Special relativity corrections for space-based lidars

The theory of special relativity is used to analyze some of the physical phenomena associated with space-based coherent Doppler lidars aimed at Earth and the atmosphere. Two important cases of diffuse scattering and retroreflection by lidar targets are treated. For the case of diffuse scattering, we show that for a coaligned transmitter and receiver on the moving satellite, there is no angle between transmitted and returned radiation. However, the ray that enters the receiver does not correspond to a retroreflected ray by the target. For the retroreflection case there is misalignment between the transmitted ray and the received ray. In addition, the Doppler shift in the frequency and the amount of tip for the receiver aperture when needed are calculated. The error in estimating wind because of the Doppler shift in the frequency due to special relativity effects is examined. The results are then applied to a proposed space-based pulsed coherent Doppler lidar at NASA's Marshall Space Flight Center for wind and aerosol backscatter measurements. The lidar uses an orbiting spacecraft with a pulsed laser source and measures the Doppler shift between the transmitted and the received frequencies to determine the atmospheric wind velocities. We show that the special relativity effects are small for the proposed system.     

Andreev and normal reflections at normal metal—Superconductor boundaries: Limitations of the semiclassical approximation

We study the scattering of quasiparticles at a normal metal—superconductor interface using Bogoliubov-de Gennes equations, taking the motion parallel to the interface fully into account. We show that while the Andreev reflection is the dominant scattering process in case of nearly perpendicular impacts (as predicted by the semiclassical theory), the normal reflection becomes increasingly important for quasiparticles with large momenta parallel to the interface, and the semiclassical approximation becomes progressively inadequate. We work out consequence of this feature for spectra of bound states in superconductor—normal metal—superconductor junctions.     

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis

We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a farzone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.     

Scattering from a cylindrical reflector: modified theory of physical optics solution

The problem of scattering from a perfectly conducting cylindrical reflector is examined with the method of the modified theory of physical optics. In this technique the physical optics currents are modified by using a variable unit vector on the scatterer's surface. These current components are obtained for the reflector, which is fed by an offset electric line source. The scattering integral is expressed by using these currents and evaluated asymptotically with the stationary phase method. The results are compared numerically by using physical optics theory, geometrical optics diffraction theory, and the exact solution of the Helmholtz equation. It is found that the modified theory of physical optics scattering field equations agrees with the geometrical optics diffraction theory and the exact solution of the Helmholtz equation.     

Analysis of the resonant scattering of light by cylinders at oblique incidence

We study the resonant scattering of light at oblique incidence by dielectric uncoated and coated cylinders. We develop a stable algorithm that permits us to calculate the resonances of a single dielectric cylinder as the tilting angle varies. This algorithm is based on semiclassical formulas for the distance between resonances. Results show that the resonances and the resonant electromagnetic energy flux near and internal to the cylindrical surface are highly sensitive to variations in the tilting angle. In addition, the coating effects are studied for scattering of light at oblique incidence by an infinite, perfect cylindrical conductor coated by a dielectric layer. In this case the resonance calculations show a peculiar similarity between this light scattering and atomic-molecular scattering. A physical interpretation for these effects is given, based on an analogy of optics and quantum mechanics.     

Scattering of vertical shear waves by a cluster of nanosized cylindrical holes with surface effect

This study considers the multiple scattering of vertical shear waves (SV-waves) by a cluster of nanosized cylindrical holes. When the radius of the holes shrinks to nanometers, surface effects play an important role in their mechanical performance, and the surface elasticity theory is adopted to analyze diffraction phenomena. By using the displacement potential method and wave functions expansion method, the scattering fields around the holes are derived. Both the dynamic stress concentration around the holes and the scattering cross section are calculated to illustrate the effect of surface effects on the multiple scattering of an SV-wave.     

Narrow resonances and ripple fluctuations in light scattering by a spheroid

We develop a semiclassical theory to explain the rapid ripple fluctuations in the extinction efficiency of light scattering by a transparent prolate spheroid. The theory is based on uniform asymptotic expansion of spheroidal radial functions. We have calculated the extinction efficiency for normal and oblique incidence. Our results suggest that the excitation of resonant electromagnetic modes inside a spheroidal particle is an important factor in the ripple structure. To verify this assumption and based on a Breit-Wigner formula, we develop a method to fit the peaks that appear in the spheroid's extinction cross section when some scattering parameters vary. In other words, our calculations suggest that narrow resonances are related to ripple fluctuations, whereas broad resonances contribute to extinction cross-sectional background.     

Linear systems formulation of scattering theory for rough surfaces with arbitrary incident and scattering angles

Scattering effects from microtopographic surface roughness are merely nonparaxial diffraction phenomena resulting from random phase variations in the reflected or transmitted wavefront. Rayleigh-Rice, Beckmann-Kirchhoff. or Harvey-Shack surface scatter theories are commonly used to predict surface scatter effects. Smooth-surface and/or paraxial approximations have severely limited the range of applicability of each of the above theoretical treatments. A recent linear systems formulation of nonparaxial scalar diffraction theory applied to surface scatter phenomena resulted first in an empirically modified Beckmann-Kirchhoff surface scatter model, then a generalized Harvey-Shack theory that produces accurate results for rougher surfaces than the Rayleigh-Rice theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff and the original Harvey-Shack theories. These new developments simplify the analysis and understanding of nonintuitive scattering behavior from rough surfaces illuminated at arbitrary incident angles.     

Fundamental limits of the accuracy of the photoelectric recording of radiation: Interferometric and anemometer aspects

The fundamental limits of the accuracy of the photoelectric recording of the amplitude, visibility and phase of an interference field are investigated using a semiclassical approach by methods of information theory and parameter estimation. A receiving scheme with moving scattering particles is analyzed, which enables the laser anemometer aspect to be included and enables the effect of the phase and number of fringes to be investigated. Translated from Izmeritel’naya Tekhnika, No. 8, pp. 26–30, August, 1996.     

Renormalization-group theory of critical phenomena near the Lambda transition of4He

A review is given on the present status of the renormalization-group theory of observable static and dynamic critical phenomena near the Lambda transition of⁴He. New results of the Aachen theory group, in particular concerning the superfluid density, light scattering intensity, critical first sound, and finite-size effects, are reported. Future directions of theoretical research are briefly discussed.     

A theory of superconductivity in ternary rare-earth compounds. II

In an earlier paper a theory of superconductivity in ternary rare-earth compounds which examined the effects of elastic scattering of conduction electrons by localized 4f electrons was presented. In this paper the theory is extended by treating both elastic and inelastic scattering. Expressions for the phase diagram and the upper critical field are derived and compared with expressions from other theories.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Materials Sciences Division.     

Light emission from whispering-gallery modes in microscopic spheres

The emission of light from whispering-gallery modes excited in microscopic spheres is examined. An evanescent wave is produced by total internal reflection of an optical beam at a planar glass-air interface. This evanescent wave is used to excite whispering-gallery modes in single microscopic spheres placed behind the glass-air interface. The intensity of light emitted into the air half-space from such spheres is measured as a function of scattering angle for both p- and s-polarized input beams. These data are compared with a simple theory for the emission from a point source above a planar glass substrate.     

Acoustic scattering of spherical waves incident on a long fluid-saturated poroelastic cylinder

Acoustic scattering of spherical waves generated by a monopole point source in a perfect (inviscid and ideal) compressible fluid by a fluid-saturated porous cylinder of infinite length is studied theoretically in the present study. The formulation utilizes the Biot theory of dynamic poroelasticity along with the appropriate wave-field expansions, the translational addition theorem for spherical wave functions, and the pertinent boundary conditions to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with a numerical example in which a monopole point source within water is located near a porous cylinder with a water-saturated Ridgefield sandstone formation. The numerical results reveal the effects of source excitation frequency, the cylinder interface permeability condition, and the location of the point source and the field point on the backscattered pressure magnitudes. Limiting cases are considered, and the obtained numerical results are validated by already well-known solutions.     

Inelastic scattering in planetary atmospheres. 2: Polarization of the rotational component

The inelastic part of Rayleigh scattering, which we previously showed can account for the partially filled line profiles of the blue sky observed at high spectral resolution, also explains the variation of polarization across a line profile. At lower spectral resolution, only the rotational part of the molecular scattering is needed to account for the polarization phenomena; translational (Brillouin) shifts can be neglected. Aerosol scattering, like the ground reflection, reduces the polarizations observed in the zenith sky by diluting the molecular (Rayleigh) component. Although the theory agrees well with existing data, more observations of high quality are needed for a thorough test of the Ring effect.     

Anomalous magnetoconductance beyond the diffusion limit

The weak localization contribution to the conductance depends sensitively on the applied magnetic field. This anomalous magnetoconductance provides a unique tool for the identification of weak localization and other phenomena associated with it. The standard theory of the anomalous magnetoconductance is based on the diffusion approximation, which applies to the case where the number of elastic scattering events is very large during a time of phase coherence in the electronic wave. For a strictly two-dimensional film, an arbitrary number of scattering events is considered and marked deviations are found from the standard theory if this number is not large.     

Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere

This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.     

Two different regimes in a V-type three-level atom trapped in an optical cavity

In this paper two different behaviors of a V-type three-level atom which is driven by a classical field in an optical cavity are shown. We show that the behavior of an atom depends on the values of the critical photon number. The system treatment for large enough values of the critical photon number is described by the semiclassical laser theory. In contrast, for small enough values of the critical photon number, the system shows new quantum properties. In the former case, it is shown that the system performs like a conventional laser and in the latter one, the system acts as an effective two-level model. The behaviors of the system are investigated both in the semiclassical approximation and full quantum theory. For comparing the results, computer simulations are implemented.