Self-trapped elliptical super-Gaussian beam in cubic–quintic media

Jana, Soumendu; Singh, Ajitpal; Porsezian, K.; Mithun, Thudiyangal

doi:10.1016/j.optcom.2014.06.061

Cited by 11 publications

(1 citation statement)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We expect our methods to have applications to related problems in nonlinear optics, for nonlinearities other than the ones studied here, for different beams, such as super-Gaussian beams [24], and for optical bullets [30,42]. We are encouraged by the fact that there is some recent experimental evidence [12] of breathing in optical solitons, albeit in a dissipative setting.…”

Section: Conclusion and Discussionmentioning

confidence: 89%

Analytic methods to find beating transitions of asymmetric Gaussian beams in GNLS equations

Ianetz

Schiff

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

In a simple model of propagation of asymmetric Gaussian beams in nonlinear waveguides, described by a reduction to ordinary differential eqautions of generalized nonlinear Schrödinger equations (GNLSEs) with cubic-quintic (CQ) and saturable (SAT) nonlinearities and a graded-index profile, the beam widths exhibit two different types of beating behavior, with transitions between them. We present an analytic model to explain these phenomena, which originate in a 1 : 1 resonance in a 2 degreeof-freedom Hamiltonian system. We show how small oscillations near a fixed point close to 1 : 1 resonance in such a system can be approximated using an integrable Hamiltonian and, ultimately, by a single first order differential equation. In particular, the beating transitions can be located from coincidences of roots of a pair of quadratic equations, with coefficients determined (in a highly complex manner) by the internal parameters and initial conditions of the original system. The results of the analytic model agree with numerics of the original system over large parameter ranges, and allow new predictions that can be verified directly. In the CQ case we identify a band of beam energies for which there is only a single beating transition (as opposed to 0 or 2) as the eccentricity is increased. In the SAT case we explain the sudden (dis)appearance of beating transitions for certain values of the other parameters as the grade-index is changed.

show abstract