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Showing papers on "Wavelength published in 2000"


Journal ArticleDOI
08 Sep 2000-Science
TL;DR: In this article, a 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.
Abstract: We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.

3,758 citations


15 Dec 2000
TL;DR: In this article, the authors proposed coupled plasmon modes for energy transfer in chains of closely spaced metal nanoparticles, which can be obtained at a length scale much less than wavelength of visible light.
Abstract: Electromagnetic energy transfer in plasmon wires consisting of chains of closely spaced metal nanoparticles can occur below the diffraction limit by means of coupled plasmon modes. Coherent propagation with group velocities that exceed 0.1 c is possible in straight wires and around sharp corners (bending radius much less than wavelength of visible light). Energy transmission through chain networks is possible at high efficiencies and is a strong function of the frequency and polarization direction of the plasmon mode. Although these structures exhibit transmission losses due to heating of about 3 dB/500 nm, they have optical functionality that cannot be obtained in other ways at a length scale ≪1 μm.

689 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed coupled plasmon modes for energy transfer in chains of closely spaced metal nanoparticles, and showed that they can be obtained at a length scale that cannot be obtained in other ways.
Abstract: Electromagnetic energy transfer in plasmon wires consisting of chains of closely spaced metal nanoparticles can occur below the diffraction limit by means of coupled plasmon modes. Coherent propagation with group velocities that exceed 0.1 c is possible in straight wires and around sharp corners (bending radius much less than wavelength of visible light). Energy transmission through chain networks is possible at high efficiencies and is a strong function of the frequency and polarization direction of the plasmon mode. Although these structures exhibit transmission losses due to heating of about 3 dB/500 nm, they have optical functionality that cannot be obtained in other ways at a length scale \ensuremath{\ll}1 \ensuremath{\mu}m.

668 citations


Journal ArticleDOI
Abstract: Analytic properties of the reflection coefficient of a multilayer metal-backed slab are considered. The result is a new form of the dispersion relationship, which characterizes the integral of the reflectance over wavelength in terms of the total thickness and averaged static permeability of the slab. The relation may be transformed to an inequality, which produces the least thickness to bandwidth ratio achievable for a physically realizable radar absorber. The particular cases of broad-band and narrow-band absorbers are discussed. The least thickness of a 10-dB broad-band dielectric radar absorber is shown to be 1/17 of the largest operating wavelength. The discussion also involves the results of a numerical study.

608 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed an accurate vector analysis of the lowest electromagnetic modes of photonic crystal fibers, and the likeness of their propagation characteristics to those of step index fibers was emphasized.

317 citations


Journal ArticleDOI
TL;DR: What are believed to be the first experimental observations of the existence of long-range plasmon-polariton waves, guided by a thin metal film of finite width, are presented.
Abstract: What are believed to be the first experimental observations of the existence of long-range plasmon–polariton waves, guided by a thin metal film of finite width, are presented. A waveguide composed of an 8-µm-wide, 20-nm-thick, 3.5-mm-long Au metal film embedded in SiO2 was successfully excited at a free-space wavelength of 1.55 µm in an end-fire experiment. The theoretical nature of the phenomenon is described, and experimental observations of field confinement provided by this metal waveguide are presented in detail.

308 citations


Journal ArticleDOI
TL;DR: In this article, a resonant cavity-enhanced light transmission mechanism in metallic gratings with subwavelength apertures is theoretically interpreted for operation with visible light and it is shown that under appropriate boundary conditions, the aperture behaves as open Fabry-Perot resonant cavities delivering a high photon flux, and that the coupling between the incident light and the fundamental mode supported by the aperture is strongly controlled by surface waves.

254 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the breaking probability for the dominant surface waves observed in three geographically diverse natural bodies of water: Lake Washington, the Black Sea, and the Southern Ocean, and found that the traditional approach of relating breaking probability to the wind speed or wave age provided reasonable correlations within individual datasets, but when the diverse datasets are combined, these correlations are significantly degraded.
Abstract: The breaking probability is investigated for the dominant surface waves observed in three geographically diverse natural bodies of water: Lake Washington, the Black Sea, and the Southern Ocean. The breaking probability is taken as the average number of breaking waves passing a fixed point per wave period. The data covered a particularly wide range of dominant wavelengths (3–300 m) and wind speeds (5–20 m s−1). In all cases, the wave breaking events were detected visually. It was found that the traditional approach of relating breaking probability to the wind speed or wave age provided reasonable correlations within individual datasets, but when the diverse datasets are combined, these correlations are significantly degraded. Motivated by the results of recent computational studies of breaking onset in wave groups, the authors investigated the hypothesis that nonlinear hydrodynamic processes associated with wave groups are more fundamental to the process of breaking than previously advocated aerod...

209 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived independent stability conditions for the P and S waves by exact separation of equations for the two types of waves and showed that the S -wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5 (that is usually used in modeling).
Abstract: We investigated stability and grid dispersion in the 3D fourth-order in space, second-order in time, displacement-stress staggered-grid finite-difference scheme. Though only displacement-stress scheme is explicitly treated, all results also apply to the velocity-stress and displacement-velocity-stress finite-difference schemes. We derived independent stability conditions for the P and S waves by exact separation of equations for the two types of waves. Since the S -wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5 (that is usually used in modeling), we recommend to sample a minimum S wavelength by six grid spacings. Grid dispersion is strongest for a wave propagating in the direction of a coordinate axis and weakest for a wave propagating along a body diagonal. Grid dispersion in the fourth-order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than grid dispersion in the second-order scheme for s = 1/10 and s = 1/12, respectively.

202 citations


Journal ArticleDOI
TL;DR: In this article, the effects of multiple parallel planar fractures on the apparent attenuation of normally incident one-dimensional elastic waves are studied. But the authors focus on the attenuative effect of each fracture with the displacement discontinuity model, and do not consider complex interfracture multiple wave reflections with the method of characteristics.

198 citations


Journal ArticleDOI
TL;DR: In this paper, near-field and far-field wave features generated by underwater landslides are described qualitatively and quantitatively, and the characteristic time of landslide motion and maximum nearfield wave amplitude suffice to scale many of these water wave features.
Abstract: Near-field and far-field wave features generated by solid block underwater landslides are described qualitatively and quantitatively. The characteristic time of landslide motion and maximum near-field wave amplitude suffice to scale many of these water wave features. Criteria are provided to determine if water waves generated by underwater landslides propagate as deepwater or shallow water waves. Estimates of the dominant far-field wavelength are provided for both cases. A precise location is given for the beginning of far-field wave propagation for deepwater waves. Weakly nonlinear and dispersive effects of shallow water wave propagation are examined. Around 5% of solid block maximum kinetic energy is converted into wave energy.

Journal ArticleDOI
TL;DR: In this article, a multiple wavelength surface plasmon resonance apparatus for imaging applications is presented, which can be used for biosensing, e.g., for monitoring of chemical and biological reactions in real time with label-free molecules.
Abstract: A new, multiple wavelength surface plasmon resonance apparatus for imaging applications is presented. It can be used for biosensing, e.g., for monitoring of chemical and biological reactions in real time with label-free molecules. A setup with a fixed incident angle in the Kretschmann configuration with gold as the supporting metal is described, both theoretically and experimentally. Simulations of the sensor response based on independently recorded optical (ellipsometric) data of gold show that the sensitivity for three-dimensional recognition layers (bulk) increases with increasing wavelength. For two-dimensional recognition layers (adlayer) maximum sensitivity is obtained within a limited wavelength range. In this situation, the rejection of bulk disturbances, e.g., emanating from temperature variations, decreases, with increasing wavelength. For imaging surface plasmon resonance the spatial resolution decreases with increasing wavelength. Hence, there is always a compromise between spatial resolution, bulk disturbance rejection, and sensitivity. Most importantly, by simultaneously using multiple wavelengths, it is possible to maintain a high sensitivity and accuracy over a large dynamic range. Furthermore, our simulations show that the sensitivity is independent of the refractive index of the prism. (C) 2000 American Institute of Physics. [S0034-6748(00)02909-9].

Journal ArticleDOI
TL;DR: A method to calculate the average blocking probability in all-optical networks using limited-range wavelength conversion using Birman's (1996) model for no wavelength conversion and an analytical expression to compute the blocking probabilities in networks for fixed routing.
Abstract: In this paper we propose a method to calculate the average blocking probability in all-optical networks using limited-range wavelength conversion. Previous works have shown that there is a remarkable improvement in blocking probability while using limited-range wavelength conversion, but these analytical models were either for a path or for a mesh-torus network. Using a graph-theoretical approach, we extend Birman's (1996) model for no wavelength conversion and derive an analytical expression to compute the blocking probabilities in networks for fixed routing. The proposed model is applicable to any network topology. We consider the case where an incoming wavelength can be converted to d adjacent outgoing wavelengths on either side of the input wavelength, in addition to the input wavelength itself, where d is the degree of conversion. When d=0 and d=((C-1)/2), where C is the capacity of a link, the proposed model reduces to the model previously given for no wavelength conversion and the model previously given for full wavelength conversion respectively. Using this model we demonstrate that the performance improvement obtained by full wavelength conversion over no wavelength conversion can almost be achieved by using limited-range wavelength conversion with the degree of conversion, d, being only 1 or 2. In the example networks we considered, for blocking probabilities up to a few percent, the carried traffic with limited conversion degree d=2 was almost equal to the carried traffic for full wavelength conversion. Comparisons to simulations show that our analytical model is accurate for a variety of networks, for various values of the conversion degree (d=1,2,3), and hop length (1-4), and over a wide range of blocking probabilities (>0.0001). The method is also accurate in estimating the blocking probabilities on individual paths (and not just the average blocking probability in the network).

Journal ArticleDOI
TL;DR: The complete optical spectrum of liquid water determined by making use of intense monochromatic x-rays supplied by the wiggler line X21 of the National Synchrotron Light Source is shown.
Abstract: Interaction of light with matter is of paramount importance in nature. The most fundamental property of a material in relation to light is its oscillator strength distribution, i.e., how strongly it absorbs light as a function of wavelength. Once the oscillator strength distribution is determined precisely for a wide enough energy range, the optical constants such as absorbance and reflectance as well as a number of other properties of the material, some of which are seemingly unrelated to photoabsorption, can be deduced. Most important of all is the fact that the interaction of matter with fast charged particles can be described by its complete optical spectra [Inokuti, M. (1986) Photochem. Photobiol. 44, 279–285]. Despite their importance, however, the complete optical spectra of volatile liquids including water have never been obtained accurately because of experimental difficulties inherent in vacuum UV spectroscopy. Inelastic x-ray scattering spectroscopy can provide quantitative data equivalent to those from vacuum UV absorption spectra. Herein, we show the complete optical spectrum of liquid water determined by making use of intense monochromatic x-rays supplied by the wiggler line X21 of the National Synchrotron Light Source.

Journal ArticleDOI
TL;DR: Light waves are shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism, suggesting lossless guiding along this photonic one-dimensional conduction channel.
Abstract: Highly efficient transmission of 1.5 {micro}m light in a two-dimensional (2D) photonic crystal slab waveguide is experimentally demonstrated. The light wave is shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism. At certain wavelength ranges, a complete transmission is observed, suggesting a lossless guiding along this photonic 1D conduction channel.

Journal ArticleDOI
TL;DR: A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM) by use of a total-internal-reflection geometry.
Abstract: A high-resolution fluorescence microscopy technique has been developed that achieves a lateral resolution of better than one sixth of the emission wavelength (FWHM). By use of a total-internal-reflection geometry, standing evanescent waves are generated that spatially modulate the excitation of the sample. An enhanced two-dimensional image is formed from a weighted sum of images taken at different phases and directions of the standing wave. The performance of such a system is examined through theoretical calculations of both the point-spread function and the optical transfer function.

Journal ArticleDOI
TL;DR: The spectrally selective optical properties of wavelength selective radiation emitters and filters based on periodically microstructured metal surfaces were investigated in this article, where the angle dependent emissivity of tungsten gratings with periods of 1.4 μm and 2.0 μm was measured.
Abstract: The spectrally selective optical properties of wavelength selective radiation emitters and filters based on periodically microstructured metal surfaces were investigated. Metal surfaces were structured by the use of a holographic mask and subsequent etching processes. Due to the microstructure, thermally excited surface plasmons couple to electromagnetic radiation. Therefore a structured tungsten surface can act as a selective radiation emitter. The calculation of the absorptance by a rigorous diffraction theory allows the prediction of the emissivity of such structures. The angle dependent emissivity of tungsten gratings with periods of 1.4 μm and 2.0 μm was measured. A peak emissivity of 70% at a wavelength of 1.6 μm was achieved. Band pass filters for the near infrared spectral range based on perforated metal films were investigated theoretically and experimentally. Filters with a grating period of 2.0 μm were produced. A peak transmittance of 80% at a wavelength 2.9 μm was achieved. The optic...

Patent
28 Aug 2000
TL;DR: In this paper, a waveguide filter is presented for separating electromagnetic waves of differing wavelengths by means of transmission through, or reflection from, a two-dimensional frequency selective surface, which consists of one or more patterns so replicated and arranged as to permit the transmission of defined wavelengths of electromagnetic energy, and to reflect other wavelengths.
Abstract: A waveguide filter is hereby presented for separating electromagnetic waves of differing wavelengths by means of transmission through, or reflection from, a two-dimensional frequency selective surface. Electromagnetic energy consisting of any arbitrary wavelength enters a section of waveguide. A two-dimensional array of thin metallic film, either self-supporting or supported by a dielectric film, is transversely located at an arbitrary cross section within the waveguide. The film consists of one or more patterns so replicated and arranged as to permit the transmission of defined wavelengths of electromagnetic energy, and to reflect other wavelengths. By this means, selected wavelengths can be separated from a broad spectrum, and transmitted further along the waveguide. This invention is not limited to any defined cross-section of waveguide, and can be applied to any arbitrary shape. This invention is also not limited to any one pattern of metallic film. Also, a multiplicity of such two-dimensional films may be located longitudinally in the waveguide to increase the filtering effect. Further, such frequency selective surfaces can be combined with coupling means to effect transmission between microstrip and waveguide structures.

Journal ArticleDOI
TL;DR: In this article, the authors examined the properties of inertia-gravity waves observed in the lower stratosphere over Macquarie Island, how these properties vary with season, and the likely source of the waves.
Abstract: This study examines the properties of inertia–gravity waves observed in the lower stratosphere over Macquarie Island, how these properties vary with season, and the likely source of the waves. The waves are observed in high-resolution upper-air ozonesonde soundings of wind and temperature released from Macquarie Island during the 1994 ASHOE–MAESA program. The properties of the inertia–gravity waves observed in the soundings are quantified using hodograph and rotary spectral analyses. The analyzed waves have horizontal wavelengths between 100 and 1000 km, vertical wavelengths between about 1 and 7 km, intrinsic frequencies between f and 2f, and horizontal trace speeds between −50 and 30 m s−1. There appears to be a seasonal cycle in the inertia–gravity wave activity in the lower stratosphere, the minimum being in the austral winter when the background zonal flow is strong and westerly and its vertical shear is positive. In contrast, the variance of the horizontal perturbation winds does not show a...

Journal ArticleDOI
TL;DR: In this article, a transportable multiple-wavelength lidar is presented, which is used for the profiling of optical and physical aerosol properties, and the combined beam can be directed into the atmosphere from −90° to +90° zenith angle by means of a turnable mirror unit.
Abstract: A transportable multiple-wavelength lidar is presented, which is used for the profiling of optical and physical aerosol properties. Two Nd:YAG and two dye lasers in combination with frequency-doubling crystals emit simultaneously at 355, 400, 532, 710, 800, and 1064 nm. A beam-combination unit aligns all six laser beams onto one optical axis. Hence the same air volume is observed by all six beams. The combined beam can be directed into the atmosphere from −90° to +90° zenith angle by means of a turnable mirror unit. From the simultaneous detection of the elastic-backscatter signals and of the Raman signals backscattered by nitrogen molecules at 387 and 607 nm and by water vapor molecules at 660 nm, vertical profiles of the six backscatter coefficients between 355 and 1064 nm, of the extinction coefficients, and of the extinction-to-backscatter ratio at 355 and 532 nm, as well as of the water vapor mixing ratio, are determined. The optical thickness between the lidar and a given height can be retr...

Journal ArticleDOI
TL;DR: In this article, the authors derived analytical expressions for the evolution of phase and group delay after a wave passes through a Gaussian-shaped heterogeneity of half width L. As a function of distance χ, there are two clearly separated regimes, depending upon the wavelength λ of the wave.
Abstract: Using a simple Gaussian beam solution to the one-way scalar wave equation, we derive analytical expressions for the evolution of phase and group delay after a wave passes through a Gaussian-shaped heterogeneity of half width L. As a function of distance χ, there are two clearly separated regimes, depending upon the wavelength λ of the wave. In regime I, when χ/L ≪ πL/λ, the absolute magnitude of the phase delay decreases approximately linearly with χ, and the anomaly does not widen appreciably except by developing small sidelobes with delays of opposite sign. Tomographie inversions of such delays will be damped but are theoretically well posed. In regime II, when χ/L ≫ πL/λ, the absolute delay decreases toward zero as 1/χ, most markedly on the ray itself, and the cross-path shape of the wave front bears little resemblance to the original anomaly. Tomographic inversions of delay times in this regime are ill posed. Group delay times show a similar behavior in the two regimes. Although their rate of decrease with distance is slower in regime I, they develop more disturbing sidelobe behavior off the central ray. The effects of wave front healing for surface waves traveling in two dimensions are less severe than those for body waves in three dimensions; as a result, surface wave inversions will commonly be in regime I. Short-period body wave group delays are also in regime I; nevertheless, the damping of delays in this regime is likely to contribute significantly to the scatter of observed travel time anomalies. Tomographie inversions of long-period body waves, which fall at the limit of regime I, or even in regime II, face perceptible limitations in theoretical resolving power. Finally, we show that there is an asymmetry in the evolution of positive versus negative travel time anomalies.

01 Mar 2000
TL;DR: In this paper, the complete optical spectrum of liquid water was determined by making use of intense monochromatic x-rays supplied by the wiggler line X21 of the National Synchrotron Light Source.
Abstract: Interaction of light with matter is of paramount importance in nature. The most fundamental property of a material in relation to light is its oscillator strength distribution, i.e., how strongly it absorbs light as a function of wavelength. Once the oscillator strength distribution is determined precisely for a wide enough energy range, the optical constants such as absorbance and reflectance as well as a number of other properties of the material, some of which are seemingly unrelated to photoabsorption, can be deduced. Most important of all is the fact that the interaction of matter with fast charged particles can be described by its complete optical spectra [Inokuti, M. (1986) Photochem. Photobiol. 44, 279–285]. Despite their importance, however, the complete optical spectra of volatile liquids including water have never been obtained accurately because of experimental difficulties inherent in vacuum UV spectroscopy. Inelastic x-ray scattering spectroscopy can provide quantitative data equivalent to those from vacuum UV absorption spectra. Herein, we show the complete optical spectrum of liquid water determined by making use of intense monochromatic x-rays supplied by the wiggler line X21 of the National Synchrotron Light Source.

Journal ArticleDOI
TL;DR: In this paper, the experimental results for the cross phase modulation induced transient absorption signal in a 1 mm thick fused silica plate using a white light continuum as a probe were compared with those obtained theoretically by numerically solving the set of nonlinear coupled wave equations describing the propagation of the pump and the probe.
Abstract: We present experimental results for the cross phase modulation (xpm) induced transient absorption signal in a 1 mm thick fused silica plate using a white light continuum as a probe. The fused silica plate mimics the entrance window of a commercial flow cell commonly used in liquid-phase transient absorption measurements. The experimental results are compared with those obtained theoretically by numerically solving the set of nonlinear coupled wave equations describing the propagation of the pump and the probe. The simulations allow for the different group velocities of the pump and probe pulses, and include the influence of the first and second order dispersion on the continuum probe. From the calculations the physical origin of the complex oscillatory feature observed around the zero time delay of each wavelength of the (chirped) continuum has been accurately identified. The influence of propagation effects arising from the finite thickness of the sample is discussed in great detail, and the necessity to work with thin samples, preferably free-flowing jets, is emphasized. The good agreement between theory and experiment indicates that the xpm artifact may be useful for characterizing the continuum probe, in particular its chirp.

Journal ArticleDOI
TL;DR: An integrated geophysical and sedimentological investigation of the Selvage sediment-wave field has revealed that the sediment waves are formed beneath unconfined turbidity currents as discussed by the authors, which is very close to the antidune existence limits.
Abstract: An integrated geophysical and sedimentological investigation of the Selvage sediment-wave field has revealed that the sediment waves are formed beneath unconfined turbidity currents. The sediment waves occur on the lower continental rise and display wavelengths of up to 1 km and wave heights of up to 6 m. Wave sediments consist of interbedded turbidites and pelagic/hemipelagic marls and oozes. Nannofossil-based dating of the sediments indicates a bulk sedimentation rate of 2·4 cm 1000 years-1, and the waves are migrating upslope at a rate of 0·28 m 1000 years-1. Sediment provenance studies reveal that the turbidity currents maintaining the waves are largely sourced from volcanic islands to the south. Investigation of existing models for sediment-wave formation leads to the conclusion that the Selvage sediment waves form as giant antidunes. Simple numerical modelling reveals that turbidity currents crossing the wave field have internal Froude numbers of 0·5-1·9, which is very close to the antidune existence limits. Depositional flow velocities range from <6 to 125 cm-1. There is a rapid increase in wavelength and flow thickness in the upper 10 km of the wave field, which is unexpected, as the slope angle remains relatively constant. This anomaly is possibly linked to a topographic obstacle just upslope of the sediment waves. Flows passing over the obstacle may undergo a hydraulic jump at its boundary, leading to an increase in flow thickness. In the lower 15 km of the wave field, flow thickness decreases downslope by 60%, which is comparable with results obtained for other unconfined turbidity currents undergoing flow expansion

Journal ArticleDOI
TL;DR: In this paper, it was shown that the design wavelength of the filter can be tuned by a modest amount by tilting the filter with respect to the incident beam, theoretically as well as experimentally.

Journal ArticleDOI
TL;DR: Two sediment wave fields have been identified on the flanks of the western Canary Islands of La Palma and El Hierro, using a high-quality 2D and 3D dataset that includes GEOSEA and TOBI imagery, 3.5-kHz profiles, and short sediment cores as mentioned in this paper.

Journal ArticleDOI
TL;DR: Ono et al. as mentioned in this paper proposed to use electron Bernstein waves (EBW) for core heating in high-β spherical tokamak plasmas, like the National Spherical Torus Experiment.
Abstract: The conventional ordinary O-mode and the extraordinary X-mode in the electron cyclotron range of frequencies are not suitable for core heating in high-β spherical tokamak plasmas, like the National Spherical Torus Experiment [M. Ono, S. Kaye, M. Peng et al., in Proceedings of the 17th International Atomic Energy Agency Fusion Energy Conference (International Atomic Energy Agency, Vienna, 1999), Vol. 3, p. 1135], as they are weakly damped at high harmonics of the electron cyclotron frequency. However, electron Bernstein waves (EBW) can be effective for heating and driving currents in spherical tokamak plasmas. Power can be coupled to EBWs via mode conversion of either the X-mode or the O-mode. The two mode conversions are optimized in different regions of the parameter space spanned by the parallel wavelength and wave frequency. The conditions for optimized mode conversion to EBWs are evaluated analytically and numerically using a cold plasma model and an approximate kinetic model. From geometric optics ra...

Journal ArticleDOI
TL;DR: In this article, the authors developed finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength.
Abstract: The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.

Journal ArticleDOI
TL;DR: In this paper, the growth rate of the relativistic electron stream generated by ultra-intense laser is investigated with the help of a two-dimensional particle-in-cell simulation, which includes a binary collision.
Abstract: The magnetic instability driven by the relativistic electron stream generated by ultra-intense laser is investigated with the help of a two-dimensional particle-in-cell simulation, which includes the relativistic binary collision. The linear growth rate of the instability is also studied using the two-stream fluid model, which consists of a fast electron current and a return current. The growth rate is evaluated numerically from the linearized equations of the electron fluids with the Maxwell equations. The kinetic effects of electrons on the magnetic instability are found to reduce the growth rate. The growth rate is maximum at the wavelength near the plasma skin length because of the plasma kinetic effect. When the initial plasma temperature is high, the growth rates of shorter wavelengths are significantly reduced. In the collisional plasma, the growth rates of modes whose wavelength is shorter than the plasma skin length are suppressed and the spectral peak of the growth rate shifts to long wavelength...

Journal ArticleDOI
TL;DR: In this paper, the authors developed an asymptotic theory for the flow kinematics of a thin layer of viscous mud under water surface waves, where the mud depth, the mud Stokes' boundary layer thickness, and the wave amplitude are assumed to be comparable with one another, and much smaller than the wavelength.