Multiple light scattering from metal and dielectric rough surfaces

A numerical study is done on light scattering from one-dimensional random rough surfaces supporting both dielectrics and metals. The influence of the corrugation on the Brewster angle as well as on the angular distribution of transmitted intensity into the dielectric is investigated. The authors also obtain enhanced backscattering in the light reflected from metallic surfaces. Finally they discuss the influence of roughness on the drop of reflectance due to polariton absorption.     

Magnetic field effects on the localization of electromagnetic waves in random 1D systems which are almost periodic

The effects of an externally applied magnetic field on the Anderson localization of electromagnetic waves in an alternating layered system of vacuum and semiconducting slabs are studied. Specifically, a waveguide formed from perfectly conducting parallel plates which contain between them an array of vacuum and n-type semiconductor slabs is examined in the presence of an external static magnetic field applied parallel to both the plates and the slab surfaces. The widths of the slabs in the array are random but with a randomness such that the array of slabs is almost periodic, and we study only electromagnetic modes which propagate perpendicular to the slab surfaces. The localization length is obtained by studying the reflection and transmission properties of a finite array of slabs in the limit that it becomes semi-infinite. Two types of system are treated: (i) a reciprocal system which exhibits a localization length that does not depend on the sign of the applied magnetic field, and (ii) a non-reciprocal system which exhibits a localization length that depends on the sign of the applied magnetic field.     

Electrostatic and electromagnetic surface shape resonances

The homogeneous integral equations that give the electromagnetic field in the vicinity of a protuberance or a depression on the otherwise planar interface with vacuum of a semi-infinite dielectric medium or a thin dielectric film on a semi-infinite substrate have been obtained. The Rayleigh hypothesis, the vectorial equivalent of the Kirchhoff integral, and the extinction theorem have been used for this purpose. The assumption that the perturbation of the vacuum dielectric interface has cylindrical symmetry about the normal to the nominal surface allows a significant simplification of these integral equations to be carried out. We have used Gaussian quadrature schemes to convert the resulting integral equations into matrix equations, and have obtained the frequencies of the shape resonances by equating to zero the determinants of the matrices obtained. Calculations have been carried out for Gaussian (x ₃=Aexp(–x ² /R ²)) and exponential (x ₃=Aexp(–x /R)) surface profiles, and convergent results obtained for values ofA/R of the order of unity.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Random surfaces that suppress single scattering

We present a method for numerically generating a one-dimensional random surface, defined by the equation x(3)=zeta(x(1)), that suppresses single-scattering processes in the scattering of light from the surface within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.     

Design of two-dimensional random surfaces with specified scattering properties

A method is proposed for designing a two-dimensional randomly rough Dirichlet surface that, when illuminated at normal incidence, scatters a scalar plane wave with a specified angular distribution of its intensity. The method is validated by computer simulation calculations.     

Resonant scattering of surface-plasmon polariton pulses by nanoscale metal defects

We have theoretically investigated the dynamics of the scattering of surface-plasmon polariton (SPP) pulses by single nanoscale metal defects through a rigorous calculation of the time dependence of the reflected and transmitted SPP and of the angular distribution of the scattered light. SPP resonances that occur at deep Gaussian grooves are probed with SPP pulses, the resonant scattering being unequivocally manifested by (a) the exponential tails of the scattered SPP and light pulses and (b) the delay time of the transmitted SPP pulse.     

A reciprocal phase-perturbation theory for rough-surface scattering

We study the scattering of a scalar plane wave from a two-dimensional, randomly rough surface, on which the Dirichlet boundary condition is satisfied. The scattering amplitude is obtained in the form of the Fourier transform of an exponential, in which the exponent is written as an expansion in powers of the surface profile function. It is shown that the latter expansion can be written in such a way that the corresponding scattering matrix is manifestly reciprocal. Numerical results for the reflectivity, and for the contribution to the mean differential reflection coefficient from the incoherent component of the scattered field, are obtained and compared with the predictions of small-amplitude perturbation theory and the Kirchhoff approximation. As the wavelength of the incident wave is varied continuously the results of the phase-perturbation theory change continuously from those of the small-amplitude perturbation theory to those of the Kirchhoff approximation.     

Surface plasmons propagating parallel to the grooves of a large amplitude grating

The dispersion relation is obtained for a surface plasmon propagating parallel to the grooves of a large amplitude grating. Two variants of the Rayleigh method arc used: the first requires the evaluation of the zeros of a determinant; the second yields the dispersion relation in terms of the solution of a matrix eigenvalue problem. The dispersion relations are solved numerically for a sinusoidal and for a symmetric sawtooth grating profile, yielding in each case an infinity of discrete branches.     

Nonlinear s-polarized surface plasmon polaritons

We have examined the dispersion relations for s-polarized surface plasmon polaritons, guided by (a) the interface between a semi-infinite metal and dielectric medium, and (b) a metal film bounded by semi-infinite dielectric media for situations in which one or more of the dielectric media are characterized by an intensity-dependent refractive index. We found that s-polarized waves satisfy the dispersion relations for very thin metal films bounded by nonlinear dielectric media. These waves exist only for power levels above a threshold that depends on the material parameters. We also comment on the experimental feasibility of observing these waves.