Focusing concave lens using photonic crystals with magnetic materials

The guided modes lying in the upper gap-edge band in the photonic band structure of photonic crystals have negative values of refractive index. This feature generates many interesting optical phenomena, and some spectacular photonic devices such as focusing slabs have been developed. We report the design of a photonic-crystal, planoconcave lens for focusing incident parallel light, and theoretically analyze the chromatic aberrations for TM and TE modes. In addition to dielectric photonic crystals, the chromatic aberration of a magnetic photonic-crystal planoconcave lens was investigated because the magnetic permeability may also contribute to the periodic index contrast in photonic crystals, especially at long wavelengths. A significant difference was found in the chromatic aberration for a TM mode propagating in a dielectric than in a magnetic photonic-crystal planoconcave lens.     

Pattern-integrated interference lithography: single-exposure fabrication of photonic-crystal structures

Multibeam interference represents an approach for producing one-, two-, and three-dimensional periodic optical-intensity distributions with submicrometer features and periodicities. Accordingly, interference lithography (IL) has been used in a wide variety of applications, typically requiring additional lithographic steps to modify the periodic interference pattern and create integrated functional elements. In the present work, pattern-integrated interference lithography (PIIL) is introduced. PIIL is the integration of superposed pattern imaging with IL. Then a pattern-integrated interference exposure system (PIIES) is presented that implements PIIL by incorporating a projection imaging capability in a novel three-beam interference configuration. The purpose of this system is to fabricate, in a single-exposure step, a two-dimensional periodic photonic-crystal lattice with nonperiodic functional elements integrated into the periodic pattern. The design of the basic system is presented along with a model that simulates the resulting optical-intensity distribution at the system sample plane where the three beams simultaneously interfere and integrate a superposed image of the projected mask pattern. Appropriate performance metrics are defined in order to quantify the characteristics of the resulting photonic-crystal structure. These intensity and lattice-vector metrics differ markedly from the metrics used to evaluate traditional photolithographic imaging systems. Simulation and experimental results are presented that demonstrate the fabrication of example photonic-crystal structures in a single-exposure step. Example well-defined photonic-crystal structures exhibiting favorable intensity and lattice-vector metrics demonstrate the potential of PIIL for fabricating dense integrated optical circuits.     

Stress analysis for bonded materials with a graded interfacial layer under a rigid punch

It is well known that functionally graded materials can be used to eliminate the stress discontinuity that is often encountered in multilayer composites. In this article, the stress analysis for the coating-functionally graded interfacial layer-substrate structure under a rigid spherical punch is investigated. A linear multi-layer model is used to model the graded interfacial layer with arbitrary varying materials properties along the thickness direction. The spherical indentation problem is formulated in terms of a singular integrate equation with the method of transfer matrix and Hankel integral transform technique. The stress components in the coating-graded interfacial layer-substrate structure are calculated by solving the equation numerically. The results show that stiffens ratio and the gradient index of the graded interfacial layer has a significant effect on the distribution of stress components.     

Photonic-crystal light-emitting diodes on p-type GaAs substrates for optical communications

Oxide-confined photonic-crystal (PhC) light-emitting diodes (LEDs) on p-type GaAs substrate in the 830 nm range are reported. The device consists of a bottom distributed Bragg reflector (DBR), quantum wells (QWs), and a top DBR, with a photonic-crystal structure formed within the n-type ohmic contact ring for light extraction. The etching depth of the PhC holes is 17-pair out of the 22-pair top DBR being etched off. The internally reflected spontaneous light emission can be extracted out of PhC holes because of lower reflectance within those areas. High-resolution micrographic imaging studies indicate that the device emits light mainly through the photonic-crystal holes and it is suitable for optical communications.     

Two-dimensional photonic-crystal vertical-cavity array for nonlinear optical image processing

We investigate the electromagnetic properties of a two-dimensional (2-D) photonic-crystal array of vertical cavities for use in nonlinear optical image processing. We determine the 2-D photonic band structure of the array, and we discuss how it is influenced by the degree of interaction between cavities. We study the properties of defects in the 2-D lattice and show that neighboring cavities interact through their overlapping wave functions. This interaction can be used to produce nearest-neighbor nonlinear Boolean functions such asand, or, and xor, which are useful for optical image processing. We demonstrate the use of 2-D photonic bandgap structures for image processing by removing noise from a sample image with a nearest-neighbor and function.     

Contact behaviors of a rigid punch and a homogeneous half-space coated with a graded layer

A contact model between a homogeneous half-space with a linearly graded layer and a rigid punch is proposed and studied in the present paper. The governing equation, which describes the relation of the displacements and the normal tractions at the contact interface, is obtained by means of Fourier transform and a transfer matrix method. Appropriate collocation methods are used in order to solve the equation numerically. Singular behaviors at the edge of a flat punch are revealed. Compared to the case with a graded surface varying according to an exponential law, stress concentration is relatively weaker in the case with the graded surface varying according to a linear law. Furthermore, stress distributions in cases of a flat or cylindrical punch are given for different varying graded laws, thickness of graded layer, ratios of stiffness, and frictional coefficients. All the results are helpful for the design of strong and wear resistance coating surfaces.     

Materials characterization and mechanical properties of graded tool steels processed by a new co‐spray forming technique

In order to meet the requirements of micro cold forming tools, a new co‐spray forming process has been applied to produce graded materials from two different tool steels in this study. The two steel melts were atomized and co‐sprayed simultaneously onto a flat substrate, resulting in a flat graded deposit when the two sprays were overlapped. To eliminate porosity and break up carbide network, the graded deposits were further hot rolled. The resultant graded tool steels were investigated with respect to porosity, element distribution, microstructure, hardness, strength, and toughness. The degree of overlapping of the two sprays determined the concentration gradient of the chemical elements in the deposits. The overlapping of the spray cones also contributed to low porosity in the gradient zone of the deposits. The porosity in the graded deposits could be essentially eliminated by means of hot rolling. The carbides and grain structures of the hot rolled tool steels were fine and homogeneous. By means of combining different tool steels in a single deposit, different microstructures and properties were combined.     

Design of low-loss single-polarization single-mode photonic-crystal fiber based on polymer

A new structure for single-polarization single-mode photonic-crystal fiber is proposed and numerically analyzed by using a full vector finite element method with anisotropic perfectly matched layers. The cutoff wavelength of two linearly polarized states can be controlled artificially by varying the structure parameters of photonic crystal fiber. The confinement loss are also numerically calculated and optimized at 650 nm communication wavelength of polymer optical fiber. From the numerical results it is confirmed that the proposed fiber is low-loss single-polarization single-mode photonic-crystal fiber within the wavelength range from 0.63 to 0.73 µm, where only the slow-axis mode exists and the confinement loss is less than 0.05 dB m^?1.     

Spectral transformation of femtosecond Cr:forsterite laser pulses in a flint-glass photonic-crystal fiber

Nonlinear-optical performance of photonic-crystal fibers (PCFs) made of highly nonlinear TF10 glass is studied and compared with the general tendencies of nonlinear-optical interactions in fused-silica PCFs. The loss of TF10 glass PCFs prevents the generation of supercontinuum emission with a broad and flat spectrum, which typically requires propagation lengths comparable with or exceeding the attenuation length of the fiber. However, dispersive-wave emission of solitons, induced by high-order dispersion, phase-matched four-wave-mixing processes, and self-phase-modulation-induced spectral broadening are substantially enhanced in TF10 glass PCFs due to the high material nonlinearity, providing a high efficiency of frequency conversion of Cr:forsterite laser pulses.     

Laser ablation of dental tissues with picosecond pulses of 1.06-microm radiation transmitted through a hollow-core photonic-crystal fiber

Sequences of picosecond pulses of 1.06-microm Nd:YAG laser radiation with a total energy of approximately 2 mJ are transmitted through a hollow-core photonic-crystal fiber with a core diameter of approximately 14 microm and are focused onto a tooth's surface in vitro to ablate dental tissue. The hollow-core photonic-crystal fiber is shown to support the single-fundamental-mode regime for 1.06-microm laser radiation, serving as a spatial filter and allowing the laser beam's quality to be substantially improved. The same fiber is used to transmit emission from plasmas produced by laser pulses onto the tooth's surface in the backward direction for detection and optical diagnostics.     

Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation

In this article, an exact analytical solution for buckling analysis of moderately thick functionally graded (FG) sector plates resting on Winkler elastic foundation is presented. The equilibrium equations are derived according to the first order shear deformation plate theory. Because of the coupling between the bending and stretching equilibrium equations of FG plates, these plates have deflection under in-plane loads lower than the critical buckling load acting on the mid-plane. The conditions under which FG plates remain flat in the pre-buckling configuration are investigated and the stability equations are obtained based on the flat plate assumption in the pre-buckling state. The stability equations are simplified into decoupled equations and solved analytically for plates having simply supported boundary condition on the straight edges. The critical buckling load is obtained and the effects of geometrical parameters and power law index on the stability of functionally graded sector plates are studded. The results for the critical buckling load of moderately thick functionally graded sector plates resting on elastic foundation are reported for the first time.     

Micro-optically assisted high-index waveguide coupling

Adapting the concept of solid immersion lenses, we numerically study a micro-optical scheme for conventional high-index and photonic-crystal waveguide coupling by using a combination of different numerical methods such as ray tracing, angular-spectrum propagation, finite-difference time-domain simulations, and finite-element-method simulations. The numerical findings are discussed by means of impedance, group- or energy-velocity, spot-size, and phase-matching criteria. When fabrication constraints for high-index immersion lenses made of silicon are taken into account, a coupling efficiency of -80% can be reached for monomode silicon-on-insulator waveguides with a quadratic cross section of the core and rectangular cross sections of moderate aspect ratio. Similar coupling efficiencies of -80% can be obtained for silicon-on-insulator photonic-crystal waveguides. Tolerances that are due to misalignments and variations of the substrate thickness of the silicon lens are discussed.     

Dynamic control of the Q factor in a photonic crystal nanocavity

High-quality (Q) factor photonic-crystal nanocavities are currently the focus of much interest because they can strongly confine photons in a tiny space. Nanocavities with ultrahigh Q factors of up to 2,000,000 and modal volumes of a cubic wavelength have been realized. If the Q factor could be dynamically controlled within the lifetime of a photon, significant advances would be expected in areas of physics and engineering such as the slowing and/or stopping of light and quantum-information processing. For these applications, the transfer, storage and exchange of photons in nanocavity systems on such a timescale are highly desirable. Here, we present the first demonstration of dynamic control of the Q factor, by constructing a system composed of a nanocavity, a waveguide with nonlinear optical response and a photonic-crystal hetero-interface mirror. The Q factor of the nanocavity was successfully changed from approximately 3,000 to approximately 12,000 within picoseconds.     

Photonic and omnidirectional band gap engineering in stack of exponential graded index material and negative index material

We have investigated the photonic band gaps (PBG) and omnidirectional band gaps in one-dimensional photonic crystals made up of alternate layer of exponential graded index material and negative index material. We have considered the influence of material properties, geometrical parameters and material composition on the PBG and omnidirectional band gap. Results show that the parameters of exponential graded index material and negative index material can change the photonic and omnidirectional band structures remarkably. Number and bandwidth of PBG increases with increasing the negative index material layer thicknesses while thicknesses of graded index layer only have an effect on the bandwidth of PBGs. The bandwidth of PBG also depends on grading profile parameter of exponential graded index layers and bandwidth can be tuned with increase the value of grading profile parameter. This work can facilitate the design of filters and reflectors, and provide the basic understanding of the influence of graded index materials and metamaterials on the PBG properties.     

Fitting-based determination of an effective medium of a metallic periodic structure and application to photonic crystals

Effective permittivities of a metallic periodic structure for which the second-order effective-medium theory does not yield correct results were obtained by numerically fitting to rigorous-coupled-wave analysis (RCWA). The calculated effective medium showed good agreement with RCWA and minimal deviation in the long-wavelength limit with variation in angle of incidence, grating depth, superstrate, and fill factor. In terms of the standard deviation, the effective medium was least affected by the change in grating depths. The calculated effective permittivities were applied to a three-dimensional metallic photonic-crystal structure and produced a photonic bandgap that is consistent with published experimental data.     

The contact problem of a rigid stamp with friction on a functionally graded magneto-electro-elastic half-plane

We consider in this study the frictional sliding contact problem between a functionally graded magneto-electro-elastic material and a perfectly conducting rigid punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the unknowns are the normal contact stress, the electric displacement and the magnetic induction. These integral equations are then solved numerically to obtain the distributions of the normal contact stress, electric displacement and magnetic induction at the surface of the graded medium. The main objective of this paper is to study the effect of the non-homogeneity parameter, the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat and circular punch profiles.     

Omni-directional bands in multilayer structure containing exponentially graded materials

The omni-directional reflection (ODR) in a one-dimensional multilayered structure containing exponentially graded material is studied theoretically using the transfer matrix method. We propose a periodic multiplayer structure containing alternate layers of the exponentially graded refractive index and layers of constant refractive index. The reflectance for TE- and TM-modes of the structure are studied for different angles of incidence. We obtained two ODR bands, one in the visible and the other in the infrared region for both polarizations. The behavior of the ODR band in the infrared region is different from the usual Bragg ODR band in the visible region. The width of the ODR band for the TM-mode is larger that for the TE-mode in the wavelength range 850 nm–1050 nm. Such a structure with a large ODR band may be useful in the design of a broad infrared reflector.     

Fracture behaviors for a functionally graded superconducting cylinder with a cylindrical crack

In this study, a double exponential model is proposed to investigate the cylindrical crack problem for a functionally graded superconducting cylinder. The stress intensity factors (SIFs) are analytically obtained by transforming the corresponding crack problem into dual integral equations. The effects of applied magnetic field, model parameters, and crack configuration on the SIFs are analyzed. Some important phenomena are observed. Among others, both decreasing the graded index of Young's modulus and increasing the introduced nondimensional exponent parameter in the critical current model can inhibit crack propagation. This study should be useful for the application of superconducting devices.     

Dynamic stress from a cylindrical inclusion buried in a functionally graded piezoelectric material layer under electro-elastic waves

This paper presents a theoretical method to investigate the multiple scattering of electro-elastic waves and dynamic stress around a subsurface cylindrical inclusion in a functionally graded piezoelectric material layer bonded to homogeneous piezoelectric materials. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions around the inclusion. The image method is used to satisfy the mechanical and electrically short conditions at the free surface of the structure. Through the numerical solutions of dynamic stress concentration factors around the inclusion, it is found that when the cylindrical inclusion possesses higher rigidity and greater piezoelectric constant than the two phases of functionally graded materials, the dynamic stress around the inclusion increases greatly. When the distance between the surface of the structure and the inclusion is smaller, the effect of the properties of the inclusion becomes greater. When the cylindrical inclusion possesses lower rigidity and smaller piezoelectric constant than the two phases of functionally graded materials, the maximum dynamic stress shows little difference; however, the variation of the distribution of the dynamic stress around the inclusion is greater. The effect of the properties of the inclusion on the dynamic stress around the inclusion is greater than that on the electric field. The effects of wave frequency on the dynamic stress and electric field are also examined.     

Design of functionally graded dental multilayers

This paper presents the results of a computational and experimental effort to develop crack‐resistant dental multilayers that are inspired by the functionally graded dento‐enamel‐junction (DEJ) structure that occurs between dentin and enamel in natural teeth. The complex structures of natural teeth and ceramic crowns are idealized using flat‐layered configurations. The potential effects of teeth‐on‐teeth contact are then modelled using finite element simulations of Hertzian contact. The resulting stress distributions are compared for a range of possible bioinspired, functionally graded architecture. The computed stress distributions show that the highest stress concentrations in the top ceramic layer of crown structures are reduced significantly by the use of bioinspired functionally graded architectures. The reduced stresses are experimentally shown to be associated with significant improvements (～32%) in the pop‐in loads. The implications of the results are discussed for the design of bioinspired dental ceramic crown structures. The bioinspired functionally graded layers are also shown to promote improvements in the critical crack size.