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Physical Review A

Buildup of transverse spatial correlations in stimulated Raman scattering

M. Strauss, J. Oreg, Avi Bar-Shalom

Published Nov 1, 1988• 15 citations
Publisher

Abstract

A three-dimensional quantum theory of stimulated Raman scattering is presented which takes into account a general transverse shape of the pump laser. The transverse spatial autocorrelation function and the intensity of the Stokes pulse are derived analytically, by use of the Maxwell-Bloch equations in low-signal-gain conditions and introduction of a many-spatial-modes approximation. We find that the spatial and temporal coherence are coupled. The transverse coherence depends on the pump-laser shape, and the coherence area increases with increasing gain. Time scales for the buildup of stimulated intensity and correlations for the various transverse parts of the Stokes pulse are obtained.

DOI
10.1103/physreva.38.4712

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A three-dimensional quantum theory of stimulated Raman scattering is presented which takes into account a general transverse shape of the pump laser. The transverse spatial autocorrelation function and the intensity of the Stokes pulse are derived analytically, by use of the Maxwell-Bloch equations in low-signal-gain conditions and introduction of a many-spatial-modes approximation. We find that the spatial and temporal coherence are coupled. The transverse coherence depends on the pump-laser shape, and the coherence area increases with increasing gain. Time scales for the buildup of stimulated intensity and correlations for the various transverse parts of the Stokes pulse are obtained.
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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.
We present a three-dimensional theory of stimulated Raman scattering (SRS) or super-radiance. In particular we address how the spatial and temporal properties of the generated SRS beam or Stokes beam of radiation depends on the spatial properties of the gain medium. Maxwell equations for the Stokes field operators and of the atomic operators are solved analytically and a correlation function for the Stokes field is derived. In the analysis we identify a super-radiating part of the Stokes radiation that exhibit beam characteristics. We show how the intensity in this beam builds up in time and at some point largely dominates the total Stokes radiation of the gain medium. We show how the SRS depends on the Fresnel number and the optical depth and that in fact these two factors are the only factors describing the coherent radiation.
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A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg–Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition , where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial–temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.
The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.