Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses

Abstract

Nonlinear losses accompanying self-focusing substantially impacts the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the 2D+1 nonlinear Schrödinger equation which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as strong attractor for the self-focusing dynamics in Kerr media.PACS numbers: 42.65. Re, 42.65.Tg One of the main goals of modern nonlinear wave physics is the achievement of wave localization, stationarity and stability. While in a one-dimensional geometry (e.g., in optical fibers), nonlinearity suitably balances linear wave dispersion, leading to the soliton regime, in the multidimensional case, nonlinearity drives waves either to collapse or instability. In self-focusing of optical beams, for instance, many stabilizing mechanisms, such as Kerr saturation, plasma-induced defocusing, or stimulated Raman scattering, have been explored, and are being the subject of intense debate, mainly in the context of light filamentation in air or condensed matter [1]. These mechanisms, however, are either intrinsically lossy, or, due to the huge intensities involved, are accompanied by losses, which lead ultimately to the termination of any soliton regime. Similar pictures can be traced in all phenomena commonly discussed in the context of the nonlinear Schrödinger equation (NLSE), as Bose-Einstein condensates (BEC) or Langmuir waves in plasma [2]. Nonlinear losses (NLL) arise in BEC from two-and three-body inelastic recombination, and as the natural mechanism for energy dissipation in Langmuir turbulence [3].The question then arises of whether any stationary and localized (SL) wave propagation is possible in the presence of NLL. The response, as shown in this Letter, is affirmative. These SL waves cannot be ascribed to the class of solitary waves, but are instead nonlinear conical waves (as the non-linear X waves [4]) of dissipative type, whose stationarity is sustained by a continuous refilling of the nonlinearly absorbed central spot with the energy supplied by linear, conical tails. These waves are not only robust against NLL, but find their stabilizing mechanism against perturbations in NLL themselves.Among the linear conical waves [5], the simplest one is the monochromatic Bessel beam (BB) [6], made of a superposition of plane waves whose wave vectors are evenly distributed over the surface of a cone, resulting in a nondiffracting transversal Bessel profile. Despite the ideal nature of BBs (they carry infinite power), they not only have revealed to be a paradigm for understanding wave phenomena, but also have found applications as diverse as in frequency conversion, or in atom trapping and alignment [7]. Of particular interest for us is the finding [8] that the BB is describable in terms of the interference of two conical Hankel beams [5], carrying equal amounts of energy towards and outwards the beam ...

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