Biomedical subjects

Alexey A Egorov

Publications and source records attributed to Alexey A Egorov.

9 recordsLinked to original sources

PubMed2006

Shaping soliton properties in Mathieu lattices.

We address basic properties and stability of two-dimensional solitons in photonic lattices induced by the nondiffracting Mathieu beams. Such lattices allow for smooth topological transformation of radially symmetric Bessel lattices into quasi-one-dimensional periodic ones. The transformation of lattice topology drastically affects the properties of ground-state and dipole-mode solitons, including their shape, stability, and transverse mobility.

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PubMed2005

Soliton topology versus discrete symmetry in optical lattices.

We address the existence of vortex solitons supported by azimuthally modulated lattices and reveal how the global lattice discrete symmetry has fundamental implications on the possible topological charges of solitons. We set a general "charge rule" using group-theory techniques, which holds for all lattices belonging to a given symmetry group. Focusing on the case of Bessel lattices allows us to derive also an overall stability rule for the allowed vortex solitons.

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PubMed2004

Stable soliton complexes and azimuthal switching in modulated Bessel optical lattices.

We address azimuthally modulated Bessel optical lattices imprinted in focusing cubic Kerr-type nonlinear media, and reveal that such lattices support different types of stable solitons whose complexity increases with the growth of lattice order. We reveal that the azimuthally modulated lattices cause single solitons launched tangentially to the guiding rings to jump along consecutive sites of the optical lattice. The position of the output channel can be varied by small changes of the launching angle.

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PubMed2004

Stable soliton complexes in two-dimensional photonic lattices.

We show that two-dimensional photonic Kerr nonlinear lattices can support stable soliton complexes composed of several solitons packed together with appropriately engineered phases. This may open up new prospects for encoding pixellike images made of robust discrete or lattice solitons.

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PubMed2004

Stable multicolor periodic-wave arrays.

We study the existence and stability of periodic-wave arrays propagating in uniform quadratic nonlinear media and discover that they become completely stable above a threshold light intensity. To the best of our knowledge, this is the first example in physics of completely stable periodic-wave patterns propagating in conservative uniform media supporting bright solitons.

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PubMed2003

Stabilization of one-dimensional periodic waves by saturation of the nonlinear response.

We address the properties of (1+1)-dimensional periodic waves in conservative saturable cubic nonlinear media and discover that cnoidal- and snoidal-type waves are completely stable within a broad range of parameters. The existence of stability bands is in sharp contrast with the previously known properties of periodic waves in self-focusing Kerr nonlinear media. We also found that in self-defocusing media instability bands occur, again in contrast to the case of Kerr media.

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PubMed2003

Metastability of dark snoidal-type waves in quadratic nonlinear media.

We report the existence and basic properties of dark snoidal-type waves self-sustained in quadratic nonlinear media. Using a stability analysis technique, we reveal that they are almost completely stable, or metastable, in suitable ranges of input energy flows and material parameters. This opens the way to the experimental observation of dark-type multicolor periodic wave patterns supported by quadratic nonlinearities.

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PubMed2003

Stability analysis of spatiotemporal cnoidal waves in cubic nonlinear media.

We analyze numerically the modulational instability of spatiotemporal cnoidal waves of cn, dn, and sn types that are periodic along a single space coordinate and are uniform in time. The band of possible increments is calculated for all three types of cnoidal waves as a function of parameter describing the degree of localization of the wave field energy. It is shown that this band transforms into a set of discrete values for waves of cn and dn types in the limit of strong spatial localization. Simulation of perturbed cnoidal-wave propagation revealed suppression of collapse and multiple-wave filamentation on the developed stage of instability. Different instability scenarios are considered in detail.

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PubMed2003

Stability analysis of (1+1)-dimensional cnoidal waves in media with cubic nonlinearity.

In the present paper we perform stability analysis of stationary (1+1)-dimensional cnoidal waves of cn and dn types (anomalous group velocity dispersion) and sn type (normal group velocity dispersion). The mathematical model is based on the nonlinear Schrödinger equation. With this aim we developed a method that takes into consideration the properties of complex eigenvalues of Cauchy matrix for perturbation vectors. We show that cnoidal sn-wave is stable in the whole domain of its existence, whereas cn- and dn-waves are unstable. The instability of cn- and dn-waves is suppressed in the limiting case of strong localization when waves evolve into a set of well-separated fundamental bright solitons.

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