Correlation of Filaments in Nitrobenzene with Laser Spikes

Abbi, S. C.; Mahr, H.

doi:10.1103/physrevlett.26.604

Cited by 60 publications

(21 citation statements)

References 9 publications

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“…We now give an alternative derivation of a scalar equation for A 1 , based on the Lagrangian of the vector Helmholtz equation (1). It is straightforward to verify that the vector Helmholtz equation (1) has the Lagrangian density…”

Section: A Variational Approachmentioning

confidence: 99%

“…1). In Section 3.1 we apply perturbation analysis to the vector Helmholtz equation (1) and derive the scalar equation (21). In Section 3.2 we apply a similar perturbation analysis to the Lagrangian (22) of the vector Helmholtz equation, resulting in the Lagrangian (23), whose variational derivative leads to the scalar equation (24).…”

Section: Scalar Equations With Vectorial Effectsmentioning

confidence: 99%

“…In self-focusing experiments, a sufficiently intense laser beam can break-up into several long and narrow filaments, a phenomenon known as multiple filamentation [1,3,[7][8][9]11,12,14,15,28,30,[36][37][38]. According to the NLS model, however, if the input beam is cylindrically symmetric, then the beam should remain cylindrically symmetric during propagation.…”

Section: Vectorial Effects and Multiple Filamentationmentioning

confidence: 99%

“…According to the NLS model, beams with cylindrically symmetric input profile should remain cylindrically symmetric during propagation. However, self-focusing experiments in solids, liquids, and gases have shown that catastrophic self-focusing is often preceded by multiple filamentation, 1 in which a single input beam breaks-up into several long and narrow filaments [1,3,7,8,[10][11][12]14,15,28,30,[36][37][38]. Therefore, a self-focusing model should include a mechanism that breaks-up the cylindrical symmetry and leads to multiple filamentation.…”

Section: Introductionmentioning

confidence: 99%

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Vectorial and random effects in self-focusing and in multiple filamentation

Fibich

Ilan

2001

Physica D: Nonlinear Phenomena

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The standard explanation for multiple filamentation of laser beams is that breakup of cylindrical symmetry is initiated by noise in the input beam. In this study we propose an alternative deterministic explanation based on vectorial effects. We derive a scalar equation from the vector Helmholtz equation that describes self-focusing in the presence of vectorial and nonparaxial effects. Numerical simulations of the scalar equation show that when the input beam is sufficiently powerful, vectorial effects lead to multiple filamentation. We compare multiple filamentation due to vectorial effects with the one due to noise, and suggest how to decide which of the two leads to multiple filamentation in experiments. We also show that vectorial effects and nonparaxiality have the same effect on self-focusing of a single filament, leading to the arrest of catastrophic collapse, followed by focusing-defocusing oscillations. The magnitude of vectorial effects is, however, significantly larger than that of nonparaxiality.

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Section: A Variational Approachmentioning

confidence: 99%

Section: Scalar Equations With Vectorial Effectsmentioning

confidence: 99%

Section: Vectorial Effects and Multiple Filamentationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vectorial and random effects in self-focusing and in multiple filamentation

Fibich

Ilan

2001

Physica D: Nonlinear Phenomena

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“…Another approach for the investigation of this instability is based on the indirect (Loy and Shen, 1969)and direct (Chiligaryan, 1968;Abbi and Mahr, 1971)evidence that filamentation in a nonlinear medium is caused by the presence of irradiance spikes in the beam, normal to the direction of propagation. Following this lead, the growth of a Gaussian ripple on a plane uniform beam in plasma has been investigated (Sodha et al, 1979a;Sodha et al, 2006;Sharma et al, 2004) to a significant extent; this approach is based on the paraxial theory of self focusing of electromagnetic beams as formulated by Akhmanov et al, 1968 and developed by Sodha et al, 1976 (a,b) and his associates (Sodha et al, 1979b;Sodha et al, 1981;Sodha et al, 1992;Sodha et al, 2004;Asthana et al, 1999;Pandey and Tripathi, 1990).…”

Section: S Sodha and M Faisalmentioning

confidence: 99%

Filamentation Instability of Electromagnetic Beams in Nonlinear Media: A Tutorial Review

Sodha

Faisal²

2017

Proceedings of the Indian National Science Academy

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This paper is a tutorial presentation of spatial growth of a transverse instability, associated with the propagation of an electromagnetic beam, with uniform or Gaussian irradiance along the wavefront. There are two approaches to the study of filamentation in a plasma. The results of the two approaches have been expressed in a form where they can be compared. It has been noted that the growth of the instability in the first approach is equivalent to the self-focusing of a ripple in the second approach. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. Further a paraxial like approach has also been adopted to analyze the characteristics of propagation of aripple, when the dielectric function is determined by the composite (Gaussian and ripple) electric field profile of the beam. The effect of different parameters on the critical curves has been highlighted and the variation of the beam width parameter with the distance of propagation has been obtained for three typical cases viz of steady divergence, oscillatory divergence and self-focusing of the ripple.

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Experimente zur Selbstfokussierung einer Multimoden‐Laserstrahlung und ihre Beschreibung mit einem statistischen Modell

Gase¹,

Hein²

1976

Annalen der Physik

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I n h a l t s u b e r s i c h t . Die Selbstfokussierung der Strahlung eines Rubinlasers i m Vielmodenbetrieb, der fur spezielle Experimente der nichtlinearen Optik eingesetzt wird, wurde experimentell nntersucht. Fur die Beschreibung der Strahlung wurde ein statistisches Modell entwickelt, um die Schwelle fiir Selbstfokussierung sowie den Anteil der durch Selbstfokussierung beeinfluflten Laserenergie in Abhingigkeit von der mittleren Laserintensitiit zu berechnen. Durch Vergleich zwischen Experiment und Modell konnten Parameter der Laserstrahlung bestimmt werden.A b s t r a c t . Self-focusing of a multimode ruby laser beam used for experiments on nonlinear optics is investigated experimentally. A statistical model is developed to calculate the self-focusing threshold and the part of energy influenced by self-focusing of the laserbeam. From comparison between experiment and model quantitative data of the laser radiadion are deduced.

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Correlation of Filaments in Nitrobenzene with Laser Spikes

Cited by 60 publications

References 9 publications

Vectorial and random effects in self-focusing and in multiple filamentation

Vectorial and random effects in self-focusing and in multiple filamentation

Filamentation Instability of Electromagnetic Beams in Nonlinear Media: A Tutorial Review

Experimente zur Selbstfokussierung einer Multimoden‐Laserstrahlung und ihre Beschreibung mit einem statistischen Modell

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