Nano-optics of surface plasmon polaritons

We develop a theory for laser-induced periodic surface structure by associating each Fourier component of induced structure with the corresponding Fourier component of inhomogeneous energy deposition just beneath the surface. We assume that surface roughness, confined to a region of height much less than the wavelength of light, is responsible for the symmetry breaking leading to this inhomogeneous deposition; we find strong peaks in this deposition in Fourier space, which leads to predictions of induced fringe patterns with spacing and orientation dependent on the angle of incidence and polarization of the damaging beam. The nature of the generated electromagnetic field structures and their relation to the simple "surface-scattered wave" model for periodic surface damage are discussed. Our calculation, which is for arbitrary angle of incidence and polarization, applies a new approach to the electrodynamics of randomly rough surfaces, introducing a variational principle to deal with the longitudinal fields responsible for local field, or "depolarization," corrections. For a $p$-polarized damaging beam our results depend on shape and filling factors of the surface roughness, but for $s$-polarized light they are essentially independent of these generally unknown parameters; thus an unambiguous comparison of our theory with experiment is possible.

Laser-induced periodic surface structure. I. Theory

This review is intended to provide a critical and up-to-date survey of the analytical approximate methods that are encountered in scattering from random rough surfaces. The underlying principles of the different methods are evidenced and the functional form of the corresponding scattering amplitude or cross-section is given. The reader is referred to the original papers in order to obtain the explicit expressions of the coefficients and kernels. We have tried to identify the main strengths and weaknesses of the various theories. We provide synthetic tables of their respective performances, according to a dozen important requirements a valuable method should meet. Both scalar acoustic and vector electromagnetic theories are equally addressed.

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A critical survey of approximate scattering wave theories from random rough surfaces

Atomic beam techniques are presently being used in many branches of surface physics such as studies of the particle-surface physisorption potential, surface structure, surface phonons, nucleation and growth on metal and insulator surfaces, surface diffusion and accommodation and sticking of molecules. This review concentrates on diffractive phenomena from surfaces, which up to now were investigated mainly with helium. The theoretical background for diffraction calculations is outlined and representative examples of different applications are given. The main subjects covered are: structural determinations of chemisorbed and physisorbed systems, investigations of disordered surfaces, selective adsorption resonances, diffusion and nucleation studies and investigations of growth and phase transitions on surfaces. Diffraction results obtained with Ne, Ar, and are also summarized.

https://iopscience.iop.org/article/10.1088/0034-4885/61/12/001/pdf

Atomic beam diffraction from solid surfaces

The development of near-field optics theory is reviewed. We first recall that near-field optics is not limited to near-field microscopy. Broadly speaking, it concerns phenomena involving evanescent electromagnetic waves. The importance of such waves was ignored for a long time in optical and surface physics until the emergence of scanning near-field optical microscopes. Taking evanescent waves into account prevents the use of any simple approximation in the set of Maxwell's equations. The various theoretical approaches of near-field optics are discussed from the point of view of their ability to assess evanescent electromagnetic waves. We discuss the main results of the application of the various practical schemes which all rely on a numerical procedure. This review was received in February 1996.

https://iopscience.iop.org/article/10.1088/0034-4885/59/5/002/pdf

Near-field optics theories

The diffraction of electromagnetic waves from the rough surface of a material of finite permittivity is examined for the case where the wavelength of the incident radiation is comparable to the dimensions of the surface roughness. Two methods of calculation studied are the Rayleigh method and the extinction-theorem integral-equation method. The latter is shown to have a unique exact solution. This property is, in turn, used to show how the Rayleigh method can be modified to give convergent results. The extinction theorem is also used to reduce the Rayleigh equations to a simpler form. These reduced equations, which are extremely convenient to use in the case of small roughness, are applied in this case to find perturbative expressions for the reflected field and for the surface-plasmon dispersion relation.

Optical properties of rough surfaces: General theory and the small roughness limit

A method of testing the validity of the Rayleigh assumption is presented. The test can be applied for any one-dimensional or two-dimensional surface of analytic shape. It can be used for Dirichlet and Neumann boundary conditions and also when the surface is penetrable and a refracted field exists. The test is based on the asymptotic evaluation of the diffracted order amplitudes and in this way is similar to Millar's potential-theory analysis.

Limits of convergence of the Rayleigh method for surface scattering

In this paper we present an analysis of the conditioning character of the matrices obtained in the different methods for solving the integral equations that appear in the scattering of waves from a hard corrugated surface. It is found that the matrices derived from the Rayleigh hypothesis become ill conditioned for large corrugations when the approach is not valid at any rate. The method based on the extinction theorem developed by Masel, Merrill, and Miller is analytically correct, but it becomes ill conditioned and no practical numerical solutions can be obtained for large values of the corrugation strength, depending on the precision of the computer used. Finally the self-consistent method with the numerical procedure developed by Garcia and Cabrera is well conditioned and leads always to a good practical numerical solution for all kinds of corrugations, no matter how large.

Ill-conditioned matrices in the scattering of waves from hard corrugated surfaces

A perturbative theory of optical, rough-surface scattering must avoid certain pitfalls that are caused by components of the electric field being discontinuous at the surface. A theory which eliminates this problem is developed. The theory is simpler than other methods and is generally applicable to optical surface scattering in the perturbative limit. Scattering intensities from a rough dielectric surface are obtained, and the effect of roughness on the surface-plasmon dispersion relation is calculated. The methods developed are especially suitable for film-layered structures and are used to calculate the scattering from a surface with an overlayer.

N. R. Hill

Papers

Optical properties of rough surfaces: General theory and the small roughness limit

Limits of convergence of the Rayleigh method for surface scattering

Ill-conditioned matrices in the scattering of waves from hard corrugated surfaces

Integral-equation perturbative approach to optical scattering from rough surfaces

Van der Waals forces and molecular diffraction from metal surfaces, with application to Ag(111)