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- Boaz Ilan, Gadi Fibich, George Papanicolaou
- SIAM Journal of Applied Mathematics
- 2002

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)

- Gadi Fibich, Boaz Ilan, Semyon Tsynkov
- J. Sci. Comput.
- 2002

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)

We calculate the critical exponent of nonlinear Schrödinger (NLS) equations with anisotropic negative fourth-order dispersion using an anisotropic Gagliardo–Nirenberg inequality. We also prove global existence, and in some cases uniqueness, for subcritical solutions and for critical solutions with small L 2 norm, without making use of Strichartz-type… (More)

- Gadi Fibich, Boaz Ilan
- 2001

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)

- Gadi Fibich, Shmuel Eisenmann, Boaz Ilan, Arie Zigler
- Optics letters
- 2004

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)

- Derya Sahin, Boaz Ilan
- Journal of the Optical Society of America. A…
- 2013

We propose a generalization of radiative transport theory to account for light propagation in luminescent random media. This theory accounts accurately for the multiple absorption and reemission of light at different wavelengths and for anisotropic luminescence. To test this theory, we apply it to model light propagation in luminescent solar concentrators… (More)

- Mark J Ablowitz, Boaz Ilan, Steven T Cundiff
- Optics letters
- 2004

The carrier-envelope phase slip of an ultrashort pulse circulating in a mode-locked Ti:sapphire laser is analyzed. The laser cavity is modeled by a dispersion- and nonlinearity-managed nonlinear Schrödinger equation. The combined contributions to the phase slip induced by nonlinear phase and nonlinear dispersion are found to approach zero for strong… (More)

- Mark J Ablowitz, Boaz Ilan, Ethan Schonbrun, Rafael Piestun
- Physical review. E, Statistical, nonlinear, and…
- 2006

Localized nonlinear modes, or solitons, are obtained for the two-dimensional nonlinear Schrödinger equation with various external potentials that possess large variations from periodicity, i.e., vacancy defects, edge dislocations, and quasicrystal structure. The solitons are obtained by employing a spectral fixed-point computational scheme. Investigation of… (More)

The standard explanation for multiple filamentation of laser pulses is that it is caused by noise in the input beam. We propose an alternative explanation that is based on deterministic vectorial (polarization) effects. We present numerical simulations in support of the vectorial-effects explanation and suggest a simple experiment for deciding whether… (More)

The relation between the fundamental parameters of energy and temporal duration of ultrashort pulses, under the condition of varying the average dispersion, are demonstrated both theoretically and experimentally in a solid-state femtosecond mode-locked laser. An asymptotic theory for nonlinear and dispersion managed solitons agrees well with the… (More)