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IEEE Journal of Quantum Electronics

Power output of a pulsed Raman laser with saturable excitation

W. J. Firth

Published Dec 1, 1972• 9 citations
Publisher

Abstract

A theoretical expression is obtained for the time dependence of the Stokes power output of a pulsed Raman laser, the pump pulse duration being comparable to the relaxation time of the Raman excitation and the output saturation limited. A rate-equation approach is employed, and the pump beam is assumed to have a Gaussian intensity distribution. The theory is developed in terms of the practical example, stimulated spin-flip Raman scattering in InSb.

DOI
10.1109/jqe.1972.1076887

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Physical Review A•Jun 1, 1979•136 citations
A theoretical expression is obtained for the time dependence of the Stokes power output of a pulsed Raman laser, the pump pulse duration being comparable to the relaxation time of the Raman excitation and the output saturation limited. A rate-equation approach is employed, and the pump beam is assumed to have a Gaussian intensity distribution. The theory is developed in terms of the practical example, stimulated spin-flip Raman scattering in InSb.
A saturation model of stimulated Raman scattering, of general applicability, is put forward. The model is developed with reference to spin-flip electronic Raman scattering in InSb, where the number of excitations available for Raman scattering may be small by comparison with the incident photon numbers. A rate equation technique is used to evaluate the steady-state Stokes intensity and output powers for a Gaussian pump beam. The model is extended to take account of pump depletion and the relative importance of depletion, and saturation in limiting the conversion efficiency under different conditions is brought out. By comparison with continuous wave spin-flip measurements, values are obtained for the spin-relaxation time (τs) associated with spin reversal in InSb. For 1016free carriers per cubic centimeter at 36 kG,\tau_{s} \sim 12ns and for 1015cm-3at 16.9 kG,\tau_{s} \sim 1.3ns.
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.
Parametric instability induced by the medium saturation in stimulated Raman scattering is investigated theoretically via a generalized detuning (1) where ω p,s,o are the frequency of the pump, Stokes, and phonon, ϕ ˙ p s is the phase modulation, and the last term is the nonlinear correction of the highly excited anharmonic molecule with an amplitude Q.The steady-state gain and hence the Stokes efficiency, in the presence of the anharmonic term, are governed by a cubic equation of |Q|2which is to be solved from the Bloch and Maxwell equations including the pump depletion. Numerical results are shown for the transition diagram of Stokes efficiency vs input pump intensity at various system conditions at the steady-state. For the transient regime, with pulse duration shorter than the dephasing time, we analyze the temporal profiles of the Stokes and the depleted pump based on a transformed equation which combines Bloch and Maxwell equation as follows: (2) where Tis a nonlinear time, G s is the steady-state gain, l0is the input pump intensity, and Uis the real part of the phonon amplitude Q.For an input pulse intensity given by sech2(t/t p ), Eq. (2) is solved numerically to study the transient pulse profiles in the presence of pump depletion and medium saturation.
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.
The nonlinear process of the stimulated Raman effect is treated theoretically. Simple expressions are derived for the initial rates of change and limiting steady state values of the first two moments, the degrees of second-order coherence and the correlation function of the pump and Stokes beams. An analytical solution for the time dependence of the joint photon probability distribution of the two light beams is obtained and then employed to calculate some numerical results for various special cases of interest, and the significance of these results is discussed in physical terms. Simpler approximate expressions are also derived for the case where the pump beam is much more intense than the Stokes beam.
The authors have extended the theory of stimulated Raman scattering to include the effects of laser bandwidths, in both the transient and steady-state regimes. The case of two interacting laser beams, a pump laser and a probe (Stokes) laser, is treated. Using the phase-diffusion model for laser bandwidth, the authors demonstrate that in the absence of dispersion, the forward Raman gain is essentially independent of the laser bandwidths in the high-gain limit, while in the low-gain limit the gain coefficient is inversely proportional to the sum of the bandwidths. It is further shown that when the pump-laser bandwidth is much larger than the linewidth of the Raman medium, the stimulated Stokes output assumes the same spectrum as the pump laser in the high-gain limit. A possible interpretation of these results is discussed assuming a "phase-locking" of the Stokes phase to the fluctuations in the pump-laser phase, due to the nonlinear interaction of the two beams through the Raman medium.