Crystal Slab Research Articles

Efficient numerical method for analyzing photonic crystal slab waveguides

Computing the eigenmodes of a photonic crystal (PhC) slab waveguide is computationally expensive, since it leads to eigenvalue problems in three-dimensional domains that are large compared with the wavelength. In this paper, a procedure is developed to reduce the eigenvalue problem for PhC slab waveguides to a nonlinear problem defined on a small surface in the waveguide core. The reduction process is efficiently performed based on the so-called Dirichlet-to-Neumann maps of the unit cells. The nonlinear eigenvalue problem can be efficiently solved by standard root-finding methods, such as the secant method.

STEM HAADF Image Simulation of the Orthorhombic M1 Phase in the Mo‐V‐Nb‐Te‐O Propane Oxidation Catalyst

AbstractA full frozen phonon multislice simulation of high angle annular dark field scanning transmission electron microscopy (HAADF STEM) images from the M1 phase of the Mo‐V‐Nb‐Te‐O propane oxidation catalyst has been performed by using the latest structural model obtained using the Rietveld method. Simulated contrast results are compared with experimental HAADF images. Good agreement is observed at ring sites, however significant thickness dependence is noticed at the linking sites. The remaining discrepancies between the model based on Rietveld refinement and image simulations indicate that the sampling of a small volume element in HAADF STEM and averaging elemental contributions of a disordered site in a crystal slab by using the virtual crystal approximation might be problematic, especially if there is preferential Mo/V ordering near the (001) surface.

A Novel Micromechanical Resonator Using Two-Dimensional Phononic Crystal Slab

Two-dimensional (2-D) Silicon phononic crystal (PnC) slab of a square array of cylindrical air holes in a 10μm thick free-standing silicon plate with line defects is characterized as a cavity-mode PnC resonator. Piezoelectric aluminum nitride (AlN) film is deployed as the inter-digital transducers (IDT) to transmit and detect acoustic waves, thus making the whole microfabrication process CMOS-compatible. Both the band structure of the PnC and the transmission spectrum of the proposed PnC resonator are analyzed and optimized using finite element method (FEM). The measured quality factor (Q factor) of the microfabricated PnC resonator is over 1,000 at its resonant frequency of 152.46MHz. The proposed PnC resonator shows promising acoustic resonance characteristics for RF communications and sensing applications.

Atomistic study of the effect of crack tip ledges on the nucleation of dislocations in silicon single crystals at elevated temperature

We model a single crystal of silicon approaching dimensions of 20 nm × 20 nm × 10 nm with up to 200,000 atoms based on the ReaxFF first principles based reactive force field, applied here to examine the influence of crack tip heterogeneities on the nucleation of dislocations from crack tips as the temperature is increased well beyond 1000 K. Our study aims at generating insight into mechanisms of the brittle-to-ductile transition (BDT) observed in silicon, which is known to change the behavior of silicon crystals from predominantly brittle at low temperatures to ductile at higher temperatures, likely involving a competition between brittle bond-breaking and emission of dislocations. We first examine the crystallographic orientations most widely known to exhibit fracture, for example failure on the {1 1 1} and {1 1 0} planes. We find that even at very high temperatures considered here (around 1500 K), the material behaved in a completely brittle manner for systems with cracks oriented in the {1 1 1} and {1 1 0} planes. In contrast, when the crack plane is changed to the {1 0 0} orientation, the formation of complete dislocation loops is observed. The results reported in our paper is the first direct observation of dislocation loops in silicon driven by an increase in the temperature, and extends earlier studies that were focused solely on extremely thin quasi-two-dimensional models. We demonstrate here that the formation of these loops can be linked to the geometrical ledges at the crack tip with favorable orientations for slip on the {1 1 1} planes. The detailed mechanisms leading to the nucleation of dislocations involve changes at the crack tip with bond rotations and formation of ledges, and we find that the emergence of dislocations causes the crack to arrest, but re-initiation takes place and no conclusive nucleation of dislocations and complete arrest of the crack is observed. The thickness effect is discussed together with other sources for formation of ledges along the crack front. Our findings provide important insight towards the development of models for the brittle–ductile-transition in silicon and potentially other materials, and emphasize on the significance of thickness effects in simulations of fracture in crystal slabs.

3D integration of photonic crystal devices: vertical coupling with a silicon waveguide

Two integrated devices based on the vertical coupling between a photonic crystal microcavity and a silicon (Si) ridge waveguide are presented in this paper. When the resonator is coupled to a single waveguide, light can be spectrally extracted from the waveguide to free space through the far field emission of the resonator. When the resonator is vertically coupled to two waveguides, a vertical add-drop filter can be realized. The dropping efficiency of these devices relies on a careful design of the resonator. In this paper, we use a Fabry-Perot (FP) microcavity composed of two photonic crystal (PhC) slab mirrors. Thanks to the unique dispersion properties of slow Bloch modes (SBM) at the flat extreme of the dispersion curve, it is possible to design a FP cavity exhibiting two quasi-degenerate modes. This specific configuration allows for a coupling efficiency that can theoretically achieve 100%. Using 3D FDTD calculations, we discuss the design of such devices and show that high dropping efficiency can be achieved between the Si waveguides and the PhC microcavity.

Deformation band formation, characteristics, history

Deformation bands (DMB) are crystal slabs that develop slip on systems different from neighbours; they rotate in different directions developing intervening transition boundaries (TB) that rise rapidly in misorientation. In polycrystals, grains divide into DMB, slipping on 2 or 3 systems to provide the 5 required components with minimum energy, as confirmed through OIM boundary misorientations and band rotation poles. TEM exposed the subgrains but seldom TB, except in single crystals as layers of cells. As the TB extend and align into layer bands, the microtextures are similar in cold and hot working. In hot working, TB are quite narrow and able to migrate; at large strains, lengthening and rotating TB (like grain boundaries) are responsible for rapid accumulation of high angle facets of many subgrains. Nevertheless sub-boundaries persist defining steady-state cellular dimensions and flow stress.

Imaging properties of a two-dimensional photonic crystal with rectangular air holes embedded in a silicon slab

Abstract We investigate the superlensing effect of a two-dimensional (2D) triangular photonic crystal (PC) slab consisting of rectangular air holes in silicon. An analysis of equal-frequency contours (EFCs) shows that geometric parameters of the PC element shape can greatly change the shape of EFCs, thus change the effective phase index of the PC structure. Moreover, an effective negative refractive index n eff = −1 can be obtained at a normalized working frequency of 0.30 × 2 π c / a by adjusting the width of the rectangular air holes. Imaging capacity of this PC slab involving both the power intensity and full width at half-maximum of image is studied by the finite-difference time-domain (FDTD) method. In order to achieve a high-quality image, an appropriate surface termination of the PC slab is chosen. Coupled-mode theory analysis shows that the optimized surface termination can excite two kinds of surface modes which can couple with the Bloch wave in the PC. With the help of these surface modes, both the intensity of image and the super resolution capacity for the PC slab lens can be improved greatly.

Study of 2-D photon crystal Fano slab filters for biological sensing

A new compact optical Fano filter suitable for biological sensing is proposed, which patterns photon crystal in single crystalline silicon nanomembranes (SiNMs) and transferring onto transparent glass substrates. The effects of air hole size and silicon thickness on the transmission characteristics of new filter are numerically investigated by using three-dimensional finite-difference time-domain (FDTD) technique, the spectral response is also studied by back-filling bio-liquid. The results show that the dip wavelength will shift toward longer wavelength by either reducing air hole radius or filling bioliquid. The number of dips will increase with the increase of silicon thickness. The size of proposed filter can be less than 1 mm2.

Interference of conoscopic pictures of optical crystals

Nonconventional conoscopic pictures in poorly passing bunches of light, localized in a plane of uni-axial optical crystal are received. At usage of two crystal slabs with the optical axes oriented at angle to the plane of slab the interference conoscopic pictures are observed. The model explaining interference of conoscopic pictures is presented.

Nanoacoustic waves in nanomaterials

We discuss the formation and detection of acoustic soliton trains in crystal slabs. High-amplitude amplitude strain pulses are generated by impact of intense femtosecond optical pulses on a metallic film and injected into the crystal slab. Nonlinear acoustic propagation leads to the formation of shock fronts (N-waves), that, in absence of viscous damping and by virtue of dispersion, may develop into soliton trains at the leading edge and high frequency tails at the trailing edge. Interferometric pump-probe optical experiments are discussed to directly detect the ultrafast surface displacements when a soliton is reflected at the surface of the crystal slab. Finally, we experimentally prove that these acoustic solitons are capable of impulsively exciting THz transitions in electronic centers in solids. The coherent terahertz acoustic pulse trains are applied to manipulate the optical response of two-dimensional excitons in a III-V quantum well on the ultrafast timescale. By virtue of the deformation potential, the coherent exciton emission becomes strongly "chirped" when the acoustic pulse train passes the quantum well. This yields the prospect to perform pump-probe terahertz acoustic experiments with nanoacoustic waves in semiconductor nanomaterials.

Elastic properties of finite three-dimensional solid phononic-crystal slabs

We study theoretically, by means of layer-multiple scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in polyester matrix, embedded in air. We focus on the study of modes localized on the surfaces of the structure, investigating the physical parameters which influence and determine their appearance. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. This could be very useful in the design of devices related to frequency filtering, waveguiding, etc.

Controlling the focusing properties of a triangular-lattice metallic photonic-crystal slab

This paper studies the focusing properties of a two-dimensional photonic crystal (PC) slab consisting of a triangular lattice of metallic cylinders immersed in a dielectric background. Through the analysis of the equifrequency-surface contours and the field patterns of a point source placed in the vicinity of the PC slab, it finds that both the image distance and image quality can be controlled by simply adjusting the refractive index of the background material.

Antireflection coating for two-dimensional air hole-type photonic crystal negative refraction slab lens

We propose and optimize the antireflection coating composed of a row of tapered dielectric waveguides for two-dimensional air hole-type photonic crystal negative refraction slab lens. The image quality of the lens with the antireflection coating is improved. The simulation result using finite difference time domain method shows, at the working frequency leading to the effective index neff=-1, the reflection rate of the surface of photonic crystal with anti-reflection coating is reduced to below 1% in the range of incident angle less than 23 degrees.

TWO-DIMENSIONAL SILICON-BASED PHOTONIC CRYSTAL SLAB WITH PARTIAL AIR-BRIDGE

We describe a fabrication process of the near-infrared two-dimensional photonic crystal (PC) slab, which is sustained by part of the silica layer underneath the slab and forms a partly air-bridged type. The process involves focused ion beam (FIB) direct write following the selective wet etching of silicon on isolator (SOI) structures. By control the time of dissolving of silica layer in SOI, we successfully fabricated the sample and measured its transmittance spectrum. It is found that the observed spectrum is consistent with the theoretical band structure with FDTD method. For there is partly silica layer remained to support the air-bridge slab, the PC can be fabricated with a large area. If we change the support material under the slab, we might be able to fabricate PC laser with this kind of structure.

Mapping of complex optical field patterns in multimode photonic crystal waveguides by near-field scanning optical microscopy

We use near-field scanning optical microscopy (NSOM) operating in collection mode to map the optical field distribution of continuous wave infrared light propagating along an air-bridged W3 silicon photonic crystal (PC) slab multimode waveguide in a subwavelength resolution. The detected near-field optical intensity distribution patterns show very different longitudinal propagation features and transverse field profiles at different wavelength ranges. We have analyzed the dispersion of the guided modes in the PC waveguide and the corresponding eigenfield profile for each guided mode by means of the three-dimensional plane-wave expansion simulations. It is found that the experimentally observed complex while interesting near-field pattern features can be well explained by the field profiles of the multiple waveguide modes and their superposition at different excitation wavelengths. The detection and analysis of this multimode PC slab waveguide via NSOM could help us to understand complex wave propagation behavior and to further design novel PC devices.

Activation energy for hydrogen abstraction from methane over Li-doped MgO: A density functional theory study

Hydrogen abstraction from methane over Li-doped MgO is studied by means of density functional theory. The generalized synchronous transit method is applied to determine the transition state of the reaction. This method allows a transition state search that is more comprehensive compared with previous studies. The convergence of the calculated activation barrier with respect to cutoff energy, k-point mesh, vacuum layer thickness, and number of ionic layers in the crystal slab is examined. The activation barrier is calculated to be 0.745+/-0.01 eV (71.9+/-1.0 kJ/mol).

Elastic-plastic shock wave profiles in oriented single crystals of cyclotrimethylene trinitramine (RDX) at 2.25GPa

Plate impact experiments were performed on oriented single crystals of the energetic material cyclotrimethylene trinitramine (RDX). The experiments were performed to determine the anisotropic dynamic yield point for the RDX crystal, as well as to provide data for continuum modeling efforts. Impact was on the (111), (210), and (100) planes to access 3, 2, and 0 slip systems, respectively. Velocity history profiles were measured using Doppler interferometry. Impacts on the (210) plane resulted in nominally conventional results, with distinct elastic and plastic waves, stress relaxation, elastic precursor decay, and increasing wave separation with propagation distance. Velocity profiles from impacts on the (111) plane had no discernable precursor, although an inflection seen in the thicker samples might be the nearly overdriven elastic wave. Wave arrival times signaled a slower elastic wave speed in the (111) profiles. Several unexpected features were observed in the elastic precursor of the profiles from impacts on the (100) plane. Up to three distinct step features were resolved in these profiles in the region of the elastic precursor; these features are not understood. In preparing samples for these experiments, it was noted that the (100) crystal slabs were exceptionally brittle. Wave speeds determined from the shock experiments were consistent with both pulse-echo wave speed measurements and wave speeds calculated from the measured elastic tensor. The elastic limit, as indicated by the peak of the leading wave, was relatively isotropic.

Impact of high energy resolution detectors on the performance of a PET system dedicated to breast cancer imaging

We are developing a high resolution, high sensitivity PET camera dedicated to breast cancer imaging. We are studying two novel detector technologies for this imaging system: a scintillation detector comprising layers of small lutetium oxyorthosilicate (LSO) crystals coupled to new position sensitive avalanche photodiodes (PSAPDs), and a pure semiconductor detector comprising cadmium zinc telluride (CZT) crystal slabs with thin anode and cathode strips deposited in orthogonal directions on either side of each slab. Both detectors achieve 1 mm spatial resolution with 3–5 mm directly measured photon interaction depth resolution, which promotes uniform reconstructed spatial resolution throughout a compact, breast-size field of view. Both detector types also achieve outstanding energy resolution (<3% and <12%, respectively for LSO-PSAPD and CZT at 511 keV). This paper studies the effects that this excellent energy resolution has on the expected system performance. Results indicate the importance that high energy resolution and narrow energy window settings have in reducing background random as well as scatter coincidences without compromising statistical quality of the dedicated breast PET data. Simulations predict that using either detector type the excellent performance and novel arrangement of these detectors proposed for the system facilitate ∼20% instrument sensitivity at the system center and a peak noise-equivalent count rate of >4 kcps for 200 microCi in a simulated breast phantom.

Orbital and spin angular momentum in conical diffraction

The angular momentum Jinc of a light beam can be changed by passage through a slab of crystal. When the beam is incident along the optic axis of a biaxial crystal, which may also possess optical activity (chirality), the final angular momentum J can have both orbital (Jorb) and spin (Jsp) contributions, which we calculate paraxially exactly for arbitrary biaxiality and chirality and initially uniformly polarized beams with circular symmetry. For the familiar special case of a non-chiral crystal with fully developed conical-refraction rings, J is purely orbital and equal to Jinc/2, reflecting an interesting singularity structure in the beam. Explicit formulas and numerical computations are presented for a Gaussian incident beam. The change in angular momentum results in a torque on the crystal, along the axis of the incident beam. An additional, much larger, torque, about an axis lying in the slab, arises from the offset of the cone of conical refraction relative to the incident beam.

A study of the director distribution using deuterium NMR spectroscopy and simultaneous in situ observation of the light transmittance for a nematic subject to magnetic, electric and surface fields

Abstract It is important, both for basic science and device applications, to investigate the static and dynamic director distribution in a thin nematic liquid crystal (NLC) slab confined between two transparent electrodes. Optical and electrical measurement methods are generally used to determine the director distribution as a function of an electric field. It is to be expected that deuterium NMR spectroscopy combined with simultaneous in situ observation of the light transmittance should give us a good understanding of the director distribution for a thin NLC slab because the former is the sum of the spectra for each position in the slab and the latter by the optical anisotropy averaged over the slab. This combined method is used to investigate the director distribution in a thin NLC slab of 4-pentyl-4′-cyanobiphenyl subject to competing constraints.