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  • Yuri A. Shpolyanskiy
Yuri A. Shpolyanskiy

Yuri A. Shpolyanskiy
ITMO University | SPbNRU ITMO · Department of Photonics and Optical Information Technology

Ph.D., Dr. Sci. (Phys. Math.)

About

43
Publications
1,563
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337
Citations
Additional affiliations
April 2014 - August 2017
ITMO University
Position
  • Professor

Publications

Publications (43)
Article
A mathematical model of evolution of the space–time spectra of nonparaxial few-cycle optical waves in isotropic dielectric media with an arbitrary dispersion of the refractive index and the inertialess third-order nonlinearity has been discussed. It has been shown that, at the self-focusing of a wave single-cycle at the input to a nonlinear medium...
Article
Full-text available
The method and characteristics of several approaches to the pricing of discretely monitored arithmetic Asian options on stocks with discrete, absolute dividends are described. The contrast between method behaviors for options with an Asian tail and those with monitoring throughout their lifespan is emphasized. Rates of convergence are confirmed, bu...
Article
Full-text available
Propagation of few-cycle laser pulses with intensities of ~10^10 kW/cm^2 in optical fiber is investigated beyond the unidirectional approximation. Considered medium parameters include dispersion, Kerr and Raman nonlinearities. Generation of the octave-spanning continuum is observed for the spectrum of the forward wave. Formulation of the initial co...
Article
Full-text available
Interaction of few-cycle pulses counter-propagating in an optical fiber is studied numerically via solution of equations for bi-directional fields that are equivalent to the full scalar wave equation. It is simulated how 3-cycle optical pulse of the Ti:Sa laser is gained as it propagates through the field of the pulse on the second harmonic with hi...
Article
The aim of the BENCHOP project is to provide the finance community with a common suite of benchmark problems for option pricing. We provide a detailed description of the six benchmark problems together with methods to compute reference solutions. We have implemented seventeen different numerical methods for these problems, and compare their relativ...
Article
Full-text available
Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitati...
Article
Simple mathematical expressions are derived to show how the velocity of the center of gravity and the rms width of initially one-and-a-half-cycle pulses depend on the original central frequency and field amplitude, as well as on the properties of nonlinear media with dispersion. It is shown that self-compression of the pulse or its solitonlike (wit...
Conference Paper
Bidirectional equations for forward and backward waves of intense few-cycle femtosecond pulses are solved numerically for single-mode optical fibre with dispersion and cubic nonlinearity including Raman mechanism. Appearance of a weak backward wave which was absent in the initial distribution is shown. The role of Raman nonlinearity on the amplitud...
Article
A numerical method is presented for solving a system of equations for the forward and reverse waves of radiation with a superwide spectrum in a transparent optical waveguide with arbitrary dispersion and cubic nonlinearity. The method can be used to model the interaction of counterpropagating pulses, as well as to model the process of generating th...
Conference Paper
We simulated propagation of few-cycle femtosecond pulses in fused silica fiber based on the set of first-order equations for forward and backward waves that generalizes widely used equation of unidirectional approximation. Appearance of a weak reflected field in conditions default to the unidirectional approach is observed numerically. It arises fr...
Article
The paper discusses the spectral-broadening processes of femtosecond pulses in the high-frequency region when optical breakdown occurs in a gaseous medium. It is shown that the spectrum of the generated high-frequency radiation contains several isolated maxima whose positions are determined by the properties of the medium and by the thickness of th...
Article
Full-text available
The evolution equations for the complex envelope and electric field of optical radiation with an ultra� broad spectrum in a transparent medium in Section 3 of the article are written in the unidirectional propaga� tion approximation. This follows from the form of the equations and the literature cited, but is not explicitly indicated in the text, w...
Article
Analytical signal formalism is used for derivation of expressions for a complex envelope of radiation with ultrabroadband spectrum and an arbitrary waveform, which occur rarely in modern texts on nonlinear optics. It is demonstrated that the envelope, phase, and instantaneous frequency of femtosecond radiation pulses with an ultrabroad spectrum in...
Article
It is shown that neglecting the generation of tripled frequencies in equations for the envelopes of pulses composed of a small number of light-field vibrations can result in a substantial overestimate of their self-focusing efficiency in transparent bulk media with cubic nonlinearity.
Article
Full-text available
This paper discusses the regularities of phase self-modulation of femtosecond light pulses in a dielectric medium with normal group dispersion and cubic inertialess nonlinearity. It is shown that, with different input widths and intensities of the light pulses at definite distances, their phase modulation becomes close to linear, and this makes it...
Article
This paper shows that, for light pulses composed of a small number of vibrations with the same maximum electric field and transverse size, i.e., with the same ratio of the radiation power to the critical self-focusing power, the self-focusing efficiency in a transparent disperse medium decreases when the number of vibrations in the pulse is decreas...
Article
Two scenarios of the interaction of codirectional femtosecond pulses with different spectral compositions in a transparent isotropic medium with normal dispersion and nonlinearity have been identified. When the spectral broadening of pulses separated at the input to the medium in time and frequency is inadequate for their spectra to overlap, the in...
Article
The dependence of the rms spectral width of a light pulse consisting of several light-field oscillations on the distance passed in an optical waveguide with arbitrary dispersion and nonresonant electronic nonlinearity has been derived. This dependence allows one to rapidly predict the scenarios of the initial evolution of the spectrum (broadening,...
Article
Various scenarios of self-focusing of axisymmetric few-cycle light pulses in optical media with nonresonant dispersion and nonlinearity are investigated numerically. It is shown that the spatiotemporal dynamics leads to the formation of complex light structures like dumbbells or bubbles depending on the initial intensity. The bubble includes a cent...
Article
Fresnel formula for the normal incidence of light is generalized to the case of reflection of broad-spectrum radiation off a dielectric with nonresonant dispersion and nonlinearity. Considering reflection of few-cycle light pulses off a bloomed dielectric interface, we show that self-division of a reflected pulse can occur at low incident intensiti...
Article
The Fresnel formula for the normal incidence of a wave at the interface of dielectric media is generalized to the case of the reflection of radiation with a broad spectrum from a medium with nonresonance nonlinearity and dispersion. A model is constructed of the process whereby pulses composed of a small number of vibrations of the light field are...
Article
It is demonstrated that for femtosecond supercontinuum generation in optical waveguides with nonresonant electronic nonlinearity the squared root-mean-square pulse duration varies near-parabolically with distance, irrespectively of spectrum ultra-broadening scenarios. The derived formulas for parabolic coefficients are applied to find the areas of...
Article
We suggest a method to derive the nonlinear wave equations suitable for describing the propagation of light pulses as short as two optical cycles in transparent nonlinear optical media. The equations are suitable for efficient numerical simulation of the propagation of extremely short pulses without the need to resort to any type of envelope approx...
Article
The evolution of the field of intense ultrashort light pulses in optical waveguides is considered in the case when the width of their spectrum in the course of the self-effect process can reach values comparable to the center frequency at the input. Formulas are presented which describe the motion of the centroid and the rms duration of pulses with...
Article
We investigate an extremely complex mechanism of spectral supercontinuum generation at the propagation of intensive femtosecond laser pulses in microstructure (photonic crystal) fibers beyond the slowly-varying envelope approximation. We discuss and compare theoretical approaches grounded on the considerations of field and spectral evolution of the...
Article
Numerical modeling has been used to investigate the regularities of the spatiotemporal dynamics of the electric field of femtosecond light pulses in transparent nonlinear media with dispersion. It is shown that, with self-focusing of pulses having a small number of vibrations of a light field whose spectrum lies in the region of normal group disper...
Article
A new wave equation for the electrical field evolution of intensive femtosecond light pulses in isotropic transparent media is presented. It is demonstrated that a 'light bubble' can evolve from a few-optical cycle pulse propagating through a fused silica bulk. The two-octave spectrum supercontinuum is theoretically observed.
Article
We report experimental and theoretical investigation of supercontinuum generation in broad spectral range from 500 nm to 2500 nm induced in water and bulk fused silica by 1mJ 150-fs pulses at 780 nm excitation wavelength. We find that experiments may be modeled theoretically by considering Raman- and Kerr-type nonlinearities such as transient stimu...
Article
Techniques for constructing nonlinear evolution equations for the electric field of femtosecond light pulses in bulk and waveguide optical media with nonlinearities of various nature are formulated. A system of equations, which takes into account the material and waveguide dispersions of the medium that are linear with respect to the field in the t...
Article
Full-text available
A novel quasi-thermodynamic approach is suggested to simulate surface chemistry in III-V compound MOVPE. Blocking of free adsorption sites by methyl radicals is considered as the mechanism limiting the growth rate at low temperatures. This assumption has provided a good reproduction of experimental data on GaAs MOVPE in various types of reactor. Th...
Article
The equations describing the propagation dynamics of optical pulses consisting of several electrical field cycles and pulses with spectrum bandwidth comparable with the central frequency are presented. The numerical simulation of nonlinear optical phenomena observed in isotropic media with pumping by the pulses with the spectrum in area of the norm...
Article
On the basis of the analysis of the wave equations for an electrical field of radiation and without use of slowly varying envelope approximation the self-action of femtosecond light pulses in transparent media is investigated. The results of numerical simulation of spectral supercontinuum evolution, accompanying temporary broadening of intensive pu...
Article
Summary form only given. Spectral continuum generation by ultrashort pulses propagating in a hollow waveguide, in combination with compression by compensation of group velocity dispersion provides means for obtaining sub 10-fs optical pulses. Because of large dispersion of optical materials at UV and blue-green wavelengths, it has been difficult so...
Article
Summary form only given. The phenomena cause by the third-order nonlinear susceptibility χ(3) (including Raman and electronic parts) which influence intense femtosecond light pulses propagating in transparent isotropic media have been studied theoretically. The derived nonlinear wave equations govern the dynamics of the electric field of a pulse (b...
Article
The effect of superbroadening of the spectrum of high-power femtosecond laser pulses in transparent isotropic media is studied based on an analysis of the wave equations for the electric component of the radiation without using the approximation of slowly varying envelope. We present the results of a numerical simulation of the evolution of the inh...
Article
The reflection of intense laser pulses consisting only of several light field cycles from nonlinear, isotropic and transparent dielectric media is theoretically investigated. It is shown, that the spectrum of the reflected pulse is enriched by odd harmonics and at close linear refraction indices of bordering media the duration of the reflected puls...
Article
The new wave equation describing nonlinear propagation in isotropic dielectric media of any polarization optical pulses containing only a few oscillations of light field has been obtained. The polarization self-action of such extremely short pulses is shown to be in change of orientation of their electrical field amplitude vector along the directio...

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