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Academic Lecture: Spectral methods for numerical simulation of counter propagating optical waves interaction in nonlinear media

2018-11-01 

Topic: Spectral methods for numerical simulation of counter propagating optical waves interaction in nonlinear media

LecturerVOLKOV VASILYBelarus State university

Time9:00am-11:00 am, November 6th, 2018

Location: Room 602, 1st Experiment Building

Abstract:

Chebyshev spectral methods for two-point boundary value problems describing the processes of counterpropagating optical waves interaction in media with nonlinear refractive index are considered. On an example of linear problem fort the case of the media with periodic modulation of the refractive index, it is shown that the spectral method provide a given accuracy in two-three orders faster in comparison with the spline collocation method of the 5th accuracy order. Moreover, Chebyshev mesh has natural adaptive properties for such kind of the problems. A conservative iterative algorithm for implementation of the nonlinear spectral model is proposed. The proposed iterative method has convergence rate comparable with the Newton's method and has less sensitivity to the initial guess. On the base of the proposed numerical methods the bistability effect in the optical fiber amplifiers with bidirectional pumping is predicted.

Brief Introduction of Lecturer:

Doctor of Science. Mathematical modeling and numerical simulations, Belarus State University, February 2001.

Dissertation title: Methods of numerical simulations of nonlinear wave dynamics in optical systems.

Research supervisors: V.N.Abrashin, A.A.Afanas’ev

Ph.D., Computational Mathematics, Institute of Mathematics, National Academy of Sciences. December 1988.

Dissertation title: Methods of numerical simulations of self-action effects at propagation of optical radiation in nonlinear media.

Research supervisors: A.A.Afanas’ev, V.V.Drits

M.S., Physics, Vitebsk State Pedagogical Institute, June, 1983.

Thesis title: Pyroelectric effects in four-components segnetoceramic.

Research supervisor: M.K.Savchuk

 

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