We present results, obtained by rigorous computational approaches, for light of p- and s-polarization scattered
from two-dimensional, randomly rough, perfectly conducting, lossy metallic, and dielectric surfaces. The perfectly
conducting surfaces we study are characterized by an isotropic power spectrum of the surface roughness and by
an anisotropic power spectrum. The mean differential reflection coefficient and the full angular distribution of
the intensity of the scattered light are calculated for the perfectly conducting and metal surfaces. From the
latter calculations it is found that the computational approach used in these calculations conserves energy in the
scattering from a perfectly conducting and from a lossless metal surface with an error that is smaller than 0.5%.
Finally, we presents results obtained by a numerical, nonperturbative, solution of the reduced Rayleigh equation
for the scattering of p- and s-polarized light from two-dimensional randomly rough, metallic and dielectric
surfaces. We show that the results for the metallic surface are in good agreement with results for the same
metallic surface obtained by the rigorous computational approach.
Numerical results for the spatial distributions of the light transmitted through metallic planar lenses composed
of symmetric nanogroove arrays on the surfaces of a gold film deposited on a dielectric substrate are presented
and explained. Both the near and far-field distributions of the intensity of light transmitted through such films,
which are modeled by two aligned and reversed one-dimensional surface profile functions, are calculated by
the use of a Green's function formalism. The focusing action obtained for different groove-width variations is
investigated thoroughly. Results for an optimal transverse focus based on a quadratic variation of groove width
across the array are also obtained, in addition to the effect of groove shape on the sharpness of planar lens
focusing. Meanwhile, a significant dependence of the focal length on the wavelength of light incident from the
air side through the gold film into a dielectric substrate is found for this detector configuration.
By the use of an impedance boundary condition, the Wiener-Hopf method, and Green's second integral identity
in the plane we obtain a Kirchhoff approximation for the reflection amplitude of a surface plasmon polariton
incident from one metal surface onto its rough boundary with a co-planar surface of a second metal. An example
of the use of this result is presented.
On the basis of the geometrical optics limit of the Kirchhoff approximation we design a one-dimensional random interface between two dielectric media that refracts p- or s-polarized light incident on it at an arbitrary angle of incidence θ0 from one of them into the other at an arbitrary but specified angle of transmission θt that is not defined in terms of θ0 by Snell's law. We call such transmission nonstandard refraction.
We obtain a single integral equation for the scattering amplitude and for the transmission amplitude for light of s polarization incident on a free-standing or supported film, both of whose surfaces are one-dimensional rough
surfaces.
We present approaches to the design of two-dimensional randomly rough surfaces that produce scattered fields
with specified coherence properties, and transform an incident beam with a specified intensity profile into a
scattered beam with a different specified intensity profile. We also show how illuminating a single realization of a
randomly rough surface, drawn from an ensemble of such random surfaces, by a partially coherent polychromatic
(broadband) beam can be used to replace the average over the ensemble of realizations of the surface used to
suppress the speckle produced when the incident field is monochromatic. Finally, we describe an experimental
setup for producing a partially coherent beam by an optical feedback technique, and present experimental results
demonstrating the reduction of speckle by the use of this beam.
We present approaches to the design of a structure that produces an enhanced backscattering peak the ratio of
whose height relative to the height of the background at its position can be as high as 40-50.
We study theoretically the transmission of p- and s-polarized light through a thin, supported, silver or gold film, both of whose surfaces are one-dimensional, periodically corrugated surfaces, as a
function of the wavelength of the incident light. The calculations
are carried out by the use of reduced Rayleigh equations in the form
of a pair of coupled inhomogeneous matrix equations for the amplitudes of the scattered and transmitted Bragg beams. The results
show that enhanced transmission occurs for both p- and s-polarized
incident light for large-amplitude periodic corrugations of the two
surfaces. In p polarization an additional enhancement occurs at the
wavelengths of the surface plasmon polaritons supported by the film.
Thus, slits that pierce the film are not necessary for enhanced
transmission of light through it.
We report experimental results displaying the interference of light produced by a pair of Collett-Wolf beams. These beams are created by a Michelson interferometer, and are either symmetric or antisymmetric with respect to a plane midway between them. In the former case the output radiation from the interferometer in the far-field is a beam with an intensity distribution that displays a narrow bright line at its center that diverges with the distance from the sources much more slowly than the beam itself. In the later case the radiated beam has an intensity distribution with a narrow dark line at its center. These results suggest that the interference of a pair of symmetric Collett-Wolf beams can be used to produce a pseudo-nondiffracting beam. The experimental results are supported by the results of theoretical calculations.
We present an experimental and theoretical investigation of the statistical properties of the light transmitted through a waveguide with a randomly rough section.
We present a new formulation of the self-energy and phase perturbation theories to calculate the reflectivities of randomly rough surfaces. The reflectivities calculated on the basis of our approach are compared with the results of rigorous numerical simulations of the problem and with the results of well controlled laboratory experiments.
In a previous investigation we have studied the excitation of a surface plasmon polariton (SPP) when a volume electromagnetic wave in the form of a beam illuminates a circularly symmetric protuberance or indentation of Gaussian form on an otherwise planar metal surface in contact with vacuum. The fraction of the incident flux that was scattered into a SPP was rather small, of the order of one percent. In this paper, we propose a different form for a circularly symmetric surface defect and show that it is possible to achieve a much higher efficiency for the excitation of a SPP. The surface profile function we employ is of cosinusoidal form along the radial coordinate up to a
radius R0, and vanishes outside this radius. Here R0 is chosen such that the profile function is continuous. By exploiting the circular symmetry of the problem we expand the reduced Rayleigh equation for the p- and s-polarized components of the electromagnetic field above and on a vacuum-metal interface into a set of one-dimensional integral equations that we then solve numerically. The solution of the integral equations in the first Born approximation shows that the scattering amplitude is related to the Bragg vector of the periodic part of the surface. Thus, a specific scattering geometry can be optimized by adjusting the periodicity and consequently the Bragg vector. We report excitation efficiencies that are about 15 times larger than those achieved with a Gaussian profile.
Recently a physical medium was fabricated in which both the effective permittivity and the effective permeability are simultaneously negative over a restricted frequency range. Thus, in this frequency range such a medium is "left--handed", and is characterized by a negative refractive index. In this paper we study the scattering of p-and s-polarized electromagnetic waves from, and their transmission through, a slab of a left--handed medium whose illuminated surface is a one-dimensional randomly rough surface. We assume that the surface profile function is a single-valued function of the coordinate in the mean plane of the surface that is normal to its grooves and ridges, and constitutes a zero-mean, stationary, Gaussian random process. In the frequency range we are interested in, the electric and magnetic excitations give rise to p- and s-polarized surface polaritons, Brewster modes, and waveguide modes in the slab. The reflectivity and the transmissivity of such a slab as a function of the angle of incidence displays structure associated with the existence of a
Brewster angle in both polarizations and the existence of a critical angle for total internal reflection in both polarizations. The presence of surface roughness leads to a shift of the Brewster angle, the sign of which depends on the existence or nonexistence of surface
or guided waves at the frequency of the incident field.
The coherence theory predicts that the correlations in the fluctuations of a source distribution can cause frequency shifts in the spectrum of the emitted radiation, even when the source is at rest relative to the observer. In this paper the changes in the spectrum of light scattered from a randomly rough metal surface are investigated. The experimental results are compared with the results of rigorous computer simulations.
We present an experimental and theoretical study of light scattering and propagation in multimode optical fibers with rough surfaces. In the experiments, performed at λ=655 nm, we used multimode 200 μm diameter silica glass fibers with an etched rough section. As the guided light reaches the rough part of the fiber it is scattered, feeding other modes and leaking out into the surrounding space. After some distance, however, the leakage decreases and the light within the fiber is carried primarily by the modes with low transverse wavenumbers. The light then propagates with a relatively narrow (half-width of about 0.15 rad) and slowly reducing angular spread. To understand this behavior, we develop a diffusion model for the intermode power transfer. The model predicts the formation of a narrow central maximum with a stable propagating angular profile, and relates parameters of the fiber and the surface roughness to the characterstic decay lengths.
We propose a method for designing a one-dimensional random perfectly conducting surface which, when illuminated normally by an s-polarized plane wave, scatters it with a prescribed angular distribution of intensity. The method is applied to the design of a surface that scatters light uniformly within a specified range of scattering angles, and produces no scattering outside this range; a surface that acts as a Lambertian diffuser; and a surface that suppresses single-scattering within a specified range of scattering angles. This method is tested by computer simulations, and a procedure for fabricating such surfaces on photoresist is described.
We propose a method for designing a two-dimensional random Dirichlet
surface which, when illuminated normally by a scalar plane wave,
scatters it with a prescribed circularly symmetric distribution of
intensity. The method is applied to the design of a surface that
scatters light uniformly within a circular region and produces no
scattering outside that region, and a surface that acts as a
Lambertian diffuser. The method is tested by computer simulations,
and a procedure for fabricating such surfaces on photoresist is
described.
Recently a physical medium was fabricated in which both the effective permittivity ε(ω) and the effective permeability μ(ω) are simultaneously negative over a restricted frequency range. Thus, in this frequency range, such a medium is left--handed, and is characterized by a negative refractive index. A left--handed medium should exhibit unusual phenomena associated with the propagation and scattering of electromagnetic waves. In our paper we study the scattering of p- and s-polarized electromagnetic waves from a weakly rough one--dimensional random surface of a left--handed medium. We assume that the surface profile function is a single-valued function of the coordinate in the mean plane of the surface that is normal to its grooves and ridges, and constitutes a zero-mean, stationary, Gaussian random process. We show that in contrast to nonmagnetic media with a negative dielectric function, the planar surface of a left--handed medium can support both p- and s-polarized surface electromagnetic waves. The reflectivity of such a surface as a function of the angle of incidence displays structure associated with the existence of a Brewster angle in both polarizations and the existence of a critical angle for total internal reflection in both polarizations. The angular distribution of the intensity of the light that has been scattered incoherently displays an enhanced backscattering peak, and Yoneda bands, for both polarizations of the incident light.
In this work we consider a structure consisting of a dielectric medium characterized by a dielectric constant ε1 in the region x3 > H, a second dielectric medium characterized by a dielectric constant ε2 in the region ζ(x1) < x < H, and vacuum in the region x < ζ(x1). The surface profile function ζ(x1) is assumed to be a single-valued function of x1 that is differentiable and constitutes a random process. The structure is illuminated from the region x3 > H by s-polarized light whose plane of incidence is the x1x3-plane. By the use of geometrical optics limit of phase perturbation theory we show how to design the surface profile function ζ(x1) in such a way that the mean differential transmission coefficient has a prescribed form within a specific range of the angles of transmission, and vanishes outside this range. In particular, we consider the case that the incident s-polarized light in incident normally on this structure, and the mean intensity of the transmitted light is constant within a specific range of the angle of transmission, and vanishes outside it. Numerical simulation calculations show that the transmitted intensity indeed has this property.
In this work we present experimental and theoretical studies of the scattering of light propagating along a waveguide, a finite part of whose surface is randomly rough. We study the angular distribution of the intensity of the scattered light emerging from different parts of the rough surface. The angular distributions show a strong dependence on the distance of the radiating section from the front edge of the rough part of the waveguide. The experimental results are supported by theoretical studies of the problem. The angular distribution of the intensity of the light scattered into vacuum were calculated by means of a solution of the corresponding reduced Rayleigh equations.
In a recent theoretical study of the scattering of a surface plasmon polariton by a circularly symmetric protuberance or indentation on an otherwise planar metal surface in contact with vacuum, it was found that the angular dependence of the intensity of the volume electromagnetic waves scattered into the vacuum region possesses a maximum in the plane of incidence at a polar scattering angle of approximately 28 degree(s). This suggests that if a p-polarized volume electromagnetic field in the form of a beam of finite width is incident on the same surface defect, the efficiency of exciting a surface plasmon polariton will be greatest for a polar angle of incidence close to 28 degree(s). To test this hypothesis, in this paper we study this problem theoretically. The reduced Rayleigh equations for the amplitudes of the p- and s-polarized components of the scattered field are reduced to a set of one-dimensional integral equations by exploiting the circular symmetry of the surface defect, which is assumed to have a Gaussian form. The efficiency of exciting surface plasmon polaritons in this fashion is calculated as a function of the polar angle of incidence, and is found to be maximal when this angle is close to 28 degree(s).
The phenomenon of enhanced backscattering in the scattering of light from a randomly rough surface is the presence of a well-defined peak in the retroreflection direction in the angular dependence of the intensity of the light scattered diffusely from the surface. A striking feature of this phenomenon is that it occurs for any angle of incidence. Suppose, however, that one would like to have a random surface that displays enhanced backscattering for only a single, specified, angle of incidence. Such a surface could be useful, for example, in situations where one wishes to position a source (and hence the detector) at a specified direction with respect to the site at which the scattering surface is situated. In this paper we show how a one-dimensional random surface can be generated that produces an enhanced backscattering peak for only a specified angle of incidence when illuminated by p-polarized light whose plane of incidence is perpendicular to the generators of the surface. This surface is defined by a power spectrum (the Fourier transform of the surface height autocorrelation function) given by g(Q) = (π)/(4(Δ)k)[θ (Q-k1+Δk)θ(k1+Δk-Q)+θ(Q-k2+Δk-Q)θ (k2+Δk-Q)+θ(-Q-k1+Δk)θ (k1+Δk+Q)+θ(-Q-k2+Δk)θ (k2+Δk+Q)], where θ(z) is the Heaviside unit step function, k1= kR-k0,k2=kR-k0, k(subscript R is the real part of the wavenumber of the surface plasmon polariton of frequency ω supported by the planar vacuum-metal interface, and k0 is related to the angle of incidence measured clockwise from the x3-axis by k0=(ω/c)sinθ0. An explanation is provided for why a surface defined by this power spectrum produces enhanced backscattering at only the angle of incidence given by θs=-θ0, and it is confirmed by numerical calculations of the angular dependence of the intensity of the light scattered diffusely from it.
We present an experimental study of the reflectivity of 2D randomly rough well-characterized, isotopic metallic surfaces. We proceed by comparing the experimental data with theoretical approaches of three perturbation theories and the Kirchhoff approximation. The samples were fabricated in photoresist, and their metallized surface profiles constitute good approximations to Gaussian-correlated, Gaussian random processes. The correlation lengths of these surfaces range form approximately one fifth to two times the IR wavelength employed.
We consider a scattering system consisting of a dielectric film deposited on a semi-infinite metal, and focus on the wavelength dependence of the total integrated scattering and angle resolved scattering from such a system. In particular we study theoretically by a large scale rigorous numerical simulation approach the reflectivity, R((lambda) ), as well as the total scattered energy, U((lambda) ), of such systems as functions of the wavelength of the incident light. The scattering system consists of vacuum in the region x3 $GTR d1+(zetz) 1(x1), a dielectric film in the region, d2+(zetz) 1(x1), and a metal in the region x3 < d2 + (zetz) (x1). This system is illuminated from the vacuum side by p-polarized light whose wavelength is allowed to vary from 0.2micrometers to 1.2micrometers . The film is assumed to have a dielectric function that is insensitive to the wavelength of the incident light. In obtaining the numerical results reported here the metal substrate is taken to be silver. The dielectric function of silver for a given wavelength is obtained by interpolation from experimental values. The surface profile functions,(zetz) 1,2(x1), are assumed to be either zero or single-valued functions of x1 that are differentiable as many times as is necessary, and to constitute zero-mean, stationary Gaussian random processes. Their surface height auto-correlation function is characterized by a Gaussian power spectrum. We study and discuss the wavelength dependence of R((lambda) ) and U((lambda) ) for several scattering systems obtained by turning on and off the surface profile functions (zetz) 1,2(x1) and/or the correlation between these two surface profile functions.
The physical system we consider in this work consists of vacuum in the region x3 $GTR (zetz) (x1), and a dielectric medium characterized by a complex dielectric constant (epsilon) in the region x3 < (zetz) (x1). The surface profile function (zetz) (x1) is assumed to be a single-valued function of x1, that is differentiable as many times as is necessary, and to constitute a zero-mean stationary, Gaussian random process. It has been recently been shown that a local relation can be written between L(x1(omega) ) equalsV [deltaH2$GTR(x1,x3(omega) )/(delta) x3]x3equals0) and H(x1(omega) ) equalsV [H2$GTR(x1,x3(omega) )]x3equals0, where H2$GTR(x1,x3(omega) ) is the single nonzero component of the total magnetic field in the vacuum region, in the case of a p-polarized electromagnetic field whose plane of incidents is the x1x3-plane. This relation has the form L(x1(omega) ) equals I(x1(omega) )H(I(x1(omega) ), where the surface impedance I(I(x1(omega) ) depends on the surface profile function (zetz) (x1) and on the dielectric constant (epsilon) of the dielectric medium. A completely analogous relation exists when L(x1(omega) ) equalsV [(delta) E2$GTR(x1,x3(omega) )/(delta) x3]x3equals0) and H(x1(omega) ) EQV [E2(x1,x3(omega) )]x3equals0, where E2$GTR(x1,x3(omega) ) is the single nonzero component of the electric field in the vacuum region, in the case of an s-polarized electromagnetic field whose plane of incidence is the x1x3-plane. Our goal in this work is to obtain the relation between the values of L(x1(omega) ) and H(x1(omega) ) averaged over the ensemble of realizations of the surface profile function (zetz) (x1). This we do by the use of projection operators and Green's second integral identity in the plane.
In this work we consider a structure consisting of vacuum in the region x3$GTR(zetz) (x1); a dielectric film characterized by a real,positive, dielectric constant (epsilon) in the region -D < x3 < (zetz) (x1); and a vacuum in the region x3<-D. The surface profile function (zetz) (x1) is assumed to be a single-valued funtion of x1, that is differentiable, and constitutes a random process. This structure is illuminated from the region x3 $GTR (zetz) (x1) by s-polarized light whose plane of incidence is the x1x3-plane. By the use of the geometrical optics limit of phase perturbation theory we show how to design the surface profile function (zetz) (x1) in such a way that the mean differential transmission coefficient has a prescribed form within a specified range of the angle of transmission, and vanishes outside this range. In particular, we consider the case in which the transmitted intensity is constant within a specified range of the angle of transmission, and vanishes outsides it. Rigorous numerical simulation calculations show that the transmitted intensity indeed has this property.
In this work we study theoretically the scattering of p-polarized light of frequency (omega) from a system consisting of a dielectric medium (prism) characterized by a dielectric constant (epsilon) 0 in the region x3 $GTR D; a metal film characterized by a complex, frequency-dependent dielectric function(epsilon) 1((omega) ) in the region 0 < x3 < D; a dielectric film characterized by a dielectric constant (epsilon) 2 in the region (zetz) (x1) < x- 3) < 0; and vacuum ((epsilon) 3 equals 1) in the region x3 < (zetz) (x1). The light whose plane of incidence is the x1x3- plane, in incident through the prism. For the surface profile function (zetz) (x1) we take the form (zetz) (x1) equals -d(theta) (x1)(theta) (L-x(1), where (theta) (x1) is the Heaviside unit step function. Thus we have a dielectric film thickness d and dielectric constant (epsilon) 2 covering the half of the lower surface (x3 equals 0) of the metal film defined by x1$GTR0, or a dielectric film of thickness d and dielectric constant (epsilon) 2 covering the part of the lower surface (x3 equals 0) of the metal film defined by 0 < x1 < L. The reduced Rayleigh equation for the amplitude of the light scattered back into the prism, R(qk), is obtained, and solved by the Wiener-Hopf method, and the result is used to calculate the intensity of the scattered field in the far field region as a function of x1 for a fixed value of x3 for several values of the wavelength of the incident light. The results provide information about the scattering of the surface plasmon polariton at the metal-vacuum interface, excited by the incident light, by an index step on that interface. A brief discussion of the transmission of light through this system is also given.
We calculate the short-range contributions C(1) and C(10) to the angular intensity correlation function for the scattering of s-polarized light from a one-dimensional random interface between two dielectric media. The calculations are carried out on the basis of a new approach that separates out explicitly the contributions C(1) and C(10) to the angular intensity correlation function. The contribution C(1) displays peaks associated with the memory effect and the reciprocal memory effect. In the case of a dielectric-dielectric interface, which does not support surface electromagnetic surface waves, these peaks arise from the coherent interference of multiply-scattered lateral waves supported by the interface. The contribution C(10) is a structureless function of its arguments.
We propose a method of designing and fabricating 2D random surfaces that scatter light uniformly within a specified range of angles and produce no scattering outside that range. The proposed method is tested by means of computer simulations. Preliminary experimental results are also presented.
We investigate theoretically changes in the spectrum of light scattered from a system with a random surface (the Wolf effect). The system we consider is the Otto attenuated total reflection configuration that is widely used to couple the incident light to surface polaritons. The angular dependence of the intensity of the light scattered incoherently from this system exhibits sharp, intense peaks at the angles of optimum excitation/radiation of the surface polaritons supported by it. In the vicinity of each of these resonance angles the spectrum of the scattered light is red-shifted for scattering angles larger than this angle, and is blue-shifted for scattering angles smaller than this angle. The magnitude of the shift is three to four orders of magnitude larger than that predicted for disordered volume media. We conclude that the Otto attenuated total reflection configuration is another example of bounded systems with random surfaces which are more attractive subjects for experimental studies of the Wolf effect than systems with a single random surface or disordered volume systems.
Because their electromagnetic fields are localized to the surfaces that support them, surface electromagnetic waves are more sensitive to topographical and dielectric perturbations in their propagation path than are volume electromagnetic waves incident on the same surface perturbations. This suggests that a near-field optical microscopy based on surface electromagnetic waves could reconstruct surface profiles with greater resolution than one based on the scattering of volume electromagnetic waves from surfaces with the same profiles. In this work we examine this possibility by studying the scattering of a surface plasmon polariton propagating along a vacuum-metal interface and incident on a surface defect. We calculate the intensity of the total field in the vacuum region at constant height above the unperturbed surface to first order in the surface profile function. The result can be written in the form of a convolution of the surface profile function and a function that depends only on the properties of the metal surface. We invert this result by a Fourier transform method to obtain the surface profile function. As experimental intensity data we use the results of a rigorous numerical solution of the corresponding reduced Rayleigh equation for the scattering amplitude. We show that surface structures with lateral dimensions of the order of or smaller than one-tenth the wavelength of the incident surface plasmon polariton can be reconstructed in this way, as well as extended segments of a randomly rough surface profile.
We propose a method of designing and fabricating one- dimensional random surfaces that scatter light uniformly within a specified range of angles and produce no scattering outside this range. The proposed method is tested by means of computer simulations, and preliminary experimental results are also presented.
The enhanced backscattering of light from randomly rough metal surfaces, which manifests itself as a well-defined peak in the retroreflection direction in the angular distribution of the intensity of the light scattered incoherently has attracted a great deal of attention recently. The backscattering phenomenon is attributed to the coherent interference of multiply-scattered surface plasmon polaritons excited on a metal surface with their time-reversed partners. The coherent interference of multiply-scattered lateral waves excited in the scattering of light from strongly rough dielectric surfaces is known to lead to an enhanced backscattering peak in the angular distribution of the intensity of s-polarized light scattered from them. In this paper we present an analytical theory of the scattering of light from a one- dimensional randomly rough interface between two media. One of the media is a dipole-active medium that is characterized by a frequency-dependent dielectric function, that is negative in a restricted frequency range, while the other is characterized by a frequency-independent, real, positive dielectric constant. We assume that the interface profile function is a single-valued function of the coordinate in the mean plate of the interface that is normal to its grooves and ridges, and constitutes a zero-mean, stationary, Gaussian random process. We assume that either p- or s-polarized electromagnetic waves are incident on the interface from the medium whose dielectric constant is frequency-independent. We study the angular distribution of the light that has been scattered incoherently as a function of the frequency of the incident light. The evolution of the enhanced backscattering peak in the case of p-polarized incident light as the frequency of the incident light is tuned through the frequencies of the dipole-active excitations in the medium whose dielectric function is frequency-dependent, is studied. Different mechanisms for the formation of the enhanced backscattering peak in different frequency regions are discussed.
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