Focusing and defocusing of the nonlinear paraxial equation 
at laser–plasma interaction

Osman, Frederick; Castillo, R.; Hora, Heinrich

doi:10.1017/s026303460018108x

Cited by 13 publications

(23 citation statements)

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“…However for the non-coinciding ξ j this solution breaks into individual solitons if t → ± ∞. Using this solution and beginning at the origin z = 0, a wave formation can be acknowledged by [5] :…”

Section: Nonlinear Paraxial Equationmentioning

confidence: 91%

“…A clear view of the evolution of the envelope along the normalized propagation path results. This will also allow us to study the different cases, such as the classical situation, where Γ = 0, which results in the standard Nonlinear Paraxial equation [5] .…”

Section: Nonlinear Paraxial Equationmentioning

confidence: 99%

“…As t → ± ∞ of any initial condition, a finite set of solitons becomes present. In this problem, an analogous role is played by the particular solutions of the Nonlinear Paraxial equation [1,5] :…”

Section: Nonlinear Paraxial Equationmentioning

confidence: 99%

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Programming of the Generalised Nonlinear Paraxial Equation for the Formation of Solitons with Mathematica

Osman¹,

Beech²

2004

American J. of Applied Sciences

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This study presents the nonlinearity and dispersion effects involved in the propagation of optical solitons which can be understood by using a numerical routine to solve the Generalized Nonlinear Paraxial equation. A sequence of code has been developed in Mathematica, to explore in depth several features of the optical soliton's formation and propagation. These numerical routines were implemented through the use with Mathematica and the results give a very clear idea of this interesting and important practical phenomenon.

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Section: Nonlinear Paraxial Equationmentioning

confidence: 91%

Section: Nonlinear Paraxial Equationmentioning

confidence: 99%

See 1 more Smart Citation

Programming of the Generalised Nonlinear Paraxial Equation for the Formation of Solitons with Mathematica

Osman¹,

Beech²

2004

American J. of Applied Sciences

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“…However, in our parameter range with lower laser intensity, the relativistic contribution is entirely negligible. 21 The related periodic focusing and defocusing may be typical for an integrable nonlinear paraxial equation 22 with an appropriate initial condition. For I 0 = 150I cr [see point B in Fig.…”

Section: Numerical Simulations and Nonlinear Dynamicsmentioning

confidence: 99%

Propagation of femtosecond terawatt laser pulses in N2 gas including higher-order Kerr effects

Huang

Zhou

2012

AIP Advances

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Propagation characteristic of femtosecond terawatt laser pulses in N2 gas with higher-order Kerr effect (HOKE) is investigated. Theoretical analysis shows that HOKE acting as Hamiltonian perturbation can destroy the coherent structure of a laser field and result in the appearance of incoherent patterns. Numerical simulations show that in this case two different types of complex structures can appear. It is found that the high-order focusing terms in HOKE can cause continuous phase shift and off-axis evolution of the laser fields when irregular homoclinic orbit crossings of the field in phase space take place. As the laser propagates, small-scale spatial structures rapidly appear and the evolution of the laser field becomes chaotic. The two complex patterns can switch between each other quasi-periodically. Numerical results show that the two complex patterns are associated with the stochastic evolution of the energy contained in the higher-order shorter-wavelength Fourier modes. Such complex patterns, associated with small-scale filaments, may be typical for laser propagation in a HOKE medium

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“…There has been important work on the solution of the time-dependent nonlinear paraxial equation [Osman et al, 2000[Osman et al, , 2004, corresponding to laser plasma interaction, presenting numerical and theoretical studies in the semiclassical limit. The essential differences between the focusing and defocusing cases were investigated for an arbitrary nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Self‐focusing of an electromagnetic pulse in the ionosphere

Faisal

Bhasin

Sodha³

2009

J. Geophys. Res.

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[1] In this paper, the self-focusing of electromagnetic pulsed beams having Gaussian and sine profiles in the ionosphere have been studied. The self-focusing of an electromagnetic pulse is caused by the nonlinearity in the dielectric function caused by the nonuniform distribution of electron temperature, determined by the Ohmic heating, solar radiation and energy loss in collisions with ions and neutrals. The radial distribution of the electron temperature causes a radial distribution of electron density and thereby that of the refractive index, which causes self-focusing. The wave frequency has been assumed to be much larger than the electron collision frequency, and the temperature of the ions has been assumed to be equal to the temperature of neutrals; this assumption is justified in the ionosphere up to a height of 400 km. In the analysis, the electromagnetic wave equation and the energy balance equation has been solved simultaneously to obtain ordinary differential equations governing the beam width parameter and the electron temperature (on and away from the axis), respectively, in the paraxial approximation. For computations, the database for the midlatitude daytime ionosphere at the height of 150 km, compiled by Gurevich (1978), has been used. The transient behavior of the electron temperature (on and away from the axis) has been graphically presented for different values of pulse widths. The dependence of the beam width parameter on the distance of propagation for different times of retardation has also been plotted and discussed.

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Focusing and defocusing of the nonlinear paraxial equation at laser–plasma interaction

Cited by 13 publications

References 0 publications

Programming of the Generalised Nonlinear Paraxial Equation for the Formation of Solitons with Mathematica

Programming of the Generalised Nonlinear Paraxial Equation for the Formation of Solitons with Mathematica

Propagation of femtosecond terawatt laser pulses in N2 gas including higher-order Kerr effects

Self‐focusing of an electromagnetic pulse in the ionosphere

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