Showing papers on "Plane wave published in 2004"

Photonic Band Gap Structures

Abstract: Nanotechnology is a scientific frontier with enormous possibilities. Reducing the size of objects to nanometer scale to physically manipulate the electronic or structural properties offers a fabrication challenge with a large payoff. Nanophotonics is a subfleld of nanotechnology and a part of nanophotonics includes photonic band gap structures, which manipulate the properties of light to enable new applications by periodically modulating the relative permittivity. In photonic band gap (PBG) structures, the electromagnetic properties of materials, such as the electromagnetic density of states, phase, group velocities, signal velocities, field confinement, and field polarization are precisely controlled. The size scale of interest in PBG structures is typically of the order of a wavelength, which is not quite as demanding as required to observe quantum confinement effects in electronic materials. Nevertheless, photonic devices designed with nanophotonic technology enable new technology for devices and applications in sensing, characterization, and fabrication. Even though PBG photonic devices are complex and the fabrication is often expensive, rapid progress on PBG structures has been possible because of the development of powerful numerical computation tools that provide a detailed analysis of the electromagnetic properties of the system prior to fabrication. To design photonic devices we use a variety of computational techniques that help in evaluating performance. Several books have already been written about the optical properties of PBGs. A classic book on ID periodic structures was written by Brillouin. Yariv and Yeh's book is an excellent resource on many aspects of periodic optical media. Recent books devoted to the subject include the books by Joannopoulos et al., the very thorough book by Sakoda, and a recent book on nonlinear optics of PBGs by Slusher and Eggleton that features results of several researchers who have contributed to the subject. In addition, many good articles on PBG structures can be found in special issues or in summer school proceedings. Numerical approaches are available to completely describe the properties of electromagnetic wave propagation in PBG structures. Three methods are of general use; they are the plane wave, the transfer matrix, and the finite-difference time-domain (FDTD) methods. The results of the plane wave method with the latter two are to some degree complementary, as is demonstrated and discussed later in this chapter. Analytical methods are also available and have been especially useful for 1D systems. For instance, the development of coupled-mode equations for propagation by using multiple scales or slowly varying amplitude methods has given researchers powerful tools for studying nonlinear effects and designing new electro-optic (EO) devices, such as tunable optical sources from the ultraviolet to the terahertz regime, EO modulators, and a new generation of sensitive bio/ˆ•chem sensors.

Ab initio treatment of noncollinear magnets with the full-potential linearized augmented plane wave method

Abstract: The massively parallelized full-potential linearized augmented plane-wave bulk and film program FLEUR for first-principles calculations in the context of density functional theory was adapted to allow calculations of materials with complex magnetic structures---i.e., with noncollinear spin arrangements and incommensurate spin spirals. The method developed makes no shape approximation to the charge density and works with the continuous vector magnetization density in the interstitial and vacuum region and a collinear magnetization density in the spheres. We give an account of the implementation. Important technical aspects, such as the formulation of a constrained local moment method in a full-potential method that works with a vector magnetization density to deal with specific preselected nonstationary-state spin configurations, the inclusion of the generalized gradient approximation in a noncollinear framework, and the spin-relaxation method are discussed. The significance and validity of different approximations are investigated. We present examples to the various strategies to explore the magnetic ground state, metastable states, and magnetic phase diagrams by relaxation of spin arrangements or by performing calculations for constraint spin configurations to invest the functional dependence of the total energy and magnetic moment with respect to external parameters.

High impedance metamaterial surfaces using Hilbert-curve inclusions

Abstract: A metamaterial surface, composed of a periodic arrangement of Hilbert Curve inclusions above a conducting ground plane, is analyzed numerically and is shown to possess the properties of a high impedance surface by investigating the phase and magnitude of the reflection coefficient, /spl Gamma/, for a plane wave of normal incidence. A parametric study is presented with respect to the iteration order of the Hilbert curve, the surface height above the ground plane, and the separation distance between the neighboring Hilbert elements within the surface array.

Temperature estimation using ultrasonic spatial compound imaging

Abstract: The feasibility of temperature estimation during high-intensity focused ultrasound therapy using pulse-echo diagnostic ultrasound data has been demonstrated. This method is based upon the measurement of thermally-induced modifications in backscattered RF echoes due to thermal expansion and local changes in the speed Of Sound. It has been shown that strong ripple artifacts due to the thermo-acoustic lens effect severely corrupt the temperature estimates behind the heated region. We propose here a new imaging technique that improves the temperature estimation behind the heated region and reduces the variance of the temperature estimates in the entire image. We replaced the conventional beamforming on transmit with multiple steered plane wave insonifications using several subapertures. A two-dimensional temperature map is estimated from axial displacement maps between consecutive RF images of identically steered plane wave insonifications. Temperature estimation is then improved by averaging the two-dimensional maps from the multiple steered plane wave insonifications. Experiments were conducted in a tissue-mimicking gelatin-based phantom and in fresh bovine liver.

Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike

Abstract: The paraxial propagation of a beam incident along an optic axis of a biaxial crystal slab is studied in detail. Analytical descriptions are given for the Poggendorff bright and dark rings (associated with the conical singularity of the dispersion surface), and the axial spike (associated with the toroidal ring in the dispersion surface). The rings and spike depend on distance from the crystal. In sharpest focus, the rings are close and asymmetrical, and the spike is faint. Further away, the rings separate, they develop weak diffraction oscillations, and the spike grows in intensity. Eventually the oscillations disappear and the rings become symmetrical, and the axial spike dominates. The images depend on the profile of the incident beam; explicit formulae are given for a Gaussian beam and a coherently illuminated pinhole. Geometrical optics (extended to complex rays for the Gaussian beam) can describe some aspects of the images, in particular the Poggendorf dark ring, which arises from antifocusing and for which an explicit description is given.

Mie scattering by a uniaxial anisotropic sphere

Abstract: The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed to have a form similar to the plane wave expanded also in terms of the spherical vector wave functions. Applying the continuous boundary conditions of electromagnetic fields on the surface between the air region and uniaxial anisotropic sphere, the coefficients of transmitted fields and the scattered fields in uniaxial anisotropic media can be obtained analytically in the expansion form of vector wave eigenfunctions. Numerical results for some special cases are obtained and compared with those of the classical Lorenz-Mie theory and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach. We also present some new numerical results for the more general uniaxial dielectric material media.

Plane waves with negative phase velocity in Faraday chiral mediums.

Abstract: The propagation of plane waves in a Faraday chiral medium is investigated. Conditions for the phase velocity to be directed opposite to the direction of power flow are derived for propagation in an arbitrary direction; simplified conditions which apply to propagation parallel to the distinguished axis are also established. These negative phase-velocity conditions are explored numerically using a representative Faraday chiral medium, arising from the homogenization of an isotropic chiral medium and a magnetically biased ferrite. It is demonstrated that the phase velocity may be directed opposite to power flow, provided that the gyrotropic parameter of the ferrite component medium is sufficiently large compared with the corresponding nongyrotropic permeability parameters.

Fast computation of the geoelectric field using the method of elementary current systems and planar Earth models

Abstract: . The method of spherical elementary current systems provides an accurate modelling of the horizontal component of the geomagnetic variation field. The interpolated magnetic field is used as input to calculate the horizontal geoelectric field. We use planar layered (1-D) models of the Earth's conductivity, and assume that the electric field is related to the local magnetic field by the plane wave surface impedance. There are locations in which the conductivity structure can be approximated by a 1-D model, as demonstrated with the measurements of the Baltic Electromagnetic Array Research project. To calculate geomagnetically induced currents (GIC), we need the spatially integrated electric field typically in a length scale of 100km. We show that then the spatial variation of the electric field can be neglected if we use the measured or interpolated magnetic field at the site of interest. In other words, even the simple plane wave model is fairly accurate for GIC purposes. Investigating GIC in the Finnish high-voltage power system and in the natural gas pipeline, we find a good agreement between modelled and measured values, with relative errors less than 30% for large GIC values. Key words. Geomagnetism and paleomagnetism (geomagnetic induction; rapid time variations) – Ionosphere (electric field and currents)

Plane-wave basis finite elements and boundary elements for three-dimensional wave scattering.

Abstract: Classical finite-element and boundary-element formulations for the Helmholtz equation are presented, and their limitations with respect to the number of variables needed to model a wavelength are explained. A new type of approximation for the potential is described in which the usual finite-element and boundary-element shape functions are modified by the inclusion of a set of plane waves, propagating in a range of directions evenly distributed on the unit sphere. Compared with standard piecewise polynomial approximation, the plane-wave basis is shown to give considerable reduction in computational complexity. In practical terms, it is concluded that the frequency for which accurate results can be obtained, using these new techniques, can be up to 60 times higher than that of the conventional finite-element method, and 10 to 15 times higher than that of the conventional boundary-element method.

Plane waves in FDTD simulations and a nearly perfect total-field/scattered-field boundary

Abstract: The total-field/scattered-field (TFSF) boundary has been successfully used for a number of years to introduce energy into finite-difference time-domain (FDTD) grids. If the propagation of the incident field is grid-aligned, a perfect TFSF implementation can be realized by using an auxiliary one-dimensional FDTD simulation which models propagation of the incident field. Here "perfect" implies the incident field propagation exactly matches the way in which the field propagates in the FDTD grid. However, for propagation which is not grid-aligned, no similarly perfect implementation has previously been presented. This work provides a framework for a perfect TFSF boundary for pulsed plane waves which do not propagate in a grid-aligned fashion. To achieve this, homogeneous plane-wave propagation is rigorously quantified. Using this knowledge and a specification of the desired incident field, the dispersion relation is used to ascertain the incident field at any point in the grid. It is required to account for, unlike in the continuous world, the electric field, the magnetic field, and the wavenumber vector not forming a mutually orthogonal set. Group velocity is also considered because of its relevance to the implementation.

A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory

Abstract: We derive the spectral dispersion law for the virtually imaged phased array (VIPA) based on paraxial wave theory using the Fresnel diffraction analysis. The validity of the dispersion law is verified by comparison with experiments. This spectral dispersion law is compared to a previous law based on plane wave theory. At small incident angles where the VIPA provides its largest spectral dispersion, the paraxial wave law provides a much better fit to the data than the plane wave law does.

Near-field enhancement and imaging in double planar polariton-resonant structures

Abstract: It is shown that a system of two coupled planar material sheets possessing surface mode (polariton) resonances can be used for the purpose of evanescent field restoration and, thus, for sub-wavelength near-field imaging. The sheets are placed in free space so that they are parallel and separated by a certain distance. Due to interaction of the resonating surface modes (polaritons) of the sheets an exponential growth in the amplitude of an evanescent plane wave in the system can be achieved. This effect was predicted earlier for backward-wave (double-negative or Veselago) slab lenses. The alternative system considered here is proved to be realizable at microwaves by grids or arrays of resonant particles. The necessary electromagnetic properties of the resonating grids and the particles are investigated and established. Theoretical results are supported by microwave experiments that demonstrate amplification of evanescent modes.

Ridge waveguide as a near field aperture for high density data storage

Abstract: The performance of the ridge waveguide as a near-field aperture in data storage systems is investigated. Finite element method (FEM) and finite-difference time-domain (FDTD) based software are used in the numerical simulations. To verify their accuracy at optical frequencies, the FEM and FDTD are first compared to analytical results. The accuracy of these techniques for modeling ridge waveguides at optical frequencies is also evaluated by comparing their results with each other for a plane wave illumination. The FEM, which is capable of modeling focused beams, is then used to simulate various geometries involving ridge waveguides. Near-field radiation from ridge waveguide transducer is expressed in terms of power density quantities. Previous studies in the literature consider the performance of the transducer in free space, rather than in the presence of a recording magnetic medium. The effect of the recording magnetic medium on the transmission efficiency and spot size is discussed using numerical simula...

HAADF-STEM imaging with sub-angstrom probes: a full Bloch wave analysis.

Abstract: A full coherent Bloch wave calculation is presented to investigate high-angle annular dark-field image formation for sub-angstrom probes in scanning transmission electron microscopy (STEM). With increasing illumination angle, the contribution of the 1s bound state increases to a maximum at an optimum probe angle, after which we find increasing contributions from high-angle plane wave states around the periphery of the objective aperture. Examination of image contributions from different depths within a crystal shows an oscillatory behavior due to the beating between 1s and non-1s states. The oscillation period reduces with decreasing probe size, while the relative contribution from a specific depth increases. This signifies a changeover from a projection mode of imaging to a depth-slicing mode of imaging. This new mode appears capable of resolving three-dimensional atomic structures in future generation aberration-corrected STEM.

Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

Abstract: The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP) and quasi-SV (qSV) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle

Transmission of light through small elliptical apertures.

Abstract: The results of computer simulations based on the Finite Difference Time Domain method with local space and time grid refinement, are presented for an elliptical aperture in a thin metal film illuminated by a normally incident, monochromatic plane wave. Both cases of incident polarization parallel and perpendicular to the long axis of the ellipse are considered. An intuitive description of the behavior of the electromagnetic fields is developed in each case, and simulation results that exhibit patterns similar to those expected from this qualitative analysis are presented. The simulations reveal, in quantitative detail, the amplitude and phase behavior of the E- and B-fields in and around the aperture.

Localized and stationary light wave modes in dispersive media.

Abstract: In recent experiments, localized and stationary optical wave packets have been generated in second-order nonlinear processes with femtosecond pulses, whose asymptotic features relate to those of nondiffracting and nondispersing polychromatic Bessel beams in linear dispersive media. We investigate the nature of these linear waves and show that they can be identified with the X-shaped (O-shaped) modes of the hyperbolic (elliptic) wave equation in media with normal (anomalous) dispersion. Depending on the relative strengths of mode phase mismatch, group velocity mismatch with respect to a plane pulse, and the defeated group velocity dispersion, these modes can adopt the form of pulsed Bessel beams, focus wave modes, and X waves (O waves), respectively.

Theory and simulation of surface plasmon-coupled directional emission from fluorophores at planar structures.

Abstract: A theoretical approach to surface plasmon-coupled emission (SPCE) from planar structures is developed. It is used for simulations. The results are compared to experimental findings. The match is almost perfect concerning emission angles. Power relations and decay times are reproduced qualitatively. The theory is based on Fresnel plane wave refraction at planar multilayered structures and the Weyl identity for expressing the dipolar radiation in terms of plane waves. One-dimensional integrals, used for the numerical computations, are derived for the fields, powers, and decay enhancements. This theoretical approach is shown to be well suited for design of SPCE setups and for prediction and explanation of experimental results. It also shows promise for refinement and optimization of SPCE, concerning enhancement of weak fluorophores, and usage of decay times.

Photonic band gap analysis using finite-difference frequency-domain method

Abstract: A finite-difference frequency-domain (FDFD) method is applied for photonic band gap calculations. The Maxwell's equations under generalized coordinates are solved for both orthogonal and non-orthogonal lattice geometries. Complete and accurate band gap information is obtained by using this FDFD approach. Numerical results for 2D TE/TM modes in square and triangular lattices are in excellent agreements with results from plane wave method (PWM). The accuracy, convergence and computation time of this method are also discussed.

On the propagation of plane waves in type–III thermoelastic media

Abstract: The propagation of plane waves in infinite, three–dimensional, type–III thermoelastic media is investigated. Exact dispersion relation solutions are determined and several characterizations of the wavefield are examined. Low– and high–frequency asymptotic expressions are given, small–coupling limit results are derived, and special/limiting cases, including those corresponding to thermoelastic media of types II and I, are noted. Computational tools are used to illustrate the analytical findings and to study the effects of varying the physical parameters. Of the findings presented, the following are most significant: (i) the determination of critical values of the physical parameters and their impact on the wavefields; (ii) ascertaining that type–III media behave, essentially, like type–II (respectively, type–I) media with respect to low– (respectively, high–) frequency plane waves; (iii) establishing the Whitham stability of plane waves in type–III media; and (iv) the determination of the dispersion characteristics of type–III media.

Plane waves with negative phase velocity in isotropic chiral mediums

Abstract: The propagation of plane waves in an isotropic chiral medium (ICM) is investigated. Simple conditions are derived--in terms of the constitutive parameters of the ICM--for the phase velocity to be directed opposite to the direction of power flow. It is demonstrated that phase velocity and power flow may be oppositely directed provided that the magnetoelectric coupling is sufficiently strong.

The electromagnetic inverse-scattering problem for partly coated Lipschitz domains

Abstract: We consider the inverse-scattering problem of determining the shape of a partly coated obstacle in R3 from a knowledge of the incident time-harmonic electromagnetic plane wave and the electric far-field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method.

Seismic ground motions from a bolide shock wave

Abstract: [1] An intensely brilliant bolide accompanied by an audible sonic boom occurred on the night of 3 November 2003 (∼2150 LT or 4 November 2003, 0350 UT) in northeastern Arkansas. The sonic boom was well recorded by 22 three-component stations of the Center for Earthquake Research and Information Cooperative Seismic Network. Arrival times and wave polarizations were used to reconstruct the acoustic wave front propagating across the network and to estimate trajectory parameters of the bolide. A grid search location technique constrains the trajectory and gives a reference height of 50–100 km above the southern edge of the network, an azimuth of propagation of 270°–290° toward the northwest and a plunge of 38°–48° downward. The trajectory and date of the bolide event are consistent with a Taurid shower meteor. Transient ground motions from the sonic boom were studied using plane wave, Cagniard-deHoop, and propagator matrix theory for an incident pressure pulse impinging on a layered elastic Earth model. General characteristics of the vertical and radial polarization and wave frequency content require acoustic coupling within a thin (∼10 m) near-surface layer with low P wave (∼0.25 km/s) and S wave (∼0.125 km/s) velocities. Ground motions are generally confined to this near-surface layer, are not sensitive to deeper Earth structure within the Mississippi embayment unconsolidated sediments, and display both “leaky” mode PL (a type of dispersed, P-type seismic wave) and “locked” mode Rayleigh wave propagation. Acoustic wave/ground motion coupling studies may be a useful way to analyze near-surface site responses to determine velocity structure in earthquake shaking hazard studies.