Retroreflection Direction Research Articles

Antispecular enhancement in s- and p-polarized electromagnetic waves scattered from random gratings

The scattering of electromagnetic plane waves incident upon a random grating whose grooves are not perpendicular to the plane of incidence is studied. The results display a new effect associated with the weak localization of surface electromagnetic waves in random surfaces. This new effect is similar to enhanced backscattering in the sense that a peak in the intensity of the incoherent component of the scattered light is in a direction opposite to the specular direction, but it differs from enhanced backscattering in that this direction does not coincide with the retroreflection direction and in that it is observed in both p and s polarizations.

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

Abstract The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.

Enhanced backscattering from a rough dielectric film on a reflecting substrate

We carry out computer simulations of the scattering of a beam of light with p or s polarization from a transparent dielectric film (BaSO4) on a perfectly conducting substrate. The dielectric–vacuum interface is assumed to be a random grating; the dielectric–conductor interface is assumed to be planar. It is found that for incident light of either polarization the angular dependence of the incoherent contribution to the mean intensity of the scattered light has a well-defined peak when the scattering angle corresponds to the retroreflection direction (enhanced backscattering). The existence of enhanced backscattering of p-polarized light in this geometry contrasts with its absence in the scattering of p-polarized light from a random grating on a semi-infinite dielectric medium that is characterized by the same roughness parameters and index of refraction. The enhanced backscattering that is observed in the scattering of s-polarized light from a random grating on a semi-infinite dielectric medium is stronger when the scattering takes place from the structure studied. For both polarizations the enhancement is most pronounced when the distance of the perfectly conducting substrate from the mean dielectric–vacuum interface is several (2–10) times the distance of the focusing plane of the rough interface from the mean interface.

Enhanced backscattering of light from a random grating

By the use of Green's second integral theorem we have obtained exact expressions for the scattered electromagnetic field produced by a p- or s-polarized beam of finite width incident from the vacuum side onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic (electric) field in the vacuum and its normal derivative, evaluated on the surface of the grating in the case of p- ( s-) polarization. The coupled pair of inhomogeneous integral equations satisfied by these source functions is solved numerically for each of several thousand realizations of the surface profile, which are generated numerically and possess a Gaussian spectrum. The incoherent component of the differential reflection coefficient averaged over these realizations of the surface profile displays a well-defined peak in the retroreflection direction in the scattering of s-polarized light from a large amplitude random metallic grating but not in the scattering of s-polarized light from a small amplitude random metallic grating. The mean scattering amplitude, regarded as a function of the component of the wave vector of the scattered light parallel to the mean surface at the frequency of the incident light, displays a pole in the nonradiative region in the former case but not in the latter. This suggests that electromagnetic waves of s-polarization are trapped by large amplitude roughness but not by small amplitude roughness. Enhanced backscattering is also observed in the scattering of s-polarized light from a large amplitude random grating on the surface of a nearly transparent dielectric medium. Evidence is presented that the enhanced backscattering observed in the scattering of both p- and s-polarized light from a large amplitude random grating on a perfect conductor is not a single-scattering effect, but is already present in a double-scattering approximation. Finally, it is demonstrated that the enhanced backscattering present in our simulation results is an effect that lies outside the statistical errors caused by our use of a finite number of surface profiles in our calculations.

Enhanced backscattering of light from a non-Gaussian random metal surface

We study theoretically the scattering of a finite beam of p- or s-polarized light from a randomly rough metal surface defined by the equation x3 = ζ(x1), where the surface profile function ζ(x1) is not a Gaussian random process. The surface that we study is a parallel array of identical ridges and grooves, of Gaussian form, whose separations along the x1 axis are random, i.e., a random grating. First we show that the surface defined in this way is a non-Gaussian surface. A numerical algorithm based on the fast Fourier transform is then developed for constructing such surface profiles, and the probability-density functions for the height and slope of the surface at an arbitrary point are calculated. The angular distribution of the intensity of the incoherent component of the light scattered from an ensemble of such surfaces is then calculated by purely numerical methods for surfaces with large root-mean-square slope (=1). A well-defined peak in this angular distribution in the retroreflection direction—enhanced backscattering—is observed for both polarizations. It is shown that this enhanced backscattering is a multiple-scattering effect.

Experimental study of the opposition effect in the scattering of light from a randomly rough metal surface

The opposition effect manifested as a narrow peak in the angular distribution of the intensity of diffusely scattered light in the backward (antispecular or retroreflection) direction has been experimentally investigated. A monostatic bidirectional laser reflectometer was used to measure the opposition effect of copper and gold surfaces under illumination at 0.6328 microm. The results are compared with a recent theory of the elastic scattering of light from a randomly rough metal surface that predicts such a peak in the retroreflectance direction, which, in certain conditions, can be related to the localization of surface polaritons.

Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random metallic grating

We study the scattering of a p-polarized beam incident onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic field and its normal derivative on the surface of the grating. The integral equations satisfied by these functions are solved numerically for each of several hundred realizations of the surface profile possessing a Gaussian spectrum. The diffuse component of the differential reflection coefficient averaged over these realizations displays a well-defined peak in the retroreflection direction for metallic and perfectly conducting random gratings but not for random gratings on dielectric surfaces.

Retroreflectance from a dense distribution of spherical particles

The backscattered intensity from a dense distribution of latex microspheres is measured near the retroreflection direction. It is shown that a sharp peak appears in the retroreflection direction when the volume density is above 1%. The angular width of this peak is much smaller than (wavelength)/(particle size) and cannot be explained by Mie theory, double-passage effects, or radiative-transfer theory. When the particle size D is less than the wavelength λw, a small peak appears at the retroreflection direction. When D is 2–4 times greater than λw, the peak becomes large as the density increases. When D is many times greater than λw, the sharp peak at the retroreflection direction is superimposed upon the Mie-scattering pattern. The angular width of the peak is of the order of (a wavelength)/(a mean free path).

Retroreflectance measurements of photometric standards and coatings

Using a technique that we have developed, the opposition effect (brightening in the retroreflection direction) has been measured for MgCO(3), BaSO(4) paint, and sulfur in the visual region with incandescent illumination and found to be 1.3,1.5, and 1.3, respectively, independent of wavelength. Nextel red, blue, white, and black paints are generally similar. However, in comparison to incoherent illumination, 0.6328-microM laser illumination shows a reduction in diffuse reflectance for angles less than 40 degrees from the incident direction. In addition, the coherent opposition effect may be very large for dark paints. The opposition effect in photometric standards can lead to calibration errors at near opposition and spurious responses in integrating spheres coated with such materials.