[Paper Review] A random walk through surface scattering phenomena: Theory and phenomenology

Ingve Simonsen|arXiv (Cornell University)|Aug 1, 2004

Scientific Research and Discoveries37 references3 citations

TL;DR

This paper provides a comprehensive theoretical and computational review of electromagnetic wave scattering from randomly rough surfaces, focusing on multiple scattering phenomena such as enhanced backscattering, satellite peaks, angular intensity correlations, and second harmonic generation. It derives and applies the reduced Rayleigh equation and small-amplitude perturbation theory to explain coherent effects arising from surface disorder, offering a unified framework for understanding wave-matter interactions in disordered media across diverse scientific and technological applications.

ABSTRACT

No surface is perfectly planar at all scales. The notion of flatness of a surface therefore depends on the size of the probe used to observe it. As a consequence rough interfaces are abundant in nature. Here the old, but still active field of rough surface scattering of electromagnetic waves is addressed. This topic has implications and practical applications in fields as diverse as observational astronomy and the electronics industry. This article reviews the theoretical and computational foundation and methods used in the study of rough surface scattering. Furthermore, it presents and explains the physical origin of a series of multiple scattering surface phenomena. In particular what is discussed are: the enhanced backscattering and satellite peak phenomena, coherent effects in angular intensity correlation functions and second harmonic generated light (a non-linear effect).

Motivation & Objective

• To establish a theoretical and computational foundation for understanding electromagnetic wave scattering from randomly rough surfaces, which are ubiquitous in nature and technology.
• To explain the physical origin of coherent multiple scattering phenomena such as enhanced backscattering and satellite peaks in rough surface scattering.
• To analyze angular intensity correlation functions and second harmonic generation in rough surface systems, highlighting non-linear and correlation effects.
• To bridge theoretical models with numerical simulations, particularly for weakly and strongly rough surfaces, using perturbation theory and the reduced Rayleigh equation.
• To provide a unified framework for studying coherent and non-linear optical effects in disordered systems, relevant to applications in astronomy, materials science, and electronics.

Proposed method

• Derives the reduced Rayleigh equation from Maxwell's equations under the Rayleigh hypothesis, enabling analysis of scattering from randomly rough surfaces.
• Applies small-amplitude perturbation theory to compute scattering amplitudes, with explicit expressions for the χ-functions in both p- and s-polarization states.
• Uses the transition matrix and scattering potential formalism to describe multiple scattering processes in random media.
• Employs many-body perturbation theory and numerical simulation techniques based on the extinction theorem to model scattering from surfaces with varying roughness.
• Introduces statistical descriptions of random rough surfaces using Gaussian and self-affine models, with numerical generation of surface topographies.
• Analyzes coherent effects via reciprocity, unitarity, and energy conservation constraints in the scattering problem, ensuring theoretical consistency.

Experimental results

Research questions

• RQ1 What are the physical mechanisms behind enhanced backscattering and satellite peak formation in rough surface scattering?
• RQ2 How do angular intensity correlation functions behave for weakly and strongly rough surfaces, and what do they reveal about multiple scattering effects?
• RQ3 What role do surface plasmon polaritons play in localization and coherent backscattering on randomly rough surfaces?
• RQ4 How does second harmonic generation emerge in scattering from rough surfaces, and what are the conditions for its observation?
• RQ5 To what extent can the reduced Rayleigh equation and small-amplitude perturbation theory accurately describe scattering from surfaces with varying degrees of roughness?

Key findings

• Enhanced backscattering and satellite peaks arise from coherent multiple scattering, with the peak intensity scaling as the square of the surface correlation length in the weakly rough regime.
• Angular intensity correlation functions exhibit short-range correlations for weakly rough surfaces and long- or infinite-range correlations for strongly rough surfaces, indicating the presence of extended multiple scattering paths.
• Surface plasmon polaritons localized on randomly rough surfaces can exhibit Anderson-like localization, with a characteristic localization length determined by surface disorder and material properties.
• Second harmonic generation is significantly enhanced in strongly rough surfaces due to non-linear response and multiple scattering interference, as confirmed by numerical simulations.
• The χ-functions for p- and s-polarized waves in small-amplitude perturbation theory explicitly account for dielectric contrast and wavevector dependencies, enabling quantitative prediction of scattering amplitudes.
• The reduced Rayleigh equation provides a consistent and accurate framework for modeling scattering from rough surfaces, especially when combined with statistical surface descriptions and numerical methods.