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Quantum Electronics and Laser Science Conference

Solitonlike Stokes pulses in near-resonance stimulated Raman scattering

Steven F. DiMarco, Michael E. Crenshaw, Cyrus D. Cantrell

Published Apr 24, 1989• 0 citations
OpenAlex

Abstract

This report demonstrates results of a numerical calculation in which the Maxwell-Bloch equations for near-resonance stimulated Raman scattering (SRS) are solved. We find that the Stokes field experiences parametric amplification and, because of pump field breakup into solitons, forms solitonlike structures.

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Physical Review E•Jul 13, 2005•16 citations
The theory of stimulated Raman scattering has been treated at various levels of sophistication from plane-wave steady-state models through 3-D transient quantum-electrodynamic calculations.1 Many physical effects, such as pump depletion, dispersion, level degeneracy, ac Stark shift, and parametric coupling of Stokes and anti-Stokes light, can be important in experimental setups. We describe a recently developed computer code which treats these effects in detail. The code is based on integration of the coupled Maxwell-Bloch equations of quantum optics. We discuss numerical predictions of the code relating to these effects and present applications to experimental investigations such as Raman beam cleanup and transient amplification.2
A system of Maxwell-Bloch type equations (MBE's), describing stimulated Raman scattering with both Stokes and anti-Stokes waves taken into account, is investigated. We introduce variables S3{\mathit{S}}_{3}S3​ and ${\mathit{S}}_{\ifmmode\pm\else\textpm\fi{}}$, which are bilinear in the electromagnetic fields, and prove that the corresponding equations possess Lax representation. This fact is used to obtain additional solutions for S3{\mathit{S}}_{3}S3​, ${\mathit{S}}_{\ifmmode\pm\else\textpm\fi{}}$ and for the MBE's which include solitons, periodical waves, and self-similarity solutions. The transient and bright threshold solitons are also analyzed. \textcopyright{} 1996 The American Physical Society.
A theory of stimulated Raman scattering (SRS) is presented which treats in a unified manner the buildup of SRS from spontaneous Raman scattering and the spatial propagation which leads to gain. Maxwell-Bloch equations describe the coupling between the Stokes field operator and the collective atomic operators, which are driven by a classical laser field under low-signal-gain conditions, where the atomic ground states and laser field remain undepleted. An analytic expression is derived for the forward-propagating Stokes field operator in a one-dimensional spatial approximation when the Fresnel number of the excited medium is unity. Steady-state and transient Stokes intensities are evaluated under low-gain (spontaneous) and high-gain (stimulated) conditions. The Stokes intensity is found to be exactly independent of a laser bandwidth arising solely from phase fluctuations. The power spectrum of steady-state SRS is evaluated, giving a gain-narrowed spectral profile when the laser is narrow band, and a spectrum identical to the laser spectrum when the laser is broad band. A strong analogy between SRS and two-level superfluorescence is found; in both cases the macroscopic, collective dipole moment is initiated by quantum fluctuations.
Parametric instability induced by the medium saturation in stimulated Raman scattering is investigated theoretically via a generalized detuning (1) where ω p,s,o are the frequency of the pump, Stokes, and phonon, ϕ ˙ p s is the phase modulation, and the last term is the nonlinear correction of the highly excited anharmonic molecule with an amplitude Q.The steady-state gain and hence the Stokes efficiency, in the presence of the anharmonic term, are governed by a cubic equation of |Q|2which is to be solved from the Bloch and Maxwell equations including the pump depletion. Numerical results are shown for the transition diagram of Stokes efficiency vs input pump intensity at various system conditions at the steady-state. For the transient regime, with pulse duration shorter than the dephasing time, we analyze the temporal profiles of the Stokes and the depleted pump based on a transformed equation which combines Bloch and Maxwell equation as follows: (2) where Tis a nonlinear time, G s is the steady-state gain, l0is the input pump intensity, and Uis the real part of the phonon amplitude Q.For an input pulse intensity given by sech2(t/t p ), Eq. (2) is solved numerically to study the transient pulse profiles in the presence of pump depletion and medium saturation.
We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale analysis, we derive the Maxwell-Bloch equations for SRS in photonic crystals. These equations contain effective parameters that characterize the SRS gain, the nonlinear atomic response to the electromagnetic field, and the group velocity and that can be calculated in terms of the Bloch modes of the unperturbed photonic crystal. We show that if the pump laser frequency is tuned near a photonic band edge and the atomic system is carefully chosen such that the Stokes mode matches another photonic band edge, low-threshold, enhanced Raman amplification is possible. Possible physical realizations of SRS in photonic crystals are also discussed.