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Physical Review A

Coherent propagation of Stokes light in a collisionally broadened three-level amplifier

Bruce J. Herman, Joseph H. Eberly, Michael G. Raymer

Published Apr 1, 1989• 16 citations
Publisher

Abstract

We undertake a theoretical investigation of the coherent optical propagation of Stokes light in a collisionally broadened three-level Raman amplifier. The Stokes light consists of two distinct spectral components: off-resonance stimulated Raman scattering and on-resonance stimulated fluorescence, induced by collisional transfer of population to a near-resonant intermediate state of the atomic system. Our model is based on the semiclassical Maxwell-Bloch formalism where the separation of the Stokes light into two components results in an expansion from the usual 9 to 13 atomic variables. We investigate the model both analytically and numerically. We point out the physical contributions to the simultaneous evolution of pump, fluorescence, and Raman light. We discuss the development during propagation of these separate pulses, emphasizing the nonlinear effects that lead to saturation.

DOI
10.1103/physreva.39.3447

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We undertake a theoretical investigation of the coherent optical propagation of Stokes light in a collisionally broadened three-level Raman amplifier. The Stokes light consists of two distinct spectral components: off-resonance stimulated Raman scattering and on-resonance stimulated fluorescence, induced by collisional transfer of population to a near-resonant intermediate state of the atomic system. Our model is based on the semiclassical Maxwell-Bloch formalism where the separation of the Stokes light into two components results in an expansion from the usual 9 to 13 atomic variables. We investigate the model both analytically and numerically. We point out the physical contributions to the simultaneous evolution of pump, fluorescence, and Raman light. We discuss the development during propagation of these separate pulses, emphasizing the nonlinear effects that lead to saturation.
A computational study of the optical propagation of Stokes light in a collisionally broadened three-level V-system Raman amplifier is presented. The Stokes light consists of two distinct spectral components: off-resonance stimulated Raman scattering and on-resonance stimulated fluorescence. These two signals are induced by collisional transfer of population from the excited state to the state. The intensity dependence of these effects on the buffer gas and intensity and detuning of the exciting radiations is calculated. In the calculations the probe signals and spontaneous scatterings were used to induce the stimulated signals. We have carried out the calculations over physically realistic propagation distances. The theory was compared with our experimental work and the results of the numerical analysis are used to explain some events observed in the experiments in which the physical mechanism has not yet been understood.
A computational and experimental study of the optical propagation of light in a collisionally broadened three-level Raman amplifier is presented. The Stokes light consists of two distinct spectral components: of resonance stimulated Raman scattering (SRS) and on-resonance stimulated fluorescence (ASE). The intensity dependence of these effects on the buffer gas and on the intensity and detuning of the exciting radiation are calculated. We have carried out the calculation over physically realistic propagation distance. The theoretical model for a description of ASE i SRS signals generation in such a system was developed. The numerical calculations based on the rate equations agree with the experimental results.
It is now known that conical emission in a two-level atomic system is a fundamental propagation effect brought about by the breakup of the exciting laser pulse into solitary waves.1 This report presents a semiclassical numerical calculation that extends this previous work by solving the optical Bloch and Maxwell equations for a three-level atomic vapor excited by laser fields of two different frequencies. The applied fields satisfy a two-photon resonance condition between the ground and final states and are slightly detuned from the intermediate state to enhance the nonlinear polarization.2 As the fields propagate, oscillations in the nonlinear polarization of the pump beam dominate the interaction and lead to the pump's breakup into solitary waves. The Stokes polarization, depending on the pump radiation, also experiences these oscillations. Because of the intensity-dependence of the refractive index, the solitary waves experience a curvature in the time-radius plane. This curvature manifests itself in the spectrum as a radial component of the wave vector at the Rabi frequency. The Stokes field, experiencing parametric breakup, displays a similar curvature. Spectral analysis reveals a radial component of the Stokes wave vector as well. This frequency-shifted off-axis radiation is identified as conical emission in the Stokes field.
A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.
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
We investigate the saturation effects of power broadening, Stark shifting, and population transfer on Stokes conversion in stimulated Raman scattering. We do not make the usual rotating wave approximation because the detuning from the next electronic state is assumed to be in the optical regime. Retaining the counter-rotating terms allows an exact determination of the pump and Stokes indexes of refraction. Steady-state solutions for the Stokes intensity and phase are obtained and the effects of making the rotating wave approximation (RWA) are discussed. Finally, we examine the behavior of these solutions for Stokes conversion in hydrogen gas when geometric propagation is appropriate.