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Physical Review Letters

Unifying Degenerate Four-Wave Mixing and Coherent Anti-Stokes Raman Scattering in Rare Media

Suresh Chandra

Published Mar 22, 1982• 3 citations
Publisher

Abstract

The degenerate and counterpropagating waves of the degenerate four-wave mixing process will appear nondegenerate and noncounterpropagating to a moving observer. A Lorentz-transformed degenerate four-wave mixing is seen to be indistinguishable from coherent anti-Stokes Raman scattering. Inverse transformations which render any given coherent anti-Stokes Raman scattering the appearance of a degenerate four-wave mixing are also presented.

DOI
10.1103/physrevlett.48.795

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The degenerate and counterpropagating waves of the degenerate four-wave mixing process will appear nondegenerate and noncounterpropagating to a moving observer. A Lorentz-transformed degenerate four-wave mixing is seen to be indistinguishable from coherent anti-Stokes Raman scattering. Inverse transformations which render any given coherent anti-Stokes Raman scattering the appearance of a degenerate four-wave mixing are also presented.
Degenerate four-wave mixing in diamond generates a quantum state ${\ensuremath{\rho}}_{\mathrm{SaS}}$ composed of Stokes (S) and anti-Stokes (aS) time-correlated photon pairs (SaS). Here, polarization state tomography of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ is performed in four pertinent scattering configurations: Raman shift in resonance and out of resonance with the phonon energy, and incident light polarized in the direction parallel to or $\ensuremath{\pi}/4$ rotated from a diamond crystallographic axis. We reconstruct the density matrix, calculate concurrence and purity for the four configurations, and directly measure and analyze the diagonal terms of ${\ensuremath{\rho}}_{\mathrm{SaS}}$ in different bases. We establish ${\ensuremath{\rho}}_{\mathrm{SaS}}$ as an entangled linear combination of electronic four-wave mixing and SaS Raman process, mixed with uncorrelated S and aS photons, with the weight constants depending on the scattering conditions, which can be engineered for future applications.
A theoretical analysis is made of generation and amplification of Stokes and anti-Stokes waves in gaseous media allowing for Raman and parametric processes and saturation effects. Allowance is also made for any difference between the Raman polarizabilities of the Stokes and anti-Stokes waves which may be caused in particular by the occurrence of one-photon quasiresonances of the interacting waves. Assuming that pump and Stokes (or anti-Stokes) waves are applied at the entrance to a medium (inverted or uninverted), a general solution is found for the amplitudes of the interacting waves under exact resonance and phase-matching conditions. This is used as the basis to investigate their spatial evolution (in particular, for inverse Raman light scattering) and expressions are found for the maximum efficiencies for conversion of the pump to Stokes and/or anti-Stokes waves. It is shown that depending on the relationship between the Raman polarizabilities and also on the input parameters of the waves, conditions of parametric bleaching of the medium with nonzero amplitudes of all the waves or conditions of complete conversion of the pump to the Stokes and anti-Stokes waves or to one of these are established asymptotically. An investigation is made of the stability of these solutions.
A common assumption that Raman-resonant four-wave mixing does not transfer energy between the light and the Raman medium is shown to be incorrect. The derivation of the correct energy-transfer picture is compared with those for stimulated Raman scattering and for nonresonant mixing. The physical mechanism for Raman-gain suppression due to Stokes/anti-Stokes coupling under phase-matched conditions is clarified by this understanding of the energy transfer. An experimental demonstration of the nature of the energy transfer is proposed.
In this paper, we present a model that fully describes the quasi-stationary behavior of coherent anti-Stokes Raman scattering (CARS) in an anti-Stokes Raman converter operating at exact Raman resonance. We demonstrate that the CARS mechanism actually comprises two opposite and competing interactions, which respectively create and annihilate phonons in the Raman medium. Furthermore, we show that both the phase mismatch of the CARS four-wave mixing process and the level of pump depletion determine which of these two interactions takes place along the converter path length. In addition, we demonstrate that our CARS model is fully in line with seemingly contradictory findings in Raman conversion experiments. Finally, we discuss the fundamental differences between our CARS interpretation and the CARS models presented earlier.