Enhanced backscattering and blazing effect from gratings, quasi-gratings and randomly rough surfaces

The blazing effect is probably the most important property of diffraction gratings used for spectroscopic purposes. On the other hand, the enhanced backscattering phenomenon has been generally studied in the framework of scattering from randomly rough surfaces. Using numerical results from rigorous theories, it will be shown that these phenomena, which have very different origins, should have more precise definitions. In a special case of a randomly rough surface formed by random corners, it will be shown that the effects of these phenomena are sometimes very difficult to distinguish.     

Enhanced transmission through randomly rough surfaces

We present an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar. The first is a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the transmitted light (enhanced transmission). The second is an additionally well defined peak in the forward direction in the angular distribution of the intensity of the incoherent component of the transmitted light, when the illuminated surface is not only randomly rough but has even symmetry as well (enhanced refraction). A fully automated bidirectional reflectometer has been used to measure the intensity of the incoherent component of He-Ne laser light transmitted through gold and silver films of these two types and the results are compared with the predictions of theoretical calculations of the enhancement effects.     

Enhanced transmission through randomly rough surfaces

Abstract

We present an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar. The first is a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the transmitted light (enhanced transmission). The second is an additionally well defined peak in the forward direction in the angular distribution of the intensity of the incoherent component of the transmitted light, when the illuminated surface is not only randomly rough but has even symmetry as well (enhanced refraction). A fully automated bidirectional reflectometer has been used to measure the intensity of the incoherent component of He-Ne laser light transmitted through gold and silver films of these two types and the results are compared with the predictions of theoretical calculations of the enhancement effects.     

Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces

A review is made of theoretical and experimental work on retroreflection enhancements in the diffuse component of light elastically reflected from randomly rough surfaces. These effects are seen as a narrow peak in the angular distribution of the intensity of diffusely reflected light which is centered about the direction for reflected light motion antiparallel to the original incident beam. This peak is observed in the scattering of light from many different types of rough surfaces and has been studied in fields as diverse as solid state physics, astronomy, geophysics, meterology and radar. Work covering all of these fields will be presented in this review.

Retroreflection enhancements arise both from shadow casting properties of surface irregularities and from the phase coherence of retroreflected light. These mechanisms can act to create retroreflection enhancements from rough surfaces of dielectric and/or metallic compositions and of surface disorders characterizable on length scales which are large, comparable to or small compared to the wavelength of the scattered light.

Specific discussions will be presented of three types of enhanced retroreflectance: (1) A treatment of the optical glory and Heiligenschein phenomena which are concerned with the meterological and geophysical study of light reflected from clouds and terraine will be given. (2) The theory of the opposition effect, encountered in astronomy as an enhanced retroreflection in the light scattered from atmosphereless planets and space debris, will be used to provide a theoretical basis to understand shadowing effects. (3) A recently discovered phenomenon of enhanced retroreflection from weakly rough metallic mirrors, associated with the Anderson localization of surface waves, is also presented. This last phenomenon and its relationship to the study of the Anderson localization of surface waves will be emphasized throughout our discussions.

Similar enhancement effects in the scattering of acoustic waves from rough surfaces and a brief outline of some recent work on optical backscattering enhancements due to the Anderson localization of bulk polariton modes, is also presented.     

Pulse broadening of enhanced backscattering from rough surfaces

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l≳λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Pulse broadening of enhanced backscattering from rough surfaces

Abstract

Recently, we presented a study of pulse scattering by rough surfaces based on the first-order Kirchhoff approximation which is applicable to rough surfaces with RMS slope less than 0.5 and correlation distance l?λ. However, there has been an increased interest in enhanced backscattering from rough surfaces, study of which requires inclusion of the second-order Kirchhoff approximation with shadowing corrections. This paper presents a theory for the two-frequency mutual coherence function in this region and shows that the multiple scattering on the surface gives rise to an additional pulse tail in the direction of enhanced backscattering. The theory predicts pulse broadening approximately 20% greater than that caused by single scattering alone for a delta-function incident pulse and typical surface parameters. Analytical results are compared with Monte Carlo simulations and millimetre-wave experiments for the one-dimensional rough surface with RMS height 1λ and correlation distance 1λ, showing good agreement.     

Wetting, spreading, and adsorption on randomly rough surfaces

The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first-order transition in the adsorbed film thickness, which we term "Wenzel prewetting", occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting.     

Elastoplastic contact between randomly rough surfaces

I have developed a theory of contact mechanics between randomly rough surfaces. The solids are assumed to deform elastically when the stress sigma is below the yield stress sigma(Y), and plastically when sigma reaches sigma(Y). I study the dependence of the (apparent) area of contact on the magnification. I show that in most cases the area of real contact A is proportional to the load. If the rough surface is self-affine fractal (Hurst exponent H) the whole way up to the lateral size L of the nominal contact area, then (assuming no plastic deformation) A approximately L(H).     

Numerical,analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

Abstract

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

A new bistatic model for electromagnetic scattering from randomly rough surfaces

In this paper we propose a bistatic model for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Green's function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) and the integral equation model for second-order multiple scattering (IEM2M). Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross- and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Green's function. It is expected that our result for the complementary scattering coefficient is more accurate and more general, even when the effect of the error function related terms is neglected. As a result, the proposed model is expected to have wider applicability with a better accuracy. Numerical simulations are provided to demonstrate the validity of the proposed model.     

The transverse correlation length for randomly rough surfaces

It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx ₃=(x ₁), where the surface profile function (x ₁) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x ₁)(x ₁)/²(x ₁)=W (|x ₁–x ₁|) has the Lorentzian formW(|x ₁|)=a ²/(x ₁ ² +a ²) we find that d=0.9080a; when it has the Gaussian formW(|x ₁|)=exp(–x ₁ ² /a ²), we find that d=1.2837a; and when it has the nonmonotonic formW(|x ₁|)=sin(x ₁/a)/(x ₁/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) [the Fourier transform ofW(|x ₁|)] decays to zero with increasing |Q|. We also obtain the functionP(itx ₁), which is defined in such a way that, ifx ₁=0 is a zero of (x ₁),P(x ₁)dx ₁ is the probability that the nearest zero of (x ₁) for positivex ₁ lies betweenx ₁ andx ₁+dx ₁.     

Adhesion between elastic bodies with randomly rough surfaces

I have developed a theory of adhesion between an elastic solid and a hard randomly rough substrate. The theory takes into account the fact that partial contact may occur between the solids on all length scales. I present numerical results for the case where the substrate surface is self-affine fractal. When the fractal dimension is close to 2, complete contact typically occurs in the macroasperity contact areas. For a fractal dimension larger than 2.5, the area of (apparent) contact decreases continuously when the magnification is increased.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Bistatic scattering and depolarization by randomly rough surfaces: application to the natural rough surfaces in X-band

Abstract

The scattering of waves by random rough surfaces has important applications in the remote sensing of oceans and land. The problem of developing a model for rough surfaces is very difficult since, at best, the scattering coefficient σ⁰ is dependent upon (at least) the radar frequency, geometrical and physical parameters, incident and observation angles, and polarization. The problem of electromagnetic scattering from a randomly rough surface is analysed using the Kirchhoff approximation (stationary phase, scalar approximation), the small-perturbation model and the two-scale models. A first major new consideration in this paper is the polarimetric signature calculations as a function of the transmitter location and receiver location for a bistatic radio-link. We calculate the like- and cross-polarized received power directly using the scattering coefficients, without calculating the Mueller matrix. Next, a study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models (in the bistatic case) is presented. Comparisons between the numerical calculations and the models are made for various surface rms heights and correlation lengths both normalized to the incident wavenumber (denoted by σ and L, respectively). By using these two parameters to form a two-dimensional space, the approximate regions of validity are then established. The second major new consideration is the development of a theoretical two-scale model describing bistatic reflectivity as well as the numerical results computed for the bistatic radar cross section from rough surfaces especially from the sea and snow-covered surfaces. The results are used to show the Brewster angle effect on near-grazing angle scattering.     

Heat transfer between elastic solids with randomly rough surfaces

We study the heat transfer between elastic solids with randomly rough surfaces. We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the non-contact regions. We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For solids with very smooth surfaces, as is typical in many modern engineering applications, the interfacial separation in the non-contact regions will be very small, and for this case we show the importance of the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies.     

Contact mechanics for layered materials with randomly rough surfaces

The contact mechanics model of Persson is applied to layered materials. We calculate the M function, which relates the surface stress to the surface displacement, for a layered material, where the top layer (thickness d) has different elastic properties than the semi-infinite solid below. Numerical results for the contact area as a function of the magnification are presented for several cases. As an application, we calculate the fluid leak rate for laminated rubber seals.