Nonlinear localization of light

Abstract

We briefly overview historical, fundamental, and practical aspects of light wave propagation, where strong multidimensional localization and precise control of ultrashort signals is demanded. The main topic is focused on the state of art of recently discovered nonlinear conical waves, or so-called X-shaped light bullets, which have been demonstrated to appear spontaneously in many different, frequently encountered operating regimes in transparent gaseous, liquid, and solid media. Owing to unique features of white-light frequency spectrum, strong localization, deep-field stationarity, and hot-spot regeneration property, nonlinear conical waves have great potential in all applications requiring energy transfer to matter over very limited transverse areas in thick media, which thus suffer the short focal depth of conventional laser beams. Practical applications that cover many different areas ranging from nano-science to high-field physics are discussed.

Femtosecond filamentation in transparent media

“…A more general family of envelope linear modes in the form of X-waves was shown to exist , having a stationary intensity in some reference frame (possibly different from that traveling at the group velocity of the carrier frequency) and the two branches of the X in the (k ⊥ , ) space separated by either a gap in frequency or a gap in wavenumber. The recent understanding of the unique and unexpected theory of space-time focusing in quadratic media giving rise to second harmonic generation allowed an extension of the concept of X-waves in the nonlinear regime (see Dubietis et al, 2006b;Conti et al, 2007, for a review). X-waves were shown to be spontaneously generated from conventional localized pulses in (2) media (Valiulis et al, 2001;Di Trapani et al, 2003) as well as in Kerr media (Faccio et al, 2005a, b).…”

Stationary and stable light-beam propagation in Kerr media with nonlinear absorption with controllable dissipation patterns

“…The existence of light beams, called nonlinear unbalanced Bessel beams, with the ability to propagate without any change, including no attenuation, in media with Kerr-type nonlinearities and nonlinear absorption, was described in 2004 [15]. They provided a theoretical basis for interpreting some features of light filaments generated from intense, ultrashort pulses [16][17][18], where nonlinear absorption arises from multi-photon ionization, particularly the replenishment and self-healing mecha-nisms involved in their robust and quasi-stationary propagation [19][20][21][22][23][24][25]. Stationarity with nonlinear absorption is indeed possible for less strongly localized waves than solitons, as nonlinear versions of Bessel-like and Airylike beams [26,27] carrying, ideally, an infinite amount of power, or a power reservoir.…”