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… (More)
We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt ± ∆ q ψ + |ψ| 2σ ψ = 0, in the isotropic mixed-dispersion NLS iψt + ∆ψ + ǫ∆ 2 ψ + |ψ| 2σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays. 1. Introduction. The canonical model for… (More)
The explicit contribution to the free energy barrier and proton conductance from the delocalized nature of the excess proton is examined in aquaporin channels using an accurate all-atom molecular dynamics computer simulation model. In particular, the channel permeation free energy profiles are calculated and compared for both a delocalized (fully Grotthuss… (More)
In this Letter we provide what is believed to be the first experimental evidence of suppression of the number of filaments for high-intensity laser pulses propagating in air by beam astigmatism. We also show that the number, pattern, and spatial stability of the filaments can be controlled by varying the angle that a focusing lens makes with the axial… (More)
The critical nonlinear Schrödinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L 2 norm of the… (More)
We show numerically for continuous-wave beams and experimentally for femtosecond pulses propagating in air, that the collapse distance of intense laser beams in a bulk Kerr medium scales as 1/P;1/2 for input powers P that are moderately above the critical power for self focusing, but that at higher powers the collapse distance scales as 1/P.
The nonlinear Schrödinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the non-linear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way… (More)
In this study, the minimalist synthetic LS2 channel is used as a prototype to examine the selectivity of protons over other cations. The free-energy profiles along the transport pathway of LS2 are calculated for three cation species: a realistic delocalized proton (including Grotthuss shuttling)--H(+), a classical (nonshuttling) hydronium--H(3)O(+), and a… (More)
We provide what is to our knowledge the first experimental evidence that multiple filamentation (MF) of ultra-short pulses can be induced by input beam ellipticity. Unlike noise-induced MF, which results in complete beam breakup, the MF pattern induced by small input beam ellipticity appears as a result of nucleation of annular rings surrounding the central… (More)
We derive a perturbed two-dimensional nonlinear Schrödinger equation which describes the propagation of gap-soliton bullets in nonlinear periodic waveguides at frequencies close to the gap for Bragg reflection. Analysis and simulations of this equation show that the bullets amplitude undergoes stable focusing–defocusing cycles.