# D.A. ShapiroRussian Academy of Sciences | RAS · Institute of Automation and Electrometry

D.A. Shapiro

Doctor of Philosophy

## About

155

Publications

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719

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Citations since 2016

Introduction

D.A. Shapiro currently works at the Institute of Automation and Electrometry, Russian Academy of Sciences. D.A. does research in Optics, Photonics, and Plasmonics. His current project is 'Optical diagnostics with nanoplasmonics'. It is studied by the method of theoretical physics and by numerical calculations.

**Skills and Expertise**

Additional affiliations

January 2003 - October 2015

## Publications

Publications (155)

Discrete Dipole Approximation (DDA) is one of the best methods for light scattering calculation. We expand it to solve a 2-dimensional problem in two different semi-spaces. Considering a cylinder parallel to the plane boundary, we derive a special-kind 2-dimensional Green’s tensor that intrinsically accounts for the boundary conditions for electrom...

We calculate the light transmission by a subwavelength plasmonic array using the boundary element method for parallel cylinders with different cross-sections: circular or elliptic with axis ratio 4:1. We demonstrate that plasmonic resonance is sharper for the case of horizontal ellipses. This structure is susceptible to refractive index variations...

We calculate the light transmission by a subwavelength plasmonic array using the boundary element method for parallel cylinders with different cross-sections: circular or elliptic with axes ratio 4:1. We demonstrate that the plasmonic resonance is sharper for the case of ellipses with a large horizontal axis. This structure is susceptible to the re...

We report a numerical simulation of the propagation of short (25 ps) 8QAM pulses for two polarisations in a nine-channel communication line with a frequency band of 80 GHz. It is shown that the use of large-chirp pulses and different dispersion compensators leads to effective suppression of nonlinear distortions and significantly improves the signa...

The numerical modeling of short optical pulses propagation in the communication link is carried out. The combination of high chirp and variable dispersion compensation is proposed to suppress the nonlinear noise. The variable dispersion decreases the bit error rate by 10 times. Calculations for 25 ps pulses propagating by 1000 km with 8-level ampli...

A plasmonic grating consisting of parallel gold or silver nanowires on the glass substrate is an excellent sensor for refractive index measurement of a gas or liquid medium. We suggest measuring the local field in a gap between the wires to increase the sensitivity. The local electric field contains more information on the environment since it incl...

We have performed a numerical simulation of transmission of optical DP QPSK signals at a rate of 40 Gbaud over a distance of 2000 km. It is shown that a channel with large negative dispersion and preliminary large positive pulse chirping significantly reduces nonlinear distortion and improves the signal quality. To further reduce the probability of...

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...

Transmission of optical pulses with a large positive chirp is simulated numerically in a 40 Gbit s–1 communication link with high average negative dispersion. It is shown that the use of these mechanisms effectively suppresses the nonlinear interaction of pulses and significantly improves the quality of signal transmission.

A modified Born approximation suitable for the problem of electromagnetic wave scattering by a dielectric body is constructed. A system of integral equations including exact boundary conditions at the surface is derived. It is shown that a modified series converges to the known analytical solution for the problem of a wave incident normally on a cy...

The plasmonic force due to electromagnetic waves between two metallic walls has been studied earlier for a subwavelength slit taking into consideration only zero mode. In the present paper, the effects of the second mode are analyzed. The higher modes are shown to decrease the attractive force. The magnetic field of the p-wave is compared with the...

Channels with and without memory are compared using the simplest Gaussian noise distribution model. It is shown that both channels have similar dependences of the capacity on the average signal power. At the same time, the optimal input alphabet for the channel with memory changes. The applicability of the model with nonlinear memory to the QPSK co...

A channel with weight coefficients of nonlinear finite memory is simulated numerically. Areas of the signal power are found where the capacity is higher than that of a regular Gaussian channel. It is shown that an increase in the number of accountable adjacent symbols has little effect on the channel capacity. The numerical calculation reveals that...

The attractive plasmon force between two metallic walls when the electromagnetic wave propagates through a narrow slit has been studied earlier for parallel plates and normal incidence. In present paper the effects of imperfect adjustment of plates and laser beam are analyzed. The change of force for non-parallel plates is shown to be of the first...

Light scattering is one of the most important elementary processes in near-field optics. We build up the Born series for scattering by dielectric bodies with step boundaries. The Green function for a 2-dimensional homogeneous dielectric cylinder is obtained. As an example, the formulas are derived for scattered field of two parallel cylinders. The...

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 t...

A metallic wire embedded in the dielectric substrate leads to frustration of the total internal reflection at the interface between dielectric and free space. The scattering by a gold cylinder is studied in order to exploit the light for hidden objects optical diagnostics. The p-wave incidenting by the angle close to total reflection with the frequ...

We propose a method for calculating the capacity of a finite-memory channel up to the square of the nonlinear memory parameter. A comparison with a regular Gaussian model is performed, in which the Kerr nonlinearity is considered as an additional Gaussian noise. The estimate by the regular Gaussian model is shown to yield a greater capacity as comp...

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 mag...

Single-frequency operation of a 1.03 μm fiber laser with random distributed feedback (RDFB) is demonstrated. The laser cavity is based on a 4 cm long fiber Bragg grating (FBG) consisting of 10 homogeneous subgratings with random phase and amplitude of refractive index modulation inscribed in a polarization maintaining (PM) Yb-doped fiber. Such RDFB...

An iterative method for computing the channel capacity of both discrete and continuous input, continuous output channels is proposed. The efficiency of new method is demonstrated in comparison with the classical Blahut - Arimoto algorithm for several known channels. Moreover, we also present a hybrid method combining advantages of both the Blahut A...

The magnetic field distribution and electric-field amplification factor are found in the gap between periodically arranged parallel metal cylinders scattering an evanescent wave. Such a wave appears if an original plane wave is incident from the dielectric substrate onto the interface at an angle of total internal reflection. A substantial restruct...

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 Töplitz symmetry of the matrix and an “inner bordering” procedure. The new algorithm was tested on the exactly solvable potential. It is sho...

The results of both analytical and numerical calculations of the light scattering by periodic array (either finite or infinite) of gold nanocylinders are compared. Surprisingly, the dipole approximation appears to be well applicable down to the distance between the cylinders only twice exceeding their diameter.

In order to reveal the pattern effect in the optical signal transmission it is studied as a random complex process. The different sources of detection error are studied for quadrature phase-shift keying in the absence of nonlinearity: the error in the rectangular filter width, the finite duration of the initial pulses, the deviation of detection po...

The principle of discrete Fourier transform is applied to minimize the maximum absolute value of coupled mode coefficient for multichannel FBG. Phase constants for each uniform grating inscribing in the same fiber core section are found analytically. The described approach allows refractive index optimization of multichannel FBG with arbitrary numb...

Unusual plasmons, excited by an evanescent wave in narrow slits in a periodic array of nanowires overlying a dielectric substrate, are found from Maxwell's equations by a modified boundary element method. The evanescent wave appears when the incident plane wave runs onto the boundary from the substrate under the angle of total internal reflection....

Plasmons, which are excited by an evanescent wave and localized in a narrow slit between two metallic cylinders overlying a dielectric substrate, are found by numerical solution of Maxwell equations. The simulation is carried out by a modified boundary elements method with the Green function for layered medium. For the wave incident from a dielectr...

Two variants of differential phase-shift keying with π and π/2 shifts are compared theoretically. The expressions are derived for dispersion averaged over all the realisations of the bit sequence. It is shown that in the presence of strong optical filtering the π/2 scheme yields less dispersion of pulses and much better Q-factor in agreement with t...

The causality principle is taken into account to couple amplitude and phase of the reflection coefficient in a symmetric grating for the optimization purpose. The distortion functional for group delay minimization is proposed. The minimization of mean square group delay within the Bragg reflection band is carried out at fixed integral reflectivity....

An overview of the binary collision impact theory of spectral line shapes has been given to provide a unified statistical mechanical approach to line-shape theory, laser theory, nonlinear optics, and transport phenomena in dilute gases. The computation of spectral line profiles corresponding to those obtained from ultra-high-resolution spectral lin...

Coherent preparation of quantum states of atoms and ions by laser light
can lead to electromagnetically induced transparency and related
effects. In particular, the standing wave at the adjacent transition
induces a new type of nonlinear resonance in the probe-field spectrum of
a three-level system. The resonance is due to the effect of high-order...

The scattering of electromagnetic wave by a periodic array of nanowires is
calculated by the boundary element method. The method is extended to the
infinite grating near the interface between two dielectrics. A special Green
function is derived that allows to study the evanescent wave. The Rayleigh---
Wood's anomalies are found in the period-to-wav...

The scattering of evanescent wave, one of the main processes of nanophotonics, is studied in 2D geometry using boundary integral equations and special two-domain Green function. The problem is studied for a single, a pair, and a series of nanowires.

Ion lasers, especially argon, are the most powerful sources of visible and near UV continuous coherent radiation. The active medium of lasers is low-temperature plasma. They are familiar to scientists and engineers from the 70’s. However, a series of physical effects remained unclear and there was a barrier to enhancing the power and improving the...

Two-dimensional problem of evanescent wave scattering by dielectric or
metallic cylinders near the interface between two dielectric media is solved
numerically by boundary integral equations method. A special Green function was
proposed to avoid the infinite integration. A pattern with a circular and a
prolate elliptic cylinders, respectively, is s...

The design of multichannel optical filter is studied theoretically. New efficient two-step method based on combination of 6-th moment minimization and straightforward numerical minimization is developed. It is applied to find a fiber Bragg grating profile with minimal refractive index variation for 5 ÷ 32 channels. Obtained results are closer to th...

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 re...

Shapes of pressure- and Doppler-broadened spectral lines are obtained by solving exactly a three-dimension transport and (or) relaxation equation. The speed dependence of collisional broadening and shifting caused by dephasing collisions and Dicke narrowing caused by velocity-changing collisions are taken into account within the impact approximatio...

A new method for the crest factor minimization of for multi-tone signal based on the sampling functional is proposed. The minimum of sixth moment is used as an initial value for the minimax search. For high number of tones the optimal values are better than previously reported. Application for fiber Bragg multi-channel filters for telecommunication...

The extra photon echo decay due to ion-ion, velocity-changing collisions is computed. The strong velocity dependence of the collision frequency is shown to decrease the decay constant by 30%.

As a rule the thermal motion removes the dark resonance from the spectrum of a three-level system driven by two strong fields. An example has been found where, conversely, the dark resonance manifests itself even after averaging over the velocities. The four-level system is studied with a closed cycle of four resonant fields, when two relatively st...

A one-dimensional inverse scattering problem for the Helmholtz wave equation is considered. The problem consists in reconstruction
of the refractive index of transparent inhomogeneous media from a specified complex reflection spectrum. A method previously
proposed by the authors for reconstruction of the Bragg gratings in the coupled mode approxima...

A new method for the minimization of the crest factor for multi-tone signals based on the sampling functional optimization is proposed. The minimum of smooth functional is used as an initial value for the min-max search. For the number of tones the mini-max values are better than previously reported. Applications in fiber optics are discussed.

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 inv...

Averaged coupled wave equations are derived for a fibre Bragg grating with Gaussian noise added to the refractive index. The corrections to reflection and transmission coefficients are expressed in terms of a Green matrix of the unperturbed grating. The explicit formula for the Green matrix is derived for the uniform grating. The average reflectivi...

An optimal filter for super-fast fiber-optic communication lines should cause minimal phase distortions. The simplest case
of Bragg grating with a symmetric profile is considered. A distortion functional is presented, which is the mean square group
delay over the Bragg reflection band at a fixed integral reflectivity. The functional is minimized an...

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 representatio...

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 w...

Sharp edges of the reflection spectrum of fiber Bragg gratings originate the group delay. As follows from the dispersion relations, the delay of the symmetric grating grows up with the second derivative of the reflectivity with respect to the frequency. The distortion functional is proposed for filter optimization. It is the mean square delay at fi...

Theoretical and experimental investigations were made of instabilities in high-current discharges excited in high-power ion-laser plasmas. It was established that the ion-acoustic instability makes an essential contribution to the general picture of the instabilities. A method was demonstrated for suppressing the discharge instabilities in an argon...

Expressions for the calculation of the profile of a Coulomb-broadened Lamb dip are proposed for the case of a high-power single-frequency ion laser. Measurements are reported of the width of a Lamb dip in the ultraviolet radiation emitted by an Ar2+ laser. Strong Coulomb broadening of 1600 MHz (compared with 400 MHz in the case of singly ionized io...

The Coulomb broadening of a magneto-optical resonance of degenerate two-level ions in the field of a standing wave is calculated. Under the conditions of linear polarisation of this wave, of the normal Zeeman effect, and of weak saturation, the broadening is described by familiar expressions for multistage and two-photon resonances in separate thre...

The 4-parametric family of exactly solvable profiles of the Bragg reflector is analyzed. The physical meaning of the parameter set is explained. The solution is proposed to use for approximation of the Gaussian envelope. The high quality of the approximation within the Bragg window is demonstrated numerically.

Two direct numerical methods of soving Gel'fand--Levitan--Marchenko equations are developed based on bordering procedure, hermiscity, Cholesky decomposistion, Toeplitz symmetry and piecewise-linear approximation. The proposed methods are shown to surpass the discrete layer peeling algorithm in accuracy and stability at high reflectance.

The accuracy of calculation of spectral line shapes in one-dimensional approximation is studied analytically in several limiting cases for arbitrary collision kernel and numerically in the rigid spheres model. It is shown that the deviation of the line profile is maximal in the center of the line in case of large perturber mass and intermediate val...

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 Gau...

The inverse scattering problem is studied for high-reflectance grating with noisy reflection data. An adaptive regularization procedure is proposed allowing to reconstruct FBG under relatively strong noise.

A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it notice...

New line shape calculations for CO buffered by Ar are compared to high-resolution measurements from a difference-frequency laser spectrometer, over a range of thermodynamic conditions relevant to the atmosphere. The calculations are based on solving the quantum kinetic (i.e. transport/relaxation) equation for the molecules within the impact approxi...

We examine the problem of fiber Bragg grating reconstruction from its reflection coefficient. A direct numerical method of solving the Gel'fand-Levitan-Marchenko integral equations for the problem is developed. The method is based on a bordering procedure, Cholesky decomposition, and piecewise-linear approximation. It is tested using high-reflectan...

The problem of data communication over a wavelength division multiplexing (WDM) high-data-rate communication link where wave division multiplexing is performed by using quasi-rectangular Bragg filters is studied numerically. It is shown that the optimisation of the mean dispersion of the link, the width and shape of the transfer function of filters...

The four-parametric family of exactly solvable profiles of the Bragg reflector is found. Compared to the known solution we take into account slow frequency modulation of the refractive index. The shape of the reflection spectrum is shown to be trapezoidal. The group delay characteristic is demonstrated to be nearly linear within the band of high re...

The ionic probe-field spectrum is calculated including scattering in plasma. The peak of higher spatial harmonics is shown to broaden due to Coulomb dephasing. Account of the saturation and population effects provides an agreement with experiment.

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...

Exactly solvable profiles are found for a Bragg grating with amplitude or phase modulation. A simple formulas for reflection coefficient are derived. The shape of reflection spectrum in the case of amplitude modulation is trapezoidal in semi-logarithmic coordinates. In the case of phase modulation the solution is found for grating with the Gaussian...

The probe field spectrum of a three-level A scheme with a strong standing wave at the adjacent transition is calculated numerically
taking into account velocity-varying collisions. It is shown that even a small population of the upper level changes the shape
of the spectrum and increases the absorption in the line center. Taking into account the ex...

The spectrum of a probe field in a three-level system interacting with a standing wave at the adjacent transition is calculated. The expression for a nonlinear resonance profile is obtained taking into account diffusion in the velocity space in the fourth order of perturbation theory in the standing-wave amplitude.

We have measured the shape of the Autler-Townes doublet and the peak of electromagnetically induced transparency (EIT) under
plasma conditions. We compare the experimental results with the calculated spectrum of the probe field of a three-level ArII
Λ-scheme by taking into account Coulomb collisions. We show that the Coulomb broadening of the EIT p...

The problem of probe-field spectrum is considered for a three-level ion placed in a field of an intense standing light wave.
The ion interaction with plasma and the velocity-changing Coulomb scattering are taken into account within the weak-collision
model. The system of kinetic equations for the density matrix is solved by the expansion in spatial...

The probe-field spectrum of a three-level Λ-gas
with hard collisions between particles is studied. The shape and positions of
components of the Autler–Townes doublet are obtained at different collision
frequencies. When the Doppler broadening is much greater than the collision
frequency the width of the peaks is found to be proportional to the coll...

The interaction of a two-level system with a strong standing wave is examined by the probe field resonant to the adjacent transition in the Λ configuration of Ar II. The known peak of electromagnetically induced transparency is observed in the absorption spectrum at the detuning of the probe field proportional to the detuning of the strong field. A...

Two-parametric family of exactly solvable profiles of quasi-sinusoidal Bragg gratings is found. A simple formula is derived for their reflection coefficient as a function of wavelength. The detailed analysis of the reflection spectrum width is presented. The solution is helpful as a starting point of optical filter synthesis.