Gaussian beam diffraction in inhomogeneous media: solution in frame of complex geometrical optics

2005 ◽  
Author(s):  
Yu. A. Kravtsov ◽  
P. Berczynski
Keyword(s):  
Gaussian Beam ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Beam Diffraction

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

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Paweł Berczyński ◽  
Yury Kravtsov ◽  
Grzegorz Żeglinski
Keyword(s):  
Gaussian Beam ◽  
Numerical Solutions ◽  
Beam Propagation Method ◽  
Beam Propagation ◽  
Geometrical Optics ◽  
Inhomogeneous Media ◽  
Focusing Effect ◽  
Analytical And Numerical Solutions ◽  
Cylindrically Symmetric ◽  
Beam Diffraction

AbstractThe 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.

Gaussian beam diffraction in weakly anisotropic inhomogeneous media

2009 ◽  
Vol 373 (33) ◽  
pp. 2979-2983 ◽  
Author(s):  
Yu.A. Kravtsov ◽  
P. Berczynski ◽  
B. Bieg
Keyword(s):  
Gaussian Beam ◽  
Inhomogeneous Media ◽  
Beam Diffraction

Divergence of geometrical optics series at the boundary of its applicability: An analytical example in elementary functions (2D Gaussian beam in free space)

Open Physics ◽  
2006 ◽  
Vol 4 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Yury Kravtsov ◽  
Stefan Buske
Keyword(s):  
Power Series ◽  
Gaussian Beam ◽  
Free Space ◽  
Geometrical Optics ◽  
Elementary Functions ◽  
Beam Diffraction

AbstractAn analytical example in elementary functions is presented (2D Gaussian beam diffraction in free space), which demonstrates the divergence of the geometrical optics (GO) series when the conditions for its applicability are violated. This example shows that accounting for higher terms in GO power series leads to divergence and therefore becomes completely useless beyond the boundaries of GO applicability.

scholarly journals Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Pawel Berczynski
Keyword(s):  
Gaussian Beam ◽  
Wave Front ◽  
Analytical Methods ◽  
Cylindrical Symmetry ◽  
Nonlinear Media ◽  
First Order ◽  
Self Focusing ◽  
Complex Curvature ◽  
Numerical And Analytical Methods ◽  
Beam Diffraction

AbstractThe method of paraxial complex geometrical optics (PCGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear saturable media of cylindrical symmetry. PCGO reduces the problem of Gaussian beam diffraction in nonlinear and inhomogeneous media to the system of the first order ordinary differential equations for the complex curvature of the wave front and for GB amplitude, which can be readily solved both analytically and numerically. As a result, PCGO radically simplifies the description of Gaussian beam diffraction in inhomogeneous and nonlinear media as compared to the numerical and analytical methods of nonlinear optics. The power of PCGO method is presented on the example of Gaussian beam evolution in logarithmically saturable medium with either focusing and defocusing refractive profile. Besides, the influence of initial curvature of the wave front on GB evolution in nonlinear saturable medium is discussed in this paper.

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