Variational approach to collapse of optical pulses

Desaix, M.; Anderson, D.; Lisak, M.

doi:10.1364/josab.8.002082

Cited by 226 publications

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“…We note, however, that selffocusing of dipolar spin waves in YIG films is stabilized by dissipation, rather than by saturation of nonlinearity, as was suggested for light bullets in Ref. [5].It is well-known [6,7], that, in the absence of dissipation, two-dimensional self-focusing of an input wave packet leads to a packet collapse only if the packet amplitude is sufficiently large for nonlinearity to overcome the effects of diffraction and dispersion. Thus, the twodimensional collapse is critical; i.e., it has an amplitude threshold even in a dissipationless medium.…”

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confidence: 55%

“…Thus, the analytic theory of the isotropic (cylindrical) collapse developed in Refs. [6,7] is not directly applicable to our case. Therefore, to model the observed effect of twodimensional anisotropic self-focusing of BVMSW packets in YIG films, we performed numerical simulations, based on Eq.…”

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confidence: 89%

“…It is well-known [6,7], that, in the absence of dissipation, two-dimensional self-focusing of an input wave packet leads to a packet collapse only if the packet amplitude is sufficiently large for nonlinearity to overcome the effects of diffraction and dispersion. Thus, the twodimensional collapse is critical; i.e., it has an amplitude threshold even in a dissipationless medium.…”

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confidence: 99%

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Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

et al. 1998

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The first observation of spatiotemporal self-focusing of spin waves is reported. The experimental results are obtained for dipolar spin waves in yttrium-iron-garnet films by means of a newly developed space-and time-resolved Brillouin light scattering technique. They demonstrate self-focusing of a moving wave pulse in two spatial dimensions, and formation of localized two-dimensional wave packets, the collapse of which is stopped by dissipation. Nonlinear self-focusing of wave beams and pulses is an important phenomenon in physics because it provides a mechanism for localization of wave energy in a small spatial region [1]. In a simple model based on the nonlinear Schrödinger equation with two or three spatial dimensions, self-focusing for certain initial conditions leads to the collapse of the initial wave packet, when the packet amplitude becomes infinite in a finite time [2]. In real physical experiments singularity is, of course, avoided, and the process of collapse is stopped by saturation of nonlinearity and/or by dissipation. The effects of strong self-focusing and of wave collapse have been observed thus far for light waves in nonlinear optics [3], and for nonlinear Langmuir waves in a plasma [4]. The possibility of "light bullets," i.e., stable optical wave pulses strongly localized in space and time by self-focusing, which is stabilized by saturation of nonlinearity at high wave amplitudes, has been suggested by Silberberg [5]. There exists, however, no experimental evidence for this effect in optics, likely because, in optical fibers, diffraction is much stronger than dispersion, and, therefore, both effects cannot be observed simultaneously.In this Letter we report the first experimental observation of spatiotemporal self-focusing of dipolar spin waves and formation of strongly localized two-dimensional wave packets (spin wave bullets) propagating in yttrium-irongarnet (YIG) films. Here the diffraction to dispersion ratio is much smaller than in optical fibers, which makes it possible to observe a simultaneous self-focusing of a propagating spin wave packet along both in-plane directions. The "spin wave bullets" in our experiments are formed as a result of a spatiotemporal self-focusing, similar to the self-focusing effect described in Ref.[5], as our two-dimensional input spin wave packets are self-focused along both in-plane directions (y and z), while propagating along one of them (z). We note, however, that selffocusing of dipolar spin waves in YIG films is stabilized by dissipation, rather than by saturation of nonlinearity, as was suggested for light bullets in Ref. [5].It is well-known [6,7], that, in the absence of dissipation, two-dimensional self-focusing of an input wave packet leads to a packet collapse only if the packet amplitude is sufficiently large for nonlinearity to overcome the effects of diffraction and dispersion. Thus, the twodimensional collapse is critical; i.e., it has an amplitude threshold even in a dissipationless medium.In the presence of dissipation, the amplitude of a ...

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Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

et al. 1998

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“…However, the corresponding solutions are not explicit except in the special cases of the soliton solutions. In addition, the approximate solution may be obtained by assuming the light wave has Gaussian characteristics [11][12][13][14][15]. In this paper, motivated by the requirements of the design of high power solid laser * E-mail: zchy49@sohu.com system for plasma physics, we restrict our research on the propagation of a Gaussian beam in nonlinear media, aim to find the explicit analytical solution which can help us to analyze the instability of laser beam and estimate the beam quality by the output power density (PSD) from a high power device.…”

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confidence: 99%

Instability analysis of Gaussian beam propagation in a nonlinear refractive index medium

Zhao

Tan

2008

Open Physics

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Abstract:In this paper, we use a thin filament two dimensional Gaussian beam to model the self-trapping filament. The instability of the propagation of a Gaussian beam through a nonlinear refractive index media is investigated, theoretically and numerically. Specifically, the small scale instability of the beam is examined. The numerical results show that the propagation of the two dimensional Gaussian beam presents one or more nonlinear focal points. PACS

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“…In the context of the Ritz optimization procedure, as used in the frame of optical propagation problems, 3 ' 41 3 we look for an approximate analytical solution of Eq. (1) to be found within a set of suitably chosen trial functions of the form (4) where F is a well-behaved prescribed function and the two widths o-and ,A (along the x and y directions, respectively) are permitted to assume different values. If we insert Eq.…”

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Nonlinear propagation in Kerr media of beams with unequal transverse widths

Crosignani

Porto

1993

Opt. Lett.

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We investigate three-dimensional propagation in bulk Kerr media of beams possessing different widths in the two transverse dimensions, under the combined effects of self-focusing and diffraction.This allows us to elucidate the process of self-trapping and provides a quantitative interpretation of recent experimental observations of beam self-deflection [Barthelemy et al., Opt. Lett. 17, 844 (1992)].Much attention has recently been devoted, both theoretically'-5 and experimentally, 6 -" to the investigation of self-trapped propagation of optical beams (spatial solitons), which can be achieved as a result of balance between self-focusing and diffraction in Kerr media. In the three-dimensional case (propagation along z and diffraction along the transverse directions x and y), self-trapping is unstable under radially symmetric perturbations of the circularly symmetric transverse configuration,' 2 while the analysis of the stability properties becomes more involved for asymmetric perturbations.13The three-dimensional case degenerates into the (stable) two-dimensional one if circular symmetry is removed by letting one of the two transverse widths of the beam (e.g., y) become large enough that the corresponding diffraction length exceeds the propagation length. In this situation, the y dimension is practically infinite and the significant dynamical evolution is restricted to the x dimension. However, the propagation length can be such that the nonlinearity associated with the optical Kerr effect makes itself manifest through an experimentally observable beam self-deflection,' 4 so that it becomes necessary to investigate the beam behavior without neglecting its evolution along the y dimension.In this Letter we use a general formalism based on a variational approach to describe propagation of beams with different transverse widths. This allows us, in particular, to interpret the main features of the self-deflection experiment described in Ref. 14.We recall that stationary three-dimensional propagation is described by the dimensionless nonlinear Schrddinger equation,' 2 a-u +2 a+a-72)uH-IuI 2 u=O.( 1) where (6, Y7, ;) = (kx, ky, kz) and u (n 2 /no)"' 2 E, with n 2 being the nonlinear refractive-index coefficient of the medium (whose refractive index is given by n = no + n 2 IE I2) and E labeling the slowly varying part of the electric field exp(ikz -iwt)E(x, y, z). Equation (1) (2) of the Lagrangian densitywhere the subscripts denote partial derivative. In the context of the Ritz optimization procedure, as used in the frame of optical propagation . (7) 0146-9592/93/171394-03$6.00/0

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Variational approach to collapse of optical pulses

Cited by 226 publications

References 13 publications

Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

Observation of Spatiotemporal Self-Focusing of Spin Waves in Magnetic Films

Instability analysis of Gaussian beam propagation in a nonlinear refractive index medium

Nonlinear propagation in Kerr media of beams with unequal transverse widths

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