Gaussian beam diffraction in inhomogeneous and nonlinear media: analytical and numerical solutions by complex geometrical optics

• Authors: Paweł Berczyński , Yury Kravtsov , Grzegorz Żeglinski
• Languages of publication: EN

Abstracts

EN

The method of paraxial complex geometrical optics (CGO) is presented, which describes Gaussian beam diffraction in arbitrary smoothly inhomogeneous media, including lens-like waveguides. By way of an example, the known analytical solution for Gaussian beam diffraction in free space is presented. Paraxial CGO reduces the problem of Gaussian beam diffraction in inhomogeneous media to the system of the first order ordinary differential equations, which can be readily solved numerically. As a result, CGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous media as compared to the numerical methods of wave optics. For the paraxial on-axis Gaussian beam propagation in lens-like waveguide, we compare CGO solutions with numerical results for finite differences beam propagation method (FD-BPM). The CGO method is shown to provide 50-times higher rate of calculation then FD-BPM at comparable accuracy. Besides, paraxial eikonal-based complex geometrical optics is generalized for nonlinear Kerr type medium. This paper presents CGO analytical solutions for cylindrically symmetric Gaussian beam in Kerr type nonlinear medium and effective numerical solutions for the self-focusing effect of Gaussian beam with elliptic cross section. Both analytical and numerical solutions are shown to be in a good agreement with previous results, obtained by other methods.

Keywords

EN

inhomogeneous media; Gaussian beam diffraction; complex geometrical optics; nonlinear Kerr medium

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 3
• Pages: 603-611

Dates

published

1 - 9 - 2008

online

17 - 7 - 2008

Contributors

author

Paweł Berczyński

• Institute of Physics, Szczecin University of Technology, Szczecin, 70-310, Poland

author

Yury Kravtsov

author

Grzegorz Żeglinski

• Institute of Electronics, Telecommunication and Computer Science, Szczecin University of Technology, 71-126, Szczecin, Poland

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Identifiers

DOI

10.2478/s11534-008-0094-1