Helmholtz Fermi surface harmonics: an efficient approach for treating anisotropic problems involving Fermi surface integrals

We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface (FS) of metallic materials. The method introduces a set of numerically calculated generalized orthonormal functions which are the solutions of the Helmholtz equation defined on the FS. Noteworthy, many properties of our proposed basis set are also shared by the FS harmonics introduced by Philip B Allen (1976 Phys. Rev. B 13 1416), proposed to be constructed as polynomials of the cartesian components of the electronic velocity. The main motivation of both approaches is identical, to handle anisotropic problems efficiently. However, in our approach the basis set is defined as the eigenfunctions of a differential operator and several desirable properties are introduced by construction. The method is demonstrated to be very robust in handling problems with any crystal structure or topology of the FS, and the periodicity of the reciprocal space is treated as a boundary condition for our Helmholtz equation. We illustrate the method by analysing the free-electron-like lithium (Li), sodium (Na), copper (Cu), lead (Pb), tungsten (W) and magnesium diboride (MgB2)

Control of single attosecond pulse generation from the reflection of a synthesized relativistic laser pulse on a solid surface

The influence of the carrier-envelope phase (CEP) of the driving laser pulse on the generation of single attosecond (as) pulses from surface harmonics by using the polarization gating technique is investigated in detail. It is found that the modulation depth of the high-order harmonic spectrum depends on the CEP, and a strong single 68 as pulse can be generated when the CEP is stable and has the proper value. The physical origin of the influence of the CEP is explained in terms of the oscillating mirror model. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.2997342]

Broadband XUV polarimetry of high harmonics from plasma surfaces using multiple Fresnel reflections

High-harmonic generation (HHG) by nonlinear interaction of intense laser pulses with gases or plasma surfaces is the most prominent way of creating highly coherent extreme ultraviolet (EUV/XUV) pulses. In the last years, several scientific applications have been found which require the measurement of the polarization of the harmonic radiation. We present a broadband XUV polarimeter based on multiple Fresnel reflections providing an extinction rate of 5-25 for 17-45 nm which is particularly suited for surface harmonics. The device has first been tested at a gas harmonic source providing linearly polarized XUV radiation. In a further experiment using HHG from plasma surfaces, the XUV polarimeter allowed a polarization measurement of high harmonic radiation from plasma surfaces for the first time which reveals a linear polarization state as predicted for our generation parameters. The generation and control of intense polarized XUV pulses-together with the availability of broadband polarizers in the XUV-open the way for a series of new experiments. For instance, dichroism in the XUV, elliptically polarized harmonics from aligned molecules, or the selection rules of relativistic surface harmonics can be studied with the broadband XUV polarimeter.

Temporal characterization of attosecond pulses emitted from solid-density plasmas

The generation of high harmonics from solid-density plasmas promises the production of attosecond (as) pulses orders of magnitude brighter than those from conventional rare gas sources. However, while spatial and spectral emission of surface harmonics has been characterized in detail in many experiments proof that the harmonic emission is indeed phase locked and thus bunched in as-pulses has only been delivered recently (Nomura et al 2009 Nat. Phys. 5 124-8). In this paper, we discuss the experimental setup of our extreme ultraviolet (XUV) autocorrelation (AC) device in detail and show the first two-photon ionization and subsequent AC experiment using solid target harmonics. In addition, we describe a simple analytical model to estimate the chirp between the individual generated harmonics in the sub- and mildly relativistic regime and validate it using particle-in-cell (PIC) simulations. Finally, we propose several methods applicable to surface harmonics to extend the temporal pulse characterization to higher photon energies and for the reconstruction of the spectral phase between the individual harmonics. The experiments described in this paper prove unambiguously that harmonic emission from solid-density plasmas indeed occurs as a train of sub- femtosecond pulses and thus fulfills the most important property for a next-generation as-pulse source of unprecedented brightness.

Resonant second harmonics generation of the submillimeter surface wave in the semiconductor superlattice bounded by a metal

In this study, the process of the resonant second harmonics generation of the submillimeter (SM), which is of interest for design of the semiconductor frequency multipliers is evaluated. Particularly, the possibility to use the semiconductor superlattice-metal structures as an effective second harmonics generator is demonstrated.

Modeling videokeratoscopic height data with spherical harmonics

Purpose: All currently considered parametric models used for decomposing videokeratoscopy height data are viewercentered and hence describe what the operator sees rather than what the surface is. The purpose of this study was to ascertain the applicability of an object-centered representation to modeling of corneal surfaces. Methods: A three-dimensional surface decomposition into a series of spherical harmonics is considered and compared with the traditional Zernike polynomial expansion for a range of videokeratoscopic height data. Results: Spherical harmonic decomposition led to significantly better fits to corneal surfaces (in terms of the root mean square error values) than the corresponding Zernike polynomial expansions with the same number of coefficients, for all considered corneal surfaces, corneal diameters, and model orders. Conclusions: Spherical harmonic decomposition is a viable alternative to Zernike polynomial decomposition. It achieves better fits to videokeratoscopic height data and has the advantage of an object-centered representation that could be particularly suited to the analysis of multiple corneal measurements.

The effect of the nonparabolicity of the free carriers dispersion law on the propagation of surface polaritons in a semiconductor-metal structure

The results of a study on the influence of the nonparabolicity of the free carriers dispersion law on the propagation of surface polaritons (SPs) located near the interface between an n-type semiconductor and a metal arc reported. The semiconductor plasma is assumed to be warm and nonisothermal. The nonparabolicity of the electron dispersion law has two effects. The first one is associated with nonlinear self-interaction of the SPs. The nonlinear dispersion equation and the nonlinear Schrodinger equation for the amplitude of the SP envelope are obtained. The nonlinear evolution of the SP is studied on the base of the above mentioned equations. The second effect results in third harmonics generation. Analysis shows that these third harmonics may appear as a pure surface polariton, a pseudosurface polariton, or a superposition of a volume wave and a SP depending on the wave frequency, electron density and lattice dielectric constant.

Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in the Voigt geometry

Theoretical and experimental results associated with the studies of different properties of surface-type waves (SW) in plasma-like medium-metal structures are reviewed. The propagation of surface waves in the Voigt geometry (the SW propagate across the external magnetic field, which is parallel to the interface) is considered. Various problems dealing with the linear properties of the SW (dispersion characteristics, electromagnetic fields topography, influence of the inhomogeneity of the medium, etc.); excitation mechanisms of the plasma-metal waveguide structures (parametric, drift, diffraction, etc. mechanisms); nonlinear effects associated with SW propagation (higher harmonics generation, self-interaction, nonlinear damping, nonlinear interactions, etc.) are presented. In many cases the results are valid for both gaseous and solid-state plasmas. © 1999 Elsevier Science B.V. All rights reserved.

Resonant generation of the second harmonic of a surface wave on a plasma-metal boundary

The process of resonant generation of the second harmonic of the surface wave, propagating along the external magnetic field at the plasma-metal boundary is considered. The periodic process of the energy exchange between the first and the second harmonics of the wave is investigated as well. It is shown that the process under study is periodic one. The analytical expressions are obtained and numerical estimations are presented for characteristic time of nonlinear energy exchange. The self-action effect of main frequency wave is account for harmonics interaction. It is shown that the effect leads to nonlinear phenomena attenuation, which expresses in narrowing possible value interval of harmonics amplitudes during energy exchange process and in increasing the nonlinear interaction time.

Third harmonic generation of the surface wave in the semiconductor-metal slowing-down structure

A nonlinear process is considered of the surface wave third harmonics generation in a slowing-down semiconductor-metal structure. The process is conditioned by non-parabolicity of the charge carrier dispersion law. It is shown that in narrow-gap semiconducting materials it is necessary to account for the process together with the surface wave second harmonics generation conditioned by nonlinearity of quasi-hydrodynamics and the Maxwell equations. The conclusion is made that the third harmonies amplitude in narrow-gap semiconductors may exceed substantially the signal amplitude at the 3w frequency in a gas plasma and be of the same order with the surface waves second harmonies amplitude.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds acid precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%-20% weaker than observed, The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a targe amount of high-frequency intraseasonal variations, While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency EI Nino-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15 degrees west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Anharmonic surface interactions for biomolecular screening and characterization.

The acoustic response of conventional mechanical oscillators, such as a piezoelectric crystal, is predominantly harmonic at modest amplitudes. However, here, we observe from the electrical response that significant motional anharmonicity is introduced in the presence of attached analyte. Experiments were conducted with streptavidin-coated polystyrene microbeads of various sizes attached to a quartz crystal resonator via specific and nonspecific molecular tethers in liquid. Quantitative analysis reveals that the deviation of odd Fourier harmonics of the response caused by introduction of microbeads as a function of oscillation amplitude presents a unique signature of the molecular tether. Hence, the described anharmonic detection technique (ADT) based on this function allows screening of biomolecules and provides an additional level of selectivity in receptor-based detection that is often associated with nonspecific interactions. We also propose methods to extract mechanical force-extension characteristics of the molecular tether and activation energy using this technique.

Alignment of nanoparticles formed on the surface of 6H-SiC crystals irradiated by two collinear femtosecond laser beams

Nanoripples with periods of 150 and 80 nm are formed on the surface of 6H-SiC crystals irradiated by the p-polarized 800 nm and the s-polarized 400 nm femtosecond lasers, respectively. When both of the two collinear laser beams focus simultaneously on the sample surface, nanoparticles are formed on the whole ablation area, and they array in parallel lines. We propose and confirm that the second harmonics in the sample surface excited by the incident lasers plays an important role in the formation of nanostructures.