Self-trapped cylindrical laser beams

Anderson, D.; Bonnedal, M.; Lisak, M.

doi:10.1063/1.862795

Cited by 89 publications

(38 citation statements)

References 9 publications

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“…Some aspects of this genuinely non-linear process can be investigated by considering numerical or approximate analytical methods. We adopt here the latter approach in this paper, using a powerful variational method that has been used recently in several similar investigations [14][15][16]28,29]. Equation (1) can be reformulated into a variational problem corresponding to a Lagrangian Ä so as to make AEÄ AEÞ ¼ equivalent to eq.…”

Section: Basic Formulationmentioning

confidence: 99%

Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

2000

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Using a direct variational technique involving elliptic Gaussian laser beam trial function, the combined effect of non-linearity and diffraction on wave propagation of optical beam in a homogeneous bulk Kerr-medium is presented. Particular emphasis is put on the variation of beam width and longitudinal phase delay with the distance of propagation. It is observed that no stationary self-trapping is possible. The regularized phase is also seen to be always negative.

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Section: Basic Formulationmentioning

confidence: 99%

Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

2000

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“…The lowest order solution in the physical situation when the nonlinearity balances the diffraction, i.e., the focusing case with κ > 0, corresponds to the so called Townes soliton [11], which has essentially the same properties and sech-shaped form as the one-dimensional soliton solution, cf. [12]. In particular, this solution only exists for negative eigenvalues, which are uniquely related to the maximum amplitude.…”

Section: The Nonlinear Schrödinger Equationmentioning

confidence: 99%

“…[12]. When using variational analysis, it is important to find a good set of trial functions that gives tractable calculations while maintaining sufficient accuracy.…”

Section: Nonlinear Bessel Beamsmentioning

confidence: 99%

Nonlinear Bessel beams

Johannisson

Anderson

Lisak

et al. 2003

Optics Communications

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The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schrödinger equation. The nonlinearity is shown to primarily affect the central parts of the Bessel beam, giving rise to radial compression or decompression depending on whether the nonlinearity is focusing or defocusing, respectively. The dynamical properties of Gaussiantruncated Bessel beams are also analysed in the presence of a Kerr nonlinearity. It is found that although a condition for width balance in the root-mean-square sense exists, the beam profile becomes strongly deformed during propagation and may exhibit the phenomena of global and partial collapse.

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“…͑10͒ was mainly inspired by previous work on the continuous NLS equation, where collective coordinate approaches using this kind of phase chirp have turned out to be successful. 24,25,19 In the presence of weak noise, we can expect Eq. ͑10͒ to give an approximate representation of the breather in the time regime following shortly after its creation, i.e., when the decoherence caused by the noise is still small enough to be neglected.…”

Section: Collective Coordinate Approachmentioning

confidence: 99%

Breatherlike excitations in discrete lattices with noise and nonlinear damping

Christiansen¹,

Gaididei²,

Johansson

et al. 1997

Phys. Rev. B

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We discuss the stability of highly localized, ''breatherlike,'' excitations in discrete nonlinear lattices under the influence of thermal fluctuations. The particular model considered is the discrete nonlinear Schrödinger equation in the regime of high nonlinearity, where temperature effects are included as multiplicative white noise and nonlinear damping. Numerical analysis shows that the lifetime of the breather is always finite and, in a large parameter regime, inversely proportional to the noise variance for fixed damping and nonlinearity. We also find that the decay rate of the breather decreases with increasing nonlinearity and with increasing damping. Using a collective-coordinate approximation, we show how the qualitative features of the numerical results can be analytically understood. Finally, in the dimer case we show that the multiplicative noise can be transformed into additive noise, and an exact stationary solution to the Fokker-Planck equation is obtained. From this solution, the dimer system is found to exhibit a noise ͑temperature͒ induced phase transition. ͓S0163-1829͑97͒07409-2͔

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Self-trapped cylindrical laser beams

Cited by 89 publications

References 9 publications

Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

Dynamics of self-focusing and self-phase modulation of elliptic Gaussian laser beam in a Kerr-medium

Nonlinear Bessel beams

Breatherlike excitations in discrete lattices with noise and nonlinear damping

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