Leonid L. Frumin

Nonlinear Fourier transform for optical data processing and transmission: advances and perspectives

The nonlinear Fourier transform is a transmission and signal processing technique that makes positive use of the Kerr nonlinearity in optical fibre channels. I will overview recent advances and some of challenges in this field.

Anomalous size dependence of the non-linear mobility of DNA

A strong drift velocity non-linearity of the (doublestranded) DNA molecules vs. the electric field was discovered in gel electrophoresis. The non-linear drift velocity of the longer molecules is higher than that of the short ones, depending on the molecular size in a complex fashion. This behavior contrasts with that of the ordinary, linear, drift velocity where short molecules move faster than the long ones. The molecular size dependence of the non-linear velocity or the non-linear mobility has a non-monotonous wave-like character. The non-linear mobility offers possibilities of manipulating the drift velocity at will?the DNA fragments of different size can be made to move in opposite directions in pulsed field gel electrophoresis

New approaches to coding information using inverse scattering transform

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. Here, we propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. First, we describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. As a specific elegant subclass of the general schemes, we introduce a soliton orthogonal frequency division multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm to recover the data. Then, we demonstrate how to use this new approach to control signal parameters in the case of the continuous spectrum.

The isoelectric focusing problem analytic solution.

The focusing problem under isoelectric focusing has been solved analytically precisely. The solutions determine the law of the fraction moving and narrowing in the instant electric field gradient. This is especially actually because of developing the calculation methods in electrophoretical experiment.

Light-induced attractive force between two metal bodies separated by a subwavelength slit

A novel light-induced attractive force which acts as a force with negative light pressure has been revealed. The force arises by the interaction of plasmon polaritons which are excited at the surface of metal when a transverse magnetic mode propagates through a subwavelength slit between two metal bodies. The estimation of the repulsive force acting on the metal walls of the slit in the case of subwavelength TE mode propagation along the slit is presented. The explicit analytical expressions of light-induced forces between two macroscopic metal bodies or films separated by a subwavelength slit have been derived. These forces could be used to manipulate metallic macro-, micro- and nano-objects in vacuum or in a dielectric medium. Estimations of these light-induced forces show that the forces are sufficient for measurements and practical applications.

Negative light pressure force between two metal bodies separated by a subwavelength slit

An explicit analytical expression of a light-induced attractive force between two macroscopic metal bodies or films separated by a subwavelength slit has been derived. The analytical expression obtained agrees well with the numerical calculations for the main TM mode. This force, which acts as a force with negative light pressure, arises by the interaction of plasmon-polaritons excited at the surface of metal when light propagates through the subwavelength slit. Estimations of this light-induced attractive force show that the force is sufficient to enable measurements and practical applications.

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.

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.

Parametric inverse problems of electrode kinetics

Abstract The purpose of the present paper is the development of a methodical approach to determine kinetic parameters of electrochemical reactions from experimental results using relatively simple techniques for experimental data treatment, which should be of considerable interest for analytical applications.

Asymptotic Approach in Steady‐State Electrode Kinetics for the Spherical Electrode

Using the method of matched asymptotic expansions, an approach has been suggested for obtaining the current/potential curves of a spherical electrode in electrolyte solution, taking into account the kinetics of electrode processes. Asymptotically exact expressions for current/potential curves have been obtained for complex kinetics in the general case of a redox reaction, and in more detail for a simple neutralization reaction both for the case of a pure electrolyte and for a dilute electrolyte. A correction term has been derived for the equation of the potential of Helmholtz sphere, which considers the influence of current and the diffusion limitations, upon this potential. The zero charge potential point for a spherical electrode is shown to be different from the electrolyte zero potential.