Variational analysis of solitary waves in a homogeneous cubic-quintic nonlinear medium

Abstract

Fundamental solitary waves in a cubic-quintic nonlinear medium are investigated both numerically and variationally. An equivalent particle model is used to understand the behaviour of the numerical solutions, and while a super-Gaussian trial function is found to have only a limited range of applicability in the variational analysis, a super-sech trial function is found to match the numerical solutions well for all input powers. Various limits are also investigated.' Present address: Student Support Services,

Optical soliton perturbation with full nonlinearity in non-Kerr law media

“…The term with ν is large for the case of p-toluene sulfonate crystals. It arises in the nonlinear interaction between Langmuir waves and electrons and describes the nonlinear interaction between the high frequency Langmuir waves and the ion-acoustic waves by pondermotive forces [5][6][7]. There was little attention paid to the propagation of optical beams in the fifth order nonlinear media, since no analytic solutions were known and it seemed that chances of finding any material with significant fifth order term was slim.…”

“…However, recent developments have rekindled interest in this area. The optical susceptibility of CdS x Se 1−x -doped glasses was experimentally shown to have a considerable χ (5) , the fifth order susceptibility. It was also demonstrated that there exists a significant χ (5) nonlinearity effect in a transparent glass in intense femto-second pulses at 620 nm [5][6][7].…”

“…Also, this serves as a basic model to describe the solitons in photovoltaic-photorefractive materials such as LiNbO 3 . In this case, F (s) = s p + k 2 s 2p so that the NLSE with dual-power law of nonlinearity is given by [1,7] iq t + 1 2 q xx + |q| 2n + k 2 |q| 4n q = 0 (67) Equation (67) supports solitary waves of the form [5] q(x, t) = A…”

“…It was recognized in 1960s and 70s that saturation of the nonlinear refractive index plays a fundamental role in the self-trapping phenomenon. Higher order nonlinearities arise by retaining the higher order terms in the nonlinear polarization tensor [5][6][7].…”

“…In (36), it is necessary to have 0 < n < 2 to prevent wave collapse [1,5] and, in particular, n = 2 to avoid self-focusing singularity [1]. The soliton solution of (36) is given by [1,7] q(x, t) = A…”