Numerical Method for 2d Soliton Solution at SHG in Media With Time‐dependent Combined Nonlinearity

Trofimov, Vyacheslav A.; Matusevich, O. V.

doi:10.3846/1392-6292.2008.13.123-133

Cited by 7 publications

(1 citation statement)

References 14 publications

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“…Because the matrix is nonsymmetrical, the bisection method for obtaining EVs, used in works [35,36,43], cannot be applied in our case. Therefore, EVs of real nonsymmetrical tridiagonal matrix are obtained using the QR-algorithm [7,9].…”

Section: Eigenfunction Problemmentioning

confidence: 99%

Parameter Control of Optical Soliton in One‐dimensional Photonic Crystal

Trofimov

Lysak

Matusevich

et al. 2010

Mathematical Modelling and Analysis

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Abstract. The paper deals with finding of soliton solution for Schrödinger equation with periodic linear and nonlinear properties of medium in 1D case. Such structure is named as photonic crystal. To find soliton solution the corresponding problem for finding of eigenfunctions and eigenvalues is formulated. Iterative process is proposed for solution of this problem. Using the technique of continuation on parameter we investigate a dependence of soliton location on its maximum intensity, on ratio between light frequency and frequency of structure, on ratio between dielectric permittivity of alternating linear and nonlinear layers and on position between centre of initial distribution of eigenfunction and center of considered photonic structure area. The results of this paper confirm the features of soliton self-formation investigated early in our papers [37,38,39,40,41,42], in which one considered a propagation of femtosecond laser pulse through nonlinear layered structure.

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