Extension of the geometric optics approximation to the scattering from rough layers

The algorithm to retrieve wind speed in a wide swath from the normalized radar cross section (NRCS) was developed for the data of Dual Frequency Precipitation Radar (DPR) operating in scanning mode installed onboard a Global Precipitation Measurement (GPM) satellite. The data for Ku-band radar were used. Equivalent NRCS values at nadir were estimated in a wide swath under the geometrical optics approximation from off-nadir observations. Using these equivalent NRCS nadir values and the sea buoys data, the new parameterization of dependence between NRCS at nadir and the wind speed was obtained. The algorithm was validated using ASCAT (Advanced Scatterometer) data and revealed good accuracy. DPR data are promising for determining wind speed in coastal areas.

The Wentzel, Kramers, and Brillouin (WKB) approximation of geometrical optics is widely used in plasma physics, quantum mechanics, and reduced wave modeling, in general. However, it is well-known that the approximation breaks down at focal and turning points. In this paper, we present an unsupervised numerical implementation of the recently developed metaplectic geometrical optics framework, which extends the applicability of geometrical optics beyond the limitations of WKB, such that the wave field remains finite at caustics. The implementation is in 1D and uses a combination of Gauss-Freud quadrature and barycentric rational function inter- and extrapolation to perform an inverse metaplectic transform numerically. The capabilities of the numerical implementation are demonstrated on Airy's and Weber's equations, which both have exact solutions to compare with. Finally, the implementation is applied to the plasma physics problem of linear conversion of X mode to electron Bernstein waves at the upper hybrid layer and a comparison is made with results from fully kinetic particle-in-cell simulations. In all three applications, we find good agreement between the exact results and a reduced wave modeling paradigm of metaplectic geometrical optics.

The problem of electromagnetic scattering from a randomly rough surface is analyzed using the Kirchhoff approximation (stationary phase, scalar approximation), the small perturbation model and the two-scale model. The authors show that physical and geometrical optics approximations can be used for a rough sea surface. A small perturbation model gives a satisfactory solution. Unfortunately, it only applies to a smooth sea surface. Therefore, these methods have been shown to be limited in their regions of validity. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wave number (denoted by k/spl sigma/ and kL, respectively). The two-scale model proposed in this paper is the method which tries to conciliate the two previous aspects. One application is made in the ocean surface case. A set of experimental data, describing simultaneous bistatic radar cross section and forward radar cross section measurements of sea clutter taken with a moderately high resolution X-band scatterometer system operating near grazing incidence for both horizontal and vertical polarizations over a range of low grazing bistatic angles, is used but not presented in this paper to examine the applicability of bistatic scattering models.

We study the electromagnetic scattering problem on a random rough surface when the height distribution of the profile belongs to the family of alpha-stable laws. This allows us to model peaks of very large amplitude that are not accounted for by the classical Gaussian scheme. For such probability distributions with infinite variance the usual roughness parameters such as the RMS height, the correlation length or the correlation function are irrelevant. We show, however, that these notions can be extended to the alpha-stable case and introduce a set of adapted roughness parameters that coincide with the classical quantities in the Gaussian case. Then we study the scattering problem on a stationary alpha-stable surface and compute the scattering coefficient under the first-order Kirchhoff and small-slope approximations. An analytical formula is given in the high-frequency limit, which generalizes the well known geometrical optics approximation. Some numerical results are given and discussed.

This paper introduces the background, aim, experimental design, configuration and data processing for an airborne test flight of the HY-2 Microwave scatterometer (HSCAT). The aim was to evaluate HSCAT performance and a developed data processing algorithm for the HSCAT before launch. There were three test flights of the scatterometer, on January 15, 18 and 22, 2010, over the South China Sea near Lingshui, Hainan. The test flights successfully generated simultaneous airborne scatterometer normalized radar cross section (NRCS), ASCAT wind, and ship-borne-measured wind datasets, which were used to analyze HSCAT performance. Azimuthal dependence of the NRCS relative to the wind direction was nearly cos(2w), with NRCS minima at crosswind directions, and maxima near upwind and downwind. The NRCS also showed a small difference between upwind and downwind directions, with upwind crosssections generally larger than those downwind. The dependence of airborne scatterometer NRCS on wind direction and speed showed favorable consistency with the NASA scatterometer geophysical model function (NSCAT GMF), indicating satisfactory HSCAT performance.

Wave effects in the gravitational lensing of electromagnetic radiation by compact objects in astrophysics are treated. In the regime where the influence of diffraction is severe, solutions of the wave equation appropriate for lensing in astrophysics (which is of the form of the Schroumldinger equation for Coulomb scattering) are obtained. In the WKB regime, previous formulations are refined and extended to the case in which a part of the source is directly behind the lensing mass. Wave effects tend to be largest for this geometry which requires that radiation at a caustic be treated. The autocorrelation function of the electric field and the related frequency dependence of the radiation are emphasized, in addition to the diffraction pattern, to measure the deviations from the solutions obtained in the approximation of geometrical optics. In contrast, gravitational lensing is independent of frequency in the usual treatment which is based upon geometrical optics. Numerical computations are performed to indicate how the wave effects depend upon the relevant parameters including especially the size of the source. Wave effects are most significant at radio frequencies and for lensing by stellar and planetary masses. The importance of wave effects is governed by the ratio of the Schwarzschild radius of the lensing mass to the wavelength of the radiation.

A geometrical optics approximation was used for calculations of inelastic (Raman and fluorescent) scattering on particles with large size parameters. The inelastic part of the radiation was obtained by use of the principle of ray reversibility. The technique presented simplifies the computations and provides a geometric interpretation of how far-field patterns can be calculated by use of the internal field distributions. The numerical results for homogeneous spherical particles are compared with the classic dipole solution.

In the gravitational lensing of gravitational waves, wave optics should be used instead of geometrical optics when the wavelength λ of the gravitational waves is longer than the Schwarzschild radius of the lens mass ML. For gravitational lensing of chirp signals from the coalescence of supermassive black holes at redshift zS ~ 1 relative to the Laser Interferometer Space Antenna, the wave effects become important for a lens mass smaller than ~108 M☉. For such cases, we compute how accurately we can extract the mass of the lens and the source position from the lensed signal. We consider two simple lens models: the point-mass lens and the SIS (singular isothermal sphere). We find that the lens mass and the source position can be determined to within ~0.1% of [(S/N)/103]-1 for a lens mass larger than 108 M☉ and 10% of [(S/N)/103]-1 for a lens mass smaller than 107 M☉ because of the diffraction effect, where S/N is the signal-to-noise ratio of the unlensed chirp signals. For the SIS model, if the source position is outside the Einstein radius, only a single image exists in the geometrical optics approximation, so that the lens parameters cannot be determined, while in the wave optics cases we find that the lens mass can be determined even for ML < 108 M☉. For the point-mass lens, one can extract the lens parameters even if the source position is far outside the Einstein radius. As a result, the lensing cross section is an order of magnitude larger than that for the usual strong lensing of light.

The travel time of signals reflected or refracted by a rough surface is investigated in the geometrical optics approximation. It is shown that surface roughness typically decreases the mean travel time in the case of large-scale roughness, when only one specularly reflecting point moves randomly around its unperturbed position, resulting in a negative travel-time bias (toward early echoes). In the opposite limiting case of multipath propagation, when many specular points exist on a random surface, the travel-time bias is always positive. General results are illustrated by two examples related to ocean remote sensing which involve sound scattering from the ocean surface and bottom.

Schwarzschild black-hole interiors, bounded by event horizons and terminated by spacelike singularities, are regions where all physical observers are inevitably destroyed. In the geometric optics approximation, waves follow null geodesics to the singularity. However, outside the geometric optics regime, the behavior of wave propagation can be rich and nuanced, even in such extreme habitats. In this work, we show that axial gravitational perturbations in the interior of a Schwarzschild black hole can form overdamped (nonoscillatory) quasibound states that decay before reaching the singularity. Using Kruskal-Szekeres coordinates to avoid coordinate ambiguities, we identify these modes and analyze their eigenfunctions. Contrary to earlier claims, we find that the Regge-Wheeler master function of these modes have nonzero amplitude at the future event horizon but decay before interacting with the singularity. We consider observations of the modes along timelike geodesics. This work suggests that certain gravitational fluctuations can hover transiently within the black-hole interior, challenging common assumptions about wave behavior in uncharted and extreme regions of spacetime.

We study the propagation of an electromagnetic field in a weak gravitational background generated by a rotating mass. The solution of the Maxwell equations beyond the geometrical optics shows, together with the well-known deflection and rotation of the polarization plane already present in the geometrical optics approximation, new classical dispersive effects. We analyze such effects at first order in the gravitational constant $G$. In the case of an incoming wave with linear polarization they consist in the development of a component of circular polarization, a breaking of the orthogonality of the electric and magnetic fields, and additional contributions to the deflection of the beam and the rotation of the polarization plane.

: The mixed problem for strictly hyperbolic first order systems in regions containing a multiple corner is considered. Geometric optics approximations are studied and in certain cases are used to construct counter-examples. (Author)

Textured silicon solar cells have been generally studied in the geometrical optics approximation. This description predicts no dependence of reflectance or other optical properties on the size of the texture pyramids. In this work textures are represented as two-dimensional periodic diffraction gratings and their optical properties are analyzed with rigourous numerical methods. It is concluded that reflectance significantly increases with respect to the geometrical optics limit for pyramid sizes smaller than around 300 nm. Besides, for small pyramids the light transmitted into the substrate is not tilted with respect to the normal to the surface. Additional calculations are made to assess the effect of the random distribution of the pyramids. Copyright © 2004 John Wiley & Sons, Ltd.

Light scattering by media consisting of Maxwell 3-foci concave particles in the geometrical optics approximation

Interpreting the radiative properties of advanced high strength steel using the geometric optics ray-tracing approximation