c&J -H __ __ !!!!I I May 1997 OPTICS COMMUNICATIONS ELSEVIER Optics Communications 137 (1997) 359-366 Full length article Multiple scattering in particulate surfaces: Cross-polarization ratios and shadowing effects F. GonzBlez, J.M. Saiz, P.J. Valle, F. Moreno zyxwvutsrqponmlkjihgfedcbaZYX Departamento de Fisica Aplicada, Gnrpo de Opticcr. Unirersidad de Cantabria, 39005 Santander. Spain Received 9 July 1996; revised 12 November 1996; accepted 3 December 1996 zyxwvutsrqponmlkjihgfedcbaZYXWV Abstract Multiple scattering and cross-polarization effects, as well as their relationship with the surface particle density and the angle of incidence, are experimentally analyzed for metallic particulate surfaces. The analysis includes measurements (in the plane of incidence) of the co- and cross-polarized scattered intensities from surfaces constituted by spherical metallic particles (diameter of 1.1 km approximately) on conducting flat substrates, illuminated by a He-Ne laser (A = 0.633 km). Shadowing is specially studied through its effects on the cross-polarization ratios for high values of either the angle of incidence or the surface particle density. 1. Introduction Several methods have been proposed in recent years for the analysis of multiple scattering by very rough surfaces [ 1,2] and some related effects, as the enhanced backscatter- ing (EBS) and the depolarization of the incident light. Since many years ago a well accepted mode1 of surface used for analyzing multiple scattering effects is that con- sisting of protuberances of regular shape sited on a flat substrate [3]. Furthermore, this kind of surfaces are of interest for practical applications, such as monitoring mir- ror contamination [4], detection of surface defects in semi- conductor industry [5], etc. During the last few years, many authors have focused their attention on the theoreti- cal [6- 1 l] and experimental [ 12-181 research of light scattering by protuberances on, or above, a flat interface. Most of these works considered only an isolated particle [9-l I] or a sample with low Surface Particle Density (SPD) [12-141 and therefore multiple scattering and, con- sequently, depolarization effects were not reported. In a previous work [19], a simple surface model for analyzing multiple scattering and related effects was presented. This consisted on a flat substrate with only two small scatters (assumed as dipoles) whose separation was varied in order to show when, and how, their mutual electromagnetic interaction started to play an important role. Although this mode1 reproduced and explained some experimental results for protuberances comparable to the incident wavelength, it did not take into consideration important effects, like shadowing, and their influence on the multiple scattering. The aim of this work is to give more insight into the mechanisms of multiple scattering and related effects (EBS and depolarization of the incident light), and their relation- ship with the SPD and the angle of incidence. Conse- quently, a set of experimental measurements of the co- and cross-polarized scattered intensities (both terms will be considered later) have been carried out. The surfaces are constituted by spherical metallic particles of size compara- ble to the wavelength on conducting flat substrates. A detailed analysis for different values of the SPD and for several angles of incidence is presented. We will show how geometrical shadowing plays an important role when either the angle of incidence or the SPD take high values. This paper has been organized as follows. In Section 2 we briefly show the experimental arrangement used for the measurement of co- and cross-polarized scattered intensi- ties. Also, we show a description (manufacturing, etc.) of the samples employed. In Section 3 the main experimental 0030.4018/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved. PII SOO30-4018(96)00783-3