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Zeitschrift für Physik A Hadrons and Nuclei

Quantum theory of light propagation in a fluctuating laser-active medium

R. Graham, Hermann Haken

Published Oct 1, 1968• 354 citations
Publisher
DOI
10.1007/bf01405384

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A pencil shaped region of a Raman-active medium forms a source for Stokes-shifted light via stimulated Raman Scattering (SRS) when driven by an intense laser pulse. Stokes photons are scattered spontaneously at first, and then amplified during propagation through the medium. Since the scattering is initiated by quantum noise, the actual number of photons produced in any given pulse will be highly uncertain, even if the pulse energy of the driving laser is constant1. As the Stokes light propagates through such an extended region, it's coherence properties will be changed. The spatial coherence is determined by the size and shape of the region, which may be characterized by its Fresnel number F, defined as F= A/λSL, where A is the cross-sectional area of the interaction region, which has length L, and λS is the Stokes wavelength. The rate at which the microscopic scatterers (atoms or molecules) are dephased by collisions affects the temporal coherence of the Stokes light, characterised by the temporal coherence parameter Γτ /gL, where Γ is the collisional dephasing rate, τ is the laser pulse duration and g is the steady-state Raman gain coefficient.
We present a formal quantum-mechanical treatment of the damping and fluctuations of a generic radiator atom due to collisions with foreign gas atoms. By working in the Heisenberg picture, the fluctuating noise sources are identified with the damping. Under the same approximations as the conventional line-shape broadening theory in the impact (Markov) approximation, the fluctuation-dissipation theorem is satisfied in the form of the conservation of an equal-time commutator for the atomic operators. The implications of this type of approach for the quantum theory of light propagation in an active medium is addressed. Simple cases for two-level and three-level \ensuremath{\Lambda}-type systems are given explicitly.