Plasma channel generation (or filamentation) using ultraintense laser pulses in dielectric media has a wide spectrum of applications, ranging from remote sensing to terahertz generation to lightning control. So far, laser filamentation has been triggered with the use of ultrafast pulses with axially symmetric spatial beam profiles, thereby generating straight filaments. We report the experimental observation of curved plasma channels generated in air using femtosecond Airy beams. In this unusual propagation regime, the tightly confined main intensity feature of the axially nonsymmetric laser beam propagates along a bent trajectory, leaving a curved plasma channel behind. Secondary channels bifurcate from the primary bent channel at several locations along the beam path. The broadband radiation emanating from different longitudinal sections of the curved filament propagates along angularly resolved trajectories.

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Spatial- and time-domain versions of the unidirectional pulse propagation equation (UPPE) are derived and compared from the point of view of their practical application in simulations of nonlinear optical pulse dynamics. A modification of the UPPE suitable for ultrathin optical waveguides, such as submicron silica wires, is also presented. We show in detail how various, previously published propagation equations follow from the UPPE in a unified way that clearly elucidates their underlying approximations and areas of applicability.

We present numerical simulations of nonlinear pulse propagation in air whereby an initial pulse is formed, absorbed by plasma generation, and subsequently replenished by power from the trailing edge of the pulse. This process can occur more than once for high-power input pulses and produce the illusion of long-distance propagation of one self-guided pulse.

Recent experiments on femtosecond pulses in water displayed long distance propagation analogous to that reported in air. We verify this phenomena numerically and show that the propagation is dynamic as opposed to self-guided. Furthermore, we demonstrate that the propagation can be interpreted as due to dynamic nonlinear X-waves whose robustness and role in long distance propagation is shown to follow from the interplay between nonlinearity and chromatic dispersion. The nonlinear Schrödinger equation (NLSE) in two or more dimensions is ubiquitous in physics as a model for weakly interacting nonlinear and dispersive waves, and arises in such diverse areas as Langmuir waves in plasmas, weakly interacting Bose-Einstein condensates, and optical propagation in nonlinear dielectrics [1]. The ubiquity of the NLSE means that new solutions or paradigms that arise in one area can extend into other areas. For example, previous experiments have shown that femtosecond (fs) pulses can propagate long distances though air while maintaining an almost constant fluence profile [2,3,4]. (Here long distance means that filaments of wavelength λ and radius r 0 persist for distances much longer than their associated Rayleigh range πr 2 0 /λ.) Although these results initially suggested a self-guiding mechanism, with self-focusing balanced by plasma defocusing, numerical simulations revealed that the propagation is highly dynamic, and this led us to the paradigm of dynamic spatial replenishment, whereby the propagating pulse collapses, the collapse is arrested, and the process is repeated several time as the collapse is replenished from spatially delocalized power [5]. One would then expect analogous phenomena in other fields, and indeed the dynamic spatial replenishment model in air has analogies with the Bose-Nova phenomenon in atomic gases [6].Here our goal is to elucidate the physics underlying recent observations [7] of long distance propagation of fs pulses in water. Long distance propagation has previously been explored in glass [8] and there are clear differences with respect to air propagation. For example, in silica glass, and water also, normal group-velocity dispersion (NGVD) plays a much more dominant role in comparison to air, and this gives rise to nonlinear pulse-splitting [9,10,11,12,13]. Using numerical simulations we first verify the reported properties for long distance propagation in water, and we then perform diagnostic simulations to elucidate the underlying physics. In particular, we show that long distance propagation in water is given a natural explanation by combining the paradigms of nonlinear pulse-splitting and nonlinear Xwaves. Nonlinear X-waves arise from the combination of diffraction, NGVD, and self-focusing, and have recently been introduced and examined theoretically [14] and experimentally [15]. Our main conclusion is that long distance propagation in water is best understood in terms of nonlinear X-waves.Our model for fs pulse propagation in water is based on the propagation equation for the spectral ...

In this article, we develop a classical electrodynamic theory to study the optical nonlinearities of metallic nanoparticles. The quasi-free electrons inside the metal are approximated as a classical Coulomb-interacting electron gas, and their motion under the excitation of an external electromagnetic field is described by the plasma equations. This theory is further tailored to study second-harmonic generation. Through detailed experiment-theory comparisons, we validate this classical theory as well as the associated numerical algorithm. It is demonstrated that our theory not only provides qualitative agreement with experiments, it also reproduces the overall strength of the experimentally observed second-harmonic signals.

A unidirectional optical pulse propagation equation, derived directly from Maxwell's equations, provides a seamless transition between various nonlinear envelope equations in the literature and the full vector Maxwell's equations. The equation is illustrated in the context of supercontinuum generation in air and is compared to a recent scalar model of Brabec and Krausz. Fully vectorial aspects of the model are illustrated in the context of extreme focusing of a femtosecond pulse.

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