Analysis of surface modes in photonic crystals by a plane-wave transfer-matrix method

We have developed a plane-wave transfer-matrix method (PWTMM) with the aid of the interpolation technique to analyze the dispersion relation of surface modes in photonic crystal or photonic crystal surface waveguide. The proposed approach has been applied to several surface structures in two-dimensional photonic crystals. The calculated dispersion relation of the surface modes is in good agreement with the result obtained by the conventional plane-wave expansion method in combination with the supercell technique. The developed PWTMM needs to handle only a single unit-cell layer domain and is therefore numerically friendly. The proposed approach can become an efficient and accurate numerical tool to understand and design surface modes in different two-dimensional and three-dimensional photonic crystals with complex geometries.     

非空气-石英结构PCF的带隙特性分析

光子晶体光纤是近十来年兴起的一个新兴的研究领域,是现今纤维光学的研究重点,光子带隙特性是光子晶体光纤区别传统光纤的主要特征。本文利用全矢量平面波展开法对非空气-石英结构PCF的带隙特性进行分析,并且重点讨论空气孔内填充介电材料对光子带隙存在的影响。     

Dispersion properties of liquid-core photonic crystal fibers

Dispersion properties of liquid-core photonic crystal fibers (PCFs) with large air fraction in clads between 300 to 2000?nm have been calculated by a multipole method for various liquids including CS₂, toluene, chloroform, and water for different core diameters. In calculations, air holes are assumed to be arranged in a regular hexagonal array in fused silica, and a central hole is filled with liquid to create a core. The results are compared with those obtained by a fully vectorial effective index method, and fitting parameters for core sizes are found for each liquid except for water, where the latter method does not give correct dispersions at short wavelengths. Also, the power ratios inside liquid cores and effective core areas were calculated at different wavelengths.     

Hybrid genetic optimization for design of photonic crystal emitters

A unique hybrid-optimization technique is proposed, based on genetic algorithms (GA) and gradient descent (GD) methods, for the smart design of photonic crystal (PhC) emitters. The photonic simulation is described and the granularity of photonic crystal dimensions is considered. An innovative sliding-window method for performing local heuristic search is demonstrated. Finally, the application of the proposed method on two case studies for the design of a multi-pixel photonic crystal emitter and the design of thermal emitter in thermal photovoltaic is demonstrated. Discussion in the report includes the ability of the optimal PhC structures designed using the proposed method, to produce unprecedented high emission efficiencies of 54.5% in a significantly long wavelength region and 84.9% at significantly short wavelength region.     

Elastic postbuckling analysis via finite element and perturbation techniques part II: Application to shells of revolution

The general theory developed in Part 1 of this paper for the finite element stability analysis of structural systems, using perturbation expansions in the vicinity of a critical point, is applied here to the analysis of shells of revolution. The discretization of the shell is performed by means of a semianalytical approximation, and the matrices required for the evaluation of critical points and postcritical equilibrium paths are obtained. Two cases are presented: bifurcation in axisymmetric and in asymmetric buckling modes. The derivatives required for an imperfection analysis are also obtained. A technique of switching between two paths using continuation methods is also discussed, in which the switch is performed using derivatives of the perturbation expansion. Results are presented for bifurcation in axisymmetric and in non-axisymmetric modes, and compared with known solutions or with results from changing the path using continuation methods; good correlation is shown. For structures displaying unstable bifurcation, the influence of load and geometric imperfections is evaluated.     

Study of band structure of one-dimensional photonic crystal composed of dispersive and nonlinear dielectric materials

The analysis of band structure of one-dimensional (1-D) photonic crystal containing dispersive and non-linear dispersive materials has been presented. The band spectra for the different combination of photonic crystals have been calculated by the well-known plane wave expansion method. The effect of the dispersive and non-linear materials on the band structures has been determined. The third-order nonlinearity has been considered in the non-linear material, and Lorentz–Drude model has been taken for dispersive material. The band gaps of considered photonic crystal are affected by the nonlinearity in the presence of dispersive material like gold. We have observed that the normalized frequency difference between photonic bands decreases on increasing intensity of input beam. This work may be useful in optical switching devices.     

Design of photonic crystal-based all-optical AND gate using T-shaped waveguide

Abstract

We present a new configuration of all-optical AND gate based on two-dimensional photonic crystal composed of Si rods in air. Two AND gate structures with and without probe input are proposed. The proposed structures are designed with T-shaped waveguide without using nonlinear materials and optical amplifiers. The performance of the proposed AND gate structures is analyzed and simulated by plane-wave expansion and finite difference time domain methods. The AND gate without probe input needs only one T-shaped waveguide, whereas the AND gate with probe input needs two T-shaped waveguides. The former AND gate offers a bit rate of 6.26 Tbps with a contrast ratio of 5.74 dB, whereas the latter AND gate offers a bit rate of 3.58 Tbps whose contrast ratio is 9.66 dB. It can be expected that these small size T-shaped structures are suitable for large-scale integration and can potentially be used in on-chip photonic integrated circuits.     

Evolution of complete photonic band gap in anisotropic photonic quasicrystals using liquid crystals

Abstract

In this study, we analyse the evolution of complete photonic band gap in two-dimensional photonic structures by arranging the 12-fold symmetric quasicrystalline unit cells on square and triangular lattices. The unit cells composed of circular air holes in anisotropic tellurium background and the air holes are infiltrated with liquid crystal. Using the supercell method based on plane wave expansion, we study the variation of complete band gap by changing the optical axis orientation of liquid crystals.     

Genetic optimization of two-dimensional photonic crystals for large absolute band gaps under light line

A binary genetic algorithm with floating crossover and mutation probabilities is used to design two-dimensional photonic crystals for large absolute band gaps under a light line. The unit cell is composed of a small number of round rods and is arranged in a square lattice. The photonic band structure of each chromosome is calculated by the plane-wave expansion method. Starting from randomly generated photonic crystals, the genetic algorithm finally yielded a photonic crystal with an absolute common band gap of 0.0618(2πc/a) at the mid-frequency of 0.4084(2πc/a).     

Replication of polypyrrole with photonic structures from butterfly wings as biosensor

Polypyrrole (PPy) with photonic crystal structures were synthesized from Morpho butterfly wings using a two-step templating process. In the first step photonic crystal SiO₂ butterfly wings were synthesized from Morpho butterfly wings and in the second step the SiO₂ butterfly wings were used as templates for the replication of PPy butterfly wings using an in situ polymerization method. The SiO₂ templates were then removed from the PPy butterfly wings using a HF solution. The hierarchical structures down to the nanometer level, especially the photonic crystal structures, were retained in the final PPy replicas, as evidenced directly by field-emission scanning electron microscope (FE-SEM) and transmission electron microscopy (TEM). The optical properties of the resultant PPy replicas were investigated using reflectance spectroscopy and the PPy replicas exhibit brilliant color due to Bragg diffraction through its ordered periodic structures. The preliminary biosensing application was investigated and it was found that the PPy replicas showed a much higher biological activity compared with PPy powders through their response to dopamine (DA), probably due to the hierarchical structures as well as controlled porosity inherited from Morpho butterfly wings. It is expected that our strategy will open up new avenues for the synthesis of functional polymers with photonic crystal structures, which may form applications as biosensors.     

Analysis of arbitrary defects in photonic crystals by use of the source-model technique

A novel method derived from the source-model technique is presented to solve the problem of scattering of an electromagnetic plane wave by a two-dimensional photonic crystal slab that contains an arbitrary defect (perturbation). In this method, the electromagnetic fields in the perturbed problem are expressed in terms of the field due to the periodic currents obtained from a solution of the corresponding unperturbed problem plus the field due to yet-to-be-determined correction current sources placed in the vicinity of the perturbation. Appropriate error measures are suggested, and a few representative structures are presented and analyzed to demonstrate the versatility of the proposed method and to provide physical insight into waveguiding and defect coupling mechanisms typical of finite-thickness photonic crystal slabs.     

Transverse characterization of high air-fill fraction tapered photonic crystal fiber

We demonstrate tapering of a high air-fill fraction photonic crystal fiber by using the flame-brushing technique. Transverse probing along the taper allows us to ascertain how the microstructure is preserved during tapering. Experimental results are compared with numerical simulations performed with the finite-difference time-domain and plane-wave expansion methods. Through this investigation we find that the fiber geometry is well preserved throughout the tapering process and we resolve the apparent discrepancies between simulation and experiment that arise through the finite extent of the fiber microstructure.     

Photonic bandgap calculations with Dirichlet-to-Neumann maps

A simple and efficient method for computing bandgap structures of two-dimensional photonic crystals is presented. Using the Dirichlet-to-Neumann (DtN) map of the unit cell, the bandgaps are calculated as an eigenvalue problem for each given frequency, where the eigenvalue is related to the Bloch wave vector. A linear matrix eigenvalue problem is obtained even when the medium is dispersive. For photonic crystals composed of a square lattice of parallel cylinders, the DtN map is obtained by a cylindrical wave expansion. This leads to eigenvalue problems for relatively small matrices. Unlike other methods based on cylindrical wave expansions, sophisticated lattice sums techniques are not needed.     

Modified annular photonic crystals for enhanced band gap properties and iso-frequency contour engineering

In this paper complete photonic bandgap (PBG) and iso-frequency contours (IFCs) of two-dimensional modified annular photonic crystals (MAPC) for four different configurations are numerically studied and calculated by applying plane wave expansion method. The effects of opto-geometric parameters of the designed unit-cell structures are clearly demonstrated in terms of opening frequency gaps and appearing tilted band curves. Optimal structures with large PBGs are reported. The absolute gap can be increased to a maximum value of Δω/ω=0.1766(2πc/a), where a is the lattice constant and c is the speed of light. The incorporation of additional parameters inside the unit cell of photonic crystal enables an extra degree of freedom for controlling the flow of light even in the absence of structural defects. The finite-difference time-domain method is utilized to depict the MAPC's light deflection and guiding characteristics. These proposed structures are likely to be promising candidates for applications that require polarization insensitivity due to providing large complete PBGs and possessing special IFCs.     

Analysis of photonic crystals using the hybrid finite‐element/finite‐difference time domain technique based on the discontinuous Galerkin method

Two‐dimensional photonic crystal structures are analyzed by a recently developed hybrid technique combining the finite‐element time‐domain (FETD) method and the finite‐difference time‐domain (FDTD) method. This hybrid FETD/FDTD method uses the discontinuous Galerkin method as framework for domain decomposition. To the best of our knowledge, this is the first hybrid FETD/FDTD method that allows non‐conformal meshes between different FETD and FDTD subdomains. It is also highly parallelizable. These properties are very suitable for the computation of periodic structures with curved surfaces. Numerical examples for the computation of the scattering parameters of two‐dimensional photonic bandgap structures are presented as applications of the hybrid FETD/FDTD method. Numerical results demonstrate the efficiency and accuracy of the proposed hybrid method. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of a broadband highly dispersive pure silica photonic crystal fiber

A highly dispersive dual-concentric-core pure silica photonic crystal fiber is designed with a maximum chromatic dispersion value of about -9500 ps/(nm km) around the 1.56 microm wavelength region and a full width at half-maximum (FWHM) of 55 nm. The change in the dispersion-bandwidth product as a function of period is carefully studied by using the plane wave expansion method. The coupled mode theory matches well with the plane wave expansion method that was used to simulate the chromatic dispersion. This kind of a photonic crystal fiber structure is suitable for high-dispersion application in phased array antenna systems based on photonic crystal fiber arrays.     

Photonic stop band effect in ZnO inverse photonic crystal

Three-dimensional photonic crystals are fabricated using inward-growing self-assembly technique from polymethyl methacrylate (PMMA) colloids. Their air voids are infiltrated with zinc oxide (ZnO) by sol-gel method and the PMMA template is removed by the two independent processes of heat treatment and wet chemical method resulting in ZnO inverse photonic crystal. The inversion is confirmed from the structural characterization. In X-ray diffraction (XRD) experiment, the ZnO inverse photonic crystals obtained by both the techniques do not show any signature of single-crystalline ZnO. The inverse photonic crystals obtained by chemical method are further heated at different temperatures and XRD confirms crystalline nature of ZnO for temperature treatment at 400 °C. Laser-induced emission studies on ZnO inverse photonic crystals are carried out at two different excitation wavelengths. Excitation with 355 nm enables the observation of the stop band effect for emission at 45° from the inverse crystal obtained by the inexpensive chemical method.     

Thermal properties and two-dimensional photonic band gaps

The effect of temperature on a two-dimensional square lattice photonic crystal composed of Si rods arranged in an air background was investigated theoretically using the plane-wave expansion method. Both the thermal expansion effect and thermo-optical effect are considered simultaneously. We have discussed the role of temperature in creating the complete photonic band gap as a function of temperature. Two different shapes of rods, i.e. square and circular, are considered in the presence of the two polarization states, i.e. TE and TM waves. The numerical results show that the photonic band gap can be significantly enlarged compared to the photonic band gap at room temperature. The effect of temperature on the complete photonic band width in the cylindrical rods case is more significant. Cylindrical and square Si rods may work as a temperature sensor or filter, among many other potential applications.     

The semianalytical finite element method as applied to three-dimensional thermoelastoplastic prismatic bodies. Report 2. Practical applications

Results are presented which checked the reliability of solutions obtained on the basis of the semianalytical method of finite element analysis for studying physically and geometrically nonlinear processes of thermolelastoplastic deformation of prismatic bodies. Complex three-dimensional problems on the stress-strain state of prismatic structures with variable physical-mechanical parameters along the expansion coordinate and of curvilinear prismatic structures were examined. Also examined was the formation of prismatic billets.Translated from Problemy Proshnosti, No. 12, pp. 48–51, December, 1992.     

Compact double-grating coupler between vertically stacked silicon-on-insulator waveguides

We analyze a compact double-grating coupler that provides coupling through radiation modes between two vertically stacked silicon-on-insulator waveguides. The grating is sufficiently strong to be considered a one-dimensional photonic bandgap structure that facilitates a short coupling length. Simulations suggest that a 29% coupling efficiency is achievable in coupling light from one waveguide to another with 12.9 microm long binary gratings. We found that the coupling efficiency is enhanced by Fabry-Perot resonance between two gratings. The coupling efficiency can be increased by use of a blazed grating. We use the eigenmode expansion method to design and optimize the binary grating coupler, and the results are verified by use of the finite-difference time-domain method.