Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients

Abstract

We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schrödinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.

On negative higher-order Kerr effect and filamentation

“…to higher harmonics [29] and should therefore be included in the propagation equations, unless the it is proven that it induces a negligible effect in the considered situation. In the context of filamentation, such development was already tried several years ago [12][13][14][15][16], although the significance of those works was limited by the lack of experimental knowledge of the magnitude of these terms.…”

Controllable optical rogue waves: Recurrence, annihilation and sustainment

“…To find this kind of analytic solution for Eq. (1), we employ the lens-type transformation [26][27][28][29][30][31],…”

Spectral dependence of purely-Kerr-driven filamentation in air and argon

“…1 n 2 0 (ω) 0 c j Re [χ (2j +1) (ω)]. (2) In the past years, several numerical works have investigated the influence of the quintic nonlinear response on the filamentation dynamics at a wavelength of 800 nm, although without knowledge of its actual value [6][7][8][9][10]. They suggested that this term was defocusing, but considered it as marginal.…”