Raman solitons in transient SRS

Abstract

We report the observation of Raman solitons on numerical simulations of transient stimulated Raman scattering (TSRS) with small group velocity dispersion. The theory proceeds with the inverse scattering transform (IST) for initial-boundary value problems and it is shown that the explicit theoretical solution obtained by IST for a semi-infinite medium fits strikingly well the numerical solution for a finite medium. We understand this from the rapid decrease of the medium dynamical variable (the potential of the scattering theory). The spectral transform reflection coefficient can be computed directly from the values of the input and output fields and this allows to see the generation of the Raman solitons from the numerical solution. We confirm the presence of these nonlinear modes in the medium dynamical variable by the use of a discrete spectral analysis.

The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications

“…where 18) and where the contour of integration has to be understood as being C − for the first vector of the product ΨR, and C + for the second. Thanks to the particular dependence in x of R(k, x) it is easy to compute Ψ x + ik[σ 3 , Ψ] and by algebraic manipulations to get…”

“…Note that the essential property to be used is the fact that ρ(k, t) is continuous and bounded for k ∈ R at any given t. Particular attention is required when, as t evolves, a pole of ρ is "seen" to cross the real axis. It has been demonstrated in [18] that the process is continuous, or put in other words, a resonance (pole in the lower half-plane) dissapears and a pole appears while never belonging to the real axis. The same situation arises for the Schrödinger eigenvalue problem [25].…”

“…The advantage of such a method is that, in the physically relevant case of a medium initially at rest, it allows to get all the information on the nonlinear Fourier spectrum explicitely from the input radiation fields. An interesting consequence is the possibility to build literaly the spectral transform out of measurements and compare it to the theory, which has been done successfuly on numerical simulations [18] of the finite interval, as well as experimental data [21] with infinite line damped model. The method has also been extended to treat perturbation of SRS [22], confirming the validity of approximations used for comparison with experiments in [21].…”

Polarization Simultons in Stimulated Raman Scattering by Polaritons

“…There were also achievements in the theory of solitons and SRS [6]. The numerical simulation of the transient stimulated Raman scattering based on using the inverse scattering transform technique is reported in [7]. A new type of solitons-dissipative Raman solitons-was found based on the nonlinear Ginzburg-Landau equation in [8].…”

Vectorial stimulated Raman scattering resolution on the semi-line

“…Among them, one is based on the inverse scattering transform (IST) [11][12][13][14][15][16]. It has already been shown that vectorial SRS is solvable on the line [13] what has allowed to explain the formation of the spike of pump radiation.…”