Numerical scheme with external complex scaling for 2D Schroedinger equation in paraxial optics

Vladislav V. Serov; Aleksey I. Bychenkov; Vladimir L. Derbov; Sergey I. Vinitsky

doi:10.1117/12.380099

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20 March 2000 Numerical scheme with external complex scaling for 2D Schroedinger equation in paraxial optics

Vladislav V. Serov, Aleksey I. Bychenkov, Vladimir L. Derbov, Sergey I. Vinitsky

Proceedings Volume 4002, Saratov Fall Meeting '99: Laser Physics and Spectroscopy; (2000) https://doi.org/10.1117/12.380099
Event: Saratov Fall Meeting '99, 1999, Saratov, Russian Federation

Abstract

We propose a stable numerical scheme for solving Schrodinger equations that arise in the scalar paraxial theory of optical waveguides as well as in the quantum mechanics of a particle in a potential field. The scheme makes use of a multi-coordinate version of the split-step approach combined with the complex scaling that assures the implementation of boundary conditions. Beam propagation in a Gaussian waveguide is considered to illustrate the ability of the scheme to account for both waveguide and radiation modes.

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Vladislav V. Serov, Aleksey I. Bychenkov, Vladimir L. Derbov, and Sergey I. Vinitsky "Numerical scheme with external complex scaling for 2D Schroedinger equation in paraxial optics", Proc. SPIE 4002, Saratov Fall Meeting '99: Laser Physics and Spectroscopy, (20 March 2000); https://doi.org/10.1117/12.380099

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