Experimental and numerical studies of the scattering of light from a two-dimensional randomly rough interface in the presence of total internal reflection: optical Yoneda peaks.

The scattering of polarized light from a dielectric film sandwiched between two different semi-infinite dielectric media is studied experimentally and theoretically. The illuminated interface is planar, while the back interface is a two-dimensional randomly rough interface. We consider here only the case in which the medium of incidence is optically more dense than the substrate, in which case effects due to the presence of a critical angle for total internal reflection occur. A reduced Rayleigh equation for the scattering amplitudes is solved by a rigorous, purely numerical, nonperturbative approach. The solutions are used to calculate the reflectivity of the structure and the mean differential reflection coefficient. Optical analogues of Yoneda peaks are present in the results obtained. The computational results are compared with experimental data for the in-plane mean differential reflection coefficient, and good agreement between theory and experiment is found.

Scattering of a surface plasmon polariton by a localized dielectric surface defect.

On the basis of a rigorous, nonperturbative, purely numerical solution of the corresponding reduced Rayleigh equation for the scattering amplitudes we have studied the scattering of a surface plasmon polariton by a two dimensional dielectric defect on a planar metal surface. The profile of the defect is assumed to be an arbitrary single-valued function of the coordinates in the plane of the metal surface, and to be differentiable with respect to those coordinates. When the defect is circularly symmetric and the dependence of the scattering amplitudes on the azimuthal angle is expressed by a rotational expansion, the reduced Rayleigh equation is transformed into a pair of one-dimensional integral equations for each value of the rotational quantum number. This approach is applied to a defect in the form of an isotropic Gaussian function. The differential cross sections for the scattering of the incident surface plasmon polariton into volume electromagnetic waves in the vacuum above the surface and into other surface plasmon polaritons are calculated, as well as the intensity of the field near the surface. These results differ significantly from the corresponding results for a metallic defect on a metallic substrate.

The Goos-Hänchen effect for surface plasmon polaritons.

By means of an impedance boundary condition and numerical solution of integral equations for the scattering amplitudes to which its use gives rise, we study as a function of its angle of incidence the reflection of a surface plasmon polariton beam propagating on a metal surface whose dielectric function is ɛ1(ω) when it is incident on a planar interface with a coplanar metal surface whose dielectric function is ɛ2(ω). When the surface of incidence is optically more dense than the surface of scattering, i.e. when |ɛ2(ω)|≫|ɛ1(ω)|, the reflected beam undergoes a lateral displacement whose magnitude is several times the wavelength of the incident beam. This displacement is the surface plasmon polariton analogue of the Goos-Hänchen effect. Since this displacement is sensitive to the dielectric properties of the surface, this effect can be exploited to sense modifications of the dielectric environment of a metal surface, e.g. due to adsorption of atomic or molecular layers on it.

Scattering of electromagnetic waves from two-dimensional randomly rough penetrable surfaces.

An accurate and efficient numerical simulation approach to electromagnetic wave scattering from two-dimensional, randomly rough, penetrable surfaces is presented. The use of the Müller equations and an impedance boundary condition for a two-dimensional rough surface yields a pair of coupled two-dimensional integral equations for the sources on the surface in terms of which the scattered field is expressed through the Franz formulas. By this approach, we calculate the full angular intensity distribution of the scattered field that is due to a finite incident beam of p-polarized light. We specifically check the energy conservation (unitarity) of our simulations. Only after a detailed numerical treatment of both diagonal and close-to-diagonal matrix elements is the unitarity condition found to be well satisfied for the nonabsorbing case (U>0.995), a result that testifies to the accuracy of our approach.

Cloaking from surface plasmon polaritons by a circular array of point scatterers.

In recent years it has been demonstrated both theoretically and experimentally that it is possible to cloak a predefined region of space from interaction with external volume electromagnetic waves, rendering an arbitrary object inside this region invisible to an outside observer. The several strategies that have been developed for achieving such cloaking cannot be applied directly to the cloaking of a surface feature from surface plasmon polaritons propagating on that surface. Here we demonstrate that it is possible to generate an arrangement of two concentric rings of point scatterers on a metal surface that significantly reduces the scattering of surface plasmon polaritons from an object enclosed within this circular structure.

Design and fabrication of random phase diffusers for extending the depth of focus.

We present a method for designing non-absorbing optical diffusers that, when illuminated by a converging beam, produce a specified intensity distribution along the optical axis. To evaluate the performance of the diffusers in imaging systems we calculate the three-dimensional distribution of the mean intensity in the neighborhood of focus. We find that the diffusers can be used as depth-of-focus extenders. We also propose and implement a method of fabricating the designed diffusers on photoresist-coated plates and present some experimental results obtained with the fabricated diffusers.

Synthetic spectra from rough-surface scattering.

We present a method for designing a one-dimensional, deterministic, perfectly conducting rough surface that scatters light at a fixed scattering angle with an intensity whose dependence on the frequency of a plane wave incident normally upon it reproduces the infrared spectrum of a known substance within a specified region of frequencies. Such a surface can therefore be used in a correlation spectrometer for the identification of unknown substances.

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.