Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics

Berczyński, Paweł; Kravtsov, Yu. A.

doi:10.1016/j.physleta.2004.08.056

Cited by 23 publications

(24 citation statements)

References 9 publications

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“…Substitution of (14) into the eikonal Eq. (11) leads to the following ordinary differential equation of Riccati-type for parameter B (τ) [20], similar to that obtained within Luneburg paraxial optics [17]:…”

Section: Paraxial Complex Geometrical Optics (Cgo)supporting

confidence: 68%

“…Eikonal-based form of CGO deals directly with eikonal and is also able to describe Gaussian beam diffraction. According to [20], to describe paraxial beam propagation and diffraction in inhomogeneous 2D medium it is convenient to use a 2D curvilinear frame of reference (τ ξ) associated with the central ray:…”

Section: Paraxial Complex Geometrical Optics (Cgo)mentioning

confidence: 99%

“…In a frame of paraxial approximation deviation, can be presented in the quadratic form, like in traditional paraxial optics [17,20]:…”

Section: Paraxial Complex Geometrical Optics (Cgo)mentioning

confidence: 99%

“…(15) is constant α = 1 L 2 = and according to (20), (21), with transformation τ → , ξ → , the wave field in a lens-like waveguide is of the form:…”

Section: Gaussian Beam Diffraction In Inhomogeneous Planar Waveguide mentioning

confidence: 99%

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

Berczyński

Kravtsov²,

Zegliñski

2008

Open Physics

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Abstract: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.

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Section: Paraxial Complex Geometrical Optics (Cgo)supporting

confidence: 68%

Section: Paraxial Complex Geometrical Optics (Cgo)mentioning

confidence: 99%

“…In a frame of paraxial approximation deviation, can be presented in the quadratic form, like in traditional paraxial optics [17,20]:…”

Section: Paraxial Complex Geometrical Optics (Cgo)mentioning

confidence: 99%

“…(15) is constant α = 1 L 2 = and according to (20), (21), with transformation τ → , ξ → , the wave field in a lens-like waveguide is of the form:…”

Section: Gaussian Beam Diffraction In Inhomogeneous Planar Waveguide mentioning

confidence: 99%

See 2 more Smart Citations

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

Berczyński

Kravtsov²,

Zegliñski

2008

Open Physics

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“…A surprising feature of CGO is its ability to describe Gaussian beam (GB) diffraction in both ray−based and eikonal−based approaches. Recently, CGO method has been applied to describe GB evolution in inhomogeneous media [9][10][11] and nonlinear media of Kerr type [11,12] including graded−index [13] and nonlinear fibres [14]. It is shown in Ref.…”

Section: Introductionmentioning

confidence: 99%

Gaussian beam evolution in longitudinally and transversely inhomogeneous nonlinear fibres with absorption

Berczyński

2013

Opto-Electronics Review

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The method of complex geometrical optics (CGO) is presented, which describes Gaussian beam (GB) diffraction and self-focusing in smoothly inhomogeneous and nonlinear Kerr type and saturable fibres. CGO reduces the problem of Gaussian beam evolution in inhomogeneous and nonlinear 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, CGO radically simplifies the description of Gaussian beam diffraction and self-focusing effects as compared to other methods of nonlinear optics such as variational method approach, method of moments and beam propagation method. The power of CGO method is presented on the example of Gaussian beam propagation in saturable fibres with either focusing and defocusing refractive profiles. Besides, the influence of initial curvature of the wave front, phenomenon of weak absorption and effect of either transverse and longitudinal inhomogeneity on GB propagation in nonlinear fibres is discussed in this paper.

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Elliptical Gaussian beam propagation in inhomogeneous and nonlinear fibres of Kerr type

Berczyński

2013

Opt Quant Electron

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Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics

Cited by 23 publications

References 9 publications

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

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

Gaussian beam evolution in longitudinally and transversely inhomogeneous nonlinear fibres with absorption

Elliptical Gaussian beam propagation in inhomogeneous and nonlinear fibres of Kerr type

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