‐art LED is carried out. Finally, the impact of the PhC on the LEDs emission characteristics will be discussed with respect to étendue‐limited applications.     

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.     

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.     

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     

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.     

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.     

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.     

GaN-based LEDs surrounded with a two-dimensional nanohole photonic crystal structure for effective laterally guided mode coupling

Traditional implementation of photonic crystals (PhCs) on LED light emission surfaces results in weak coupling of light with the PhCs. Here we introduce a GaN-based LED surrounded with a nanohole PhC structure along the mesa edges. The laterally guided modes in the epi-structure can be effectively coupled with the two-dimensional periodic structure. The proposed structure results in the improvement of LED light extraction and provides flexibility of radiation directionality control.     

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.     

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.     

Direct laser writing defects in holographic lithography-created photonic lattices

As a well-established laser fabrication approach, holographic lithography, or multibeam interference patterning, is known for its capability to create long-range ordered large-volume photonic crystals (PhCs) rapidly. Its broad use is, however, hampered by difficulty in inducing artificially designed defects for device functions. We use pinpoint femtosecond laser ablation to remove and two-photon photopolymerization to add desired defective features to obtain photonic acceptors and photonic donors, respectively, in an otherwise complete PhC matrix produced by holographic lithography. The combined use of the two direct laser writing technologies would immediately make holographic lithography a promising industrial tool for PhC manufacture.     

Investigation of a point-like and plane-wave excitation in 2D photonic bandgap microcavities using Green’s function method

We report on a new model for simulating wave propagation in two-dimensional photonic crystals (PhCs) by means of Green’s functions rearranged to fit on the geometrical and physical properties of the structure under investigation. The model can take into account physical effects occurring when the PhC is excited by either a point-like source, for the analysis of extended crystals with line and point defects, or a plane wave coming from infinite, to investigate mirrors and microlenses. The model has been used for studying a Fabry–Peròt cavity to evaluate its response in presence of a Hankel source or a plane wave excitation. A parametric investigation of the filter response as a function of the cavity length has been carried out and the best conditions to obtain an increase of quality factor of each resonant cavity mode have been determined.     

Woodpile photonic crystals composed of air columns

Silicon-based woodpile photonic crystals (PhCs) composed of air columns have a large gap/midgap ratio exceeding 20% over a wide dimensional range of the cross section of the air column when the cross section is deformed to a rectangular shape extended normal to the stacking direction. Such a PhC structure can be formed using a simple technique based on 45° dry etching. Furthermore, introducing twin air columns with small cross sections instead of corresponding mother air columns yields a defect state at the region where the columns cross. Since the fabrication process is a planar-type Si wafer process, fabricated PhCs can be easily combined with conventional electronic circuits and optical elements, such as Si waveguides and switches.