O. V. Belai

Group delay in Bragg grating with linear chirp

An analytic solution for Bragg grating with linear chirp in the form of confluent hypergeometric functions is analyzed in the asymptotic limit of long grating. Simple formulas for reflection coefficient and group delay are derived. The simplification makes it possible to analyze irregularities of the curves and suggest the ways of their suppression. It is shown that the increase in chirp at fixed other parameters decreases the oscillations in the group delay, but gains the oscillations in the reflection spectrum. The asymptotic considerations are in good agreement with numerical calculations.

Efficient numerical method for solving the direct Zakharov–Shabat scattering problem

A new method to solve the direct Zakharov–Shabat scattering problem is proposed based on the solution for coupled Gel’fand–Levitan–Marchenko integral equations. Speedup of computations is achieved by using the Toplitz symmetry of the matrix and an “inner bordering” procedure. The new algorithm was tested on the exactly solvable potential. It is shown that the suggested algorithm significantly surpasses the traditional transfer matrix method in efficiency.

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.

Scattering of evanescent wave by two cylinders near a flat boundary

The two-dimensional problem of the evanescent wave scattering by dielectric or metallic cylinders near the interface between two dielectric media is solved. A semianalytical method involving a special Green function and a numerical solution of the boundary integral equations is proposed. A configuration with a circular and a prolate elliptic cylinders is suggested to simulate the sample and the probe in near-field optical microscopy. The far-field energy flux through the probe is calculated as a function of its position. The oscillations of the signal are interpreted as a result of the interference between evanescent and cylindrical waves.

Inverse scattering problem for gratings with deep modulation

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.

Reconstruction of high reflectance fiber Bragg grating from noisy data

The inverse scattering problem for fiber Bragg grating reconstruction becomes incorrect with an increasing level of noise in the input data or at a high reflection. The adaptive regularization procedure is proposed to restore the correctness and minimizing the reconstruction error. The proposed method is tested using numerical modeling with the Gaussian statistics of noise.

Optical field and attractive force at the subwavelength slit.

In recent works, a novel light-induced attractive force was predicted between two metal plates. This force arises by the interaction of surface plasmons which are excited at the metal when a transverse magnetic mode propagates through a subwavelength slit between two metal bodies. In this paper, the analytical and numerical calculations of this magnetic field are presented for the perfect metal and for gold. The amplitude and the phase transient curves between the known limiting cases of narrow and wide slits compared to the wavelength are found. The curve is shown to oscillate due to the emergence of new waveguide modes. The analytic solution for the perfect metal is in agreement with the computation for gold by means of the finite element method. The simple asymptotic formula for the light-induced attractive force is found in the limit of a narrow slit.

Numerical reconstruction stability of fiber Bragg gratings

Traditional algorithms for solving the inverse scattering problem for a fiber Bragg grating are described, and a new numerical method for this problem is developed. The method is based on the fast inversion of a matrix using its Toeplitz symmetry and on a special “inner-bordering” procedure. It is shown that the method is equally efficient as the well-known discrete layer peeling method but exceeds the latter in accuracy, especially for high-reflectance gratings. The stability of the proposed method with respect to initial data errors is demonstrated.

Direct measurement of a light induced attractive force between two metal bodies seperated by a subwavelength slit

In this work the improved nanonewton force facility of the Physikalisch-Technische Bundesanstalt (PTB), the German national metrology laboratory, and its possibility of measuring a theoretical predicted negative light pressure between two metallic plates with subwavelength distance is presented. The work includes presentation of upgrades to the existing nanonewton force facility for the realization of the experiment, the measuring methods and the first results obtained with the experimental setup together with comparisons to theoretical calculations.

Effects of imperfect angular adjustment on plasmonic force

The attractive plasmonic force between two metallic walls due to electromagnetic wave in the slit has been studied earlier for parallel plates and normal incidence. In present paper the effects of imperfectly adjusted plates and laser beam are analyzed. The change of force for non-parallel plates is shown to be of the first order in angle when the wedge is oriented along wave propagation and of the second order for the transverse case. Beam inclination decreases the force due to an antisymmetric mode excited in the slit.