Discrete dipole approximation for lossy plasmonic background.

The discrete dipoles approximation method is exploited to study light scattering near a cylindrical cavity, made in an absorbing plasmonic surrounding medium. To the best of our knowledge, this is the first use of the method for the metal background. Our two-dimensional numerical simulation of the local fields demonstrates a good performance of the approach. Its high accuracy is proven by comparison with the known analytical solution.

Soliton content in the standard optical OFDM signal.

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic transmission lines. In general, the NLSE describes the co-existence of dispersive waves and soliton pulses. The propagation of a signal in such a nonlinear channel is conceptually different from linear systems. We demonstrate here that the conventional orthogonal frequency-division multiplexing (OFDM) input optical signal at powers typical for modern communication systems might have soliton components statistically created by the random process corresponding to the information content. Applying the Zakharov-Shabat spectral problem to a single OFDM symbol with multiple subcarriers, we quantify the effect of the statistical soliton occurrence in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol incorporates multiple solitons with high probability. The considered optical communication example is relevant to a more general physical problem of the generation of coherent structures from noise.

Frustration of the total reflection by a hidden scatterer.

The scattering of a wave by a cylindric object hidden within the dielectric is studied. The total reflection is frustrated because of the scattering. Magnetic and electric fields at the dielectric surface and the energy flux are calculated by the modified boundary element method at near-field and far-field distances. The total reflection is shown to rearrange the shape of a scattering indicatrix.

Scattering of evanescent electromagnetic waves by a cylinder near the flat boundary: the Green function and fast numerical method.

The scattering of plane evanescent waves by a cylinder is studied. The Green function for the Helmholtz equation for two dielectrics with flat interface is found and applied for the numerical calculation of the scattered field by the boundary elements method. The Green function keeps close track of scattering, including multiple reflections. The result may be applicable for the data analysis in near-field optical microscopy.

Inverse scattering for the one-dimensional Helmholtz equation: fast numerical method.

The inverse scattering problem for the one-dimensional Helmholtz wave equation is studied. The equation is reduced to a Fresnel set that describes multiple bulk reflection and is similar to the coupled-wave equations. The inverse scattering problem is equivalent to coupled Gel'fand-Levitan-Marchenko integral equations. In the discrete representation its matrix has Töplitz symmetry, and the fast inner bordering method can be applied for its inversion. Previously the method was developed for the design of fiber Bragg gratings. The testing example of a short Bragg reflector with deep modulation demonstrates the high efficiency of refractive-index reconstruction.