Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering

Abstract

By using the inverse spectral transform, the SRS equations are solved and the explicit output data is given for arbitrary laser pump and Stokes seed profiles injected on a vacuum of optical phonons. For long duration laser pulses, this solution is modified such as to take into account the damping rate of the optical phonon wave. This model is used to interprete the experiments of Drühl, Wenzel and Carlsten (Phys. Rev. Lett., (1983) 51, 1171), in particular the creation of a spike of (anomalous) pump radiation. The related nonlinear Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike is not a soliton.

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

“…1 -The spectral transform at time zero ρ(k, 0) is obtained form the Dirichlet conditionq(x) by finding the vector solution φ 2 (k, x, 0) of the integral equations (2.4) in the upper half k-plane, namely 23) and then ρ(k, 0) results from…”

“…As a general result, it has been shown that the dispersion relation will depend explicitely not only on the boundary values (as for infinite line [23]) but also on the spectral transform itself hence producing nonlinear time evolution of spectral data (of Riccati type) [16]. Interesting enough, such an evolution induces the motion of the poles (discrete eigenvalues of the spectral problem, associated to solitons) and thus results in creation (and anihilation) of solitons due to input boundaries.…”

“…The spectral data is then constituted by the set 23) which is complete if we prove that it allows to reconstruct the potentials r(x) and q(x) with q(0 + ) = q 0 and r(0 + ) = r 0 .…”

Raman solitons in transient SRS

“…These have been interpreted as the manifestation of solitons which, in the spectral transform scheme, would be related to discrete eigenvalues. Instead they are related to the continuous spectrum (they are not solitons) and named Raman spikes [6]. Therefore the question of the observation of the Raman soliton is open since the original work [3] in 1975.…”

Nonlinear absorption in discrete systems

“…In that last case, the nonlinear interaction induces (laser) pump depletion and phase effects result in Raman spike generation (short duration pump repletion) [2]. Although the Raman spike generation is not a solitonic effect, here also the nonlinearity is the fundamental tool [3].…”