Complex geometrical optics of Kerr type nonlinear media

Berczyński, Paweł; Kravtsov, Yu. A.; Sukhorukov, A. P.

doi:10.1016/j.physd.2009.11.002

Cited by 17 publications

(21 citation statements)

References 14 publications

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“…which leads to the known relation between the beam width w and the wave front curvature k in the form of [12] …”

Section: Solutions For Gb Propagation In Saturable Nonlinear and Absomentioning

confidence: 99%

“…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%

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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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“…which leads to the known relation between the beam width w and the wave front curvature k in the form of [12] …”

Section: Solutions For Gb Propagation In Saturable Nonlinear and Absomentioning

confidence: 99%

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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“…This paper describes the advantages of the eikonal-based form of CGO for description of Gaussian beam diraction and self-focusing in nonlinear lossy plasma. Recently, eikonal-based CGO method has been generalized for the case of inhomogeneous [1719] and nonlinear Kerr type media [20]. In the range of sub-millimeter microwaves and moderate infrared waves tokamak plasma (including JET, ITER) is weakly anisotropic, weakly inhomogeneous and weakly nonlinear.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma

Berczyński

Kravtsov

2014

Acta Phys. Pol. A

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The paper presents a simple and eective method to calculate polarization and diraction of the Gaussian beam in nonlinear and weakly dissipative plasma. The presented approach is a combination of quasi-isotropic approximation of geometric optics with complex geometrical optics. Quasi-isotropic approximation describes the evolution of polarization vector reducing the Maxwell equations to coupled ordinary dierential equations of the rst order for the transverse components of the electromagnetic eld. Complex geometrical optics describes the Gaussian beam diraction and self-focusing and deals with ordinary dierential equations for Gaussian beam width, wave front curvature, and amplitude evolution. As a result, the quasi-isotropic approximation + complex geometrical optics combination reduces the problem of diraction and polarization evolution of an electromagnetic beam to the solution of the ordinary dierential equations, which enable to prepare fast and eective numerical algorithms. Using combined complex geometrical optics/quasi-isotropic approximation for weakly anisotropic plasma, we assume that nonlinearity of anisotropy tensor is small and we restrict ourselves to considering only isotropic nonlinearity. The quasi-isotropic approximation eectively describes the evolution of microwave and IR electromagnetic beams in polarimetric and interferometric measurements in thermonuclear reactors and the complex geometrical optics method can be applied for modeling of electron cyclotron absorption and current drive in tokamaks.

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“…A surprising feature of PCGO is its ability to describe Gaussian beam (GB) diffraction in both ray-based and eikonal-based approaches. Recently, eikonal-based PCGO method has been generalized for the case of inhomogeneous [8][9][10] and nonlinear Kerr type media [10][11][12]. This paper describes the advantages of the eikonal-based form of PCGO for description of Gaussian beam diffraction and self-focusing in logarithmically saturable medium with special attention to the influence of linear refraction and the effect of initial wave front curvature.…”

Section: Introductionmentioning

confidence: 99%

Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media

Berczyński¹

2012

Open Physics

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Abstract:The 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. PACS

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Complex geometrical optics of Kerr type nonlinear media

Cited by 17 publications

References 14 publications

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

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

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma

Gaussian beam diffraction in inhomogeneous and logarithmically saturable nonlinear media

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