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Optics Communications

Theoretical analysis of the steady state behavior of a Raman anti-Stokes ring laser

Hong Yuan Ling, Jian‐Min Yuan, Lorenzo M. Narducci, J.R. Treddice, William J. Scharpf

Published Sep 1, 1990• 2 citations
Publisher
DOI
10.1016/0030-4018(90)90335-q

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Physical Review A•Jul 2, 2013•42 citations
A detailed theory of traveling-wave electronic Raman lasers is constructed, which applies in particular to the spin-flip Raman lasers of Patel and others. Ten equations are set up describing explicitly the behavior of the Stokes field, the anti-Stokes field, the input laser field, and the electronic system. Solutions of these equations are obtained in the sinusoidal steady-state limit. Depletion of the input laser field is accounted for in an approximate but novel fashion in the form of photon-number conservation. We are able to express the steady-state output power in terms of the system parameters and the boundary pump excitation alone. Analytic formulas are given for the linear gain, the threshold pump power, and the Stokes as well as the anti-Stokes power output. They describe, among other things, the saturation and fluorescence behavior of the electronic Raman laser. Various intuitive interpretations are provided for the analytical results. Our detailed predictions are in good agreement with experiments.
Analytic and numerical solutions are obtained for the equations describing the propagation of several pulses of different frequencies through a Raman medium. The transient case is treated, and the analysis includes Stokes, pump, and anti-Stokes frequency components. The effect of phase mismatch \ensuremath{\Delta}k between these waves is investigated. An analytic solution is found that describes the phenomenon of transient Stokes--anti-Stokes gain suppression in the limit \ensuremath{\Delta}k=0. For nonzero values of \ensuremath{\Delta}k, the behavior of the transient gain coefficient is found to follow a scaling rule that is the analog of a similar result known from the steady-state limit. Calculations are performed to identify conditions that enhance conversion to anti-Stokes radiation. It is found that there is an optimum strength of the Stokes seed, and that proper phase matching of the initial waves is essential.
Stimulated optical signals obtained by subjecting the system to a narrow band and a broadband pulse show both gain and loss Raman features at the red and blue side of the narrow beam, respectively. Recently observed temperature-dependent asymmetry in these features [Mallick et al., J. Raman Spectrosc. 42, 1883 (2011); Dang et al., Phys. Rev. Lett. 107, 043001 (2011)] has been attributed to the Stokes and anti-Stokes components of the third-order susceptibility, ${\ensuremath{\chi}}^{(3)}$. By treating the setup as a steady state of an open system coupled to four quantum radiation field modes, we show that Stokes and anti-Stokes processes contribute to both the loss and gain resonances. ${\ensuremath{\chi}}^{(3)}$ predicts loss and gain signals with equal intensity for electronically off-resonant excitation. Some asymmetry may exist for resonant excitation. However, this is unrelated to the Stokes vs anti-Stokes processes. Any observed temperature-dependent asymmetry must thus originate from effects lying outside the ${\ensuremath{\chi}}^{(3)}$ regime.