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Early research on self-focusing and filament formation of nanosecond and picosecond light pulses in nonlinear media is briefly reviewed. Emphasis is on physical understanding of characteristic features of the self-focusing phenomenon. Connections with the recent discovery of self-focusing and the appearance of apparently long filaments of light in air created by femtosecond light pulses are made....
These notes were written in August 30, 2006, about the history of two papers in Physical Review by I.W.G. Wagner, H.A. Haus, J.H. Marburger [1]; II. E.L. Dawes, J.H. Marburger [2] and the author’s review paper of the year 1975 “Self-focusing: theory” [3], which is reprinted in the present book.
This chapter provides a systematic account of the theory of self-focusing of waves. The parabolic equation method is applied to solve different self-focusing problems. Various self-focusing manifestations are described, specifically, the existence of homogeneous wave channels, the instability of plane waves, the formation of the regions with abnormally great field amplitudes (nonlinear foci) in cubic...
The nonlinear index of refraction is responsible for self-action effects in optical beam propagation, including self-focusing. We review self-focusing and related phenomena and discuss physical mechanisms that give rise to the refractive index nonlinearity.
This chapter presents a review of the theory of the multi-focus structure (MFS) and moving nonlinear foci (MNLF) models of self-focusing. It also reviews some experimental results on self-focusing of nanosecond-duration-pulses that support these models. Some experimental and simulation results of studies of femtosecond self-focusing in air are discussed. It is concluded that the main features of MFS-MNLF...
At high enough power, a beam propagating in a positive n2 material will spontaneously break up into multiple filaments as a result of a transverse modulational instability. This chapter briefly surveys the essential physics, presents a linearized theory and summarizes experimental examples illustrating the dependence between optimal spatial frequency, gain coefficient, self-focusing length,...
In this chapter, we give a brief review of collapses in nonlinear optics with and emphasis on their classification (weak, strong, and black holes), correspondence between solitons and collapses and effects of the group velocity dispersion as well.
Laser-beam shaping and suppression of beam self-focusing in high-peak-power Nd:glass laser systems are discussed. The role of Fresnel diffraction at apertures at the laser facility as the source of dangerous spatial scales for small-scale self-focusing is illustrated. Methods of the formation of super-Gaussian laser beams for suppressing diffraction ripples on the beam profile and their self-focusing...
A broad overview of self-action effects in atomic vapors, such as self-focusing, self-trapping and pattern-formation, is presented. Different theoretical models that describe conical emission in atomic media are discussed, together with supporting experimental results.
In this chapter, supercontinuum (SC) generation and filamentation in BK7 glass were controlled by Fresnel diffraction from a circular aperture or a straight edge. We demonstrated the salient coherent property of multiple SC sources by the periodic filamentation.
One of the major characteristics of the solid-state laser that distinguishes it from the more elegant gas laser is its ability to generate almost unbelievably high peak powers. Today you can go out and buy a Q-spoiled ruby laser with a peak power output in excess of 500 MW (and this figure can, of course, be further increased by the use of optical amplifiers). One naturally wonders whether there is...
We review the evolution of the modeling of femtosecond filamentation in transparent media from the monochromatic self-trapping model to the development of numerical models including all relevant physical effects. We discuss four self-action effects which occur during filamentation: i) the generation of single cycle pulses by filamentation in gases, ii) the beam self-cleaning effect associated with...
A long plasma channel is formed with a length up to a few hundred meters when intense femtosecond laser pulses propagate in air. We find that the propagation of the filaments in the channel shows a very complicated process including the evolution from a single filament into two and three and even more distinct filaments periodically, and the merging of multiple filaments into two filaments that propagate...
When a powerful femtosecond laser pulse propagates in a transparent optical medium, be it a gas or a condensed medium, the pulse will self-focus into a series of self-foci, giving rise to the perception of a filament. This universal nonlinear propagation phenomenon is currently an interesting research topic at the forefront of applied physics and attracts more and more people into this field. In this...
The physical picture of the phenomenon of filamentation of a powerful femtosecond laser pulse in the bulk of a transparent dielectric is considered on the basis of the experimental results at Laval University (Quebec, Canada), and the computer simulations performed at M.V. Lomonosov Moscow State University (Russia). In this chapter the dynamic moving-focus model is discussed. The quasi-stationary...
In nonlinear optics, a wave collapse manifests itself as the self-focusing of light. There exist a number of universal features associated with wave collapse, such as self-similar evolution, pulse splitting, filamentation, and shock formation, in which nonlinear optics has offered an unparalleled opportunity for study and comparison of theory with experiment. This chapter reviews recent theoretical...
In this chapter, we give a brief summary of the present status of self-focusing theory, while trying to highlight the fascinating evolution of this theory.
X waves are emerging as a universal concept that allows us to interpret experiments of filamentation and trapping in a normally dispersive medium. We briefly review the main experimental and theoretical results behind this paradigm.
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