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IEEE Journal of Quantum Electronics

Spin saturation and pump depletion in continuous spin-flip Raman oscillation

B. S. Wherrett, W. J. Firth

Published Dec 1, 1972• 20 citations
Publisher

Abstract

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.

DOI
10.1109/jqe.1972.1076892

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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.
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 depletion and saturation effect of stimulated Raman scattering in optical fibres has been investigated. Nonlinear energy coupled equations are solved analytically. Our study reveals that the Raman gain saturation effect caused by the generation of the second Stokes has to be taken into account in light amplification by stimulated Raman scattering although it can be ignored in spontaneous stimulated Raman scattering. We also show that it is advantageous to feed the fibre with small low Stokes signals in amplifying high-order Stokes signals, for easing the requirement of high pump power and long fibre length.
The effects of ground-state depletion of atoms on the characteristics of stimulated Raman scattering in metal vapors are studied by simultaneously solving the rate equation of the atomic energy levels related in the Raman scattering, and the equations describing the energy conversion from the focused pump-laser pulses to the Raman down-converted pulses. The ground states of metal atoms are depleted most strongly in the regions near the focal spots of the pump beams because of the higher intensities of light and smaller available medium volume in those regions. This will result in the unsymmetrical shapes of the Raman-shifted pulses for the front and rear edges, and will reduce the energy-conversion efficiency.
The effects of ground state depletion of atoms on the characteristics of stimulated Raman scattering in metal vapors are studied by simultaniously solving the rate-equation of the atom energy levels related in the Raman scattering, and the equations describing the energy-conversion from the focused pump laser pulses to the Raman down-converted pulses. The ground state of metal atoms are depleted most strongly in the regions near the focal spots of the pump beams because of the higher intensities of light and smaller available medium volume in thosa regions. This will result in the unsymmetrical shapes of the Raman-shifted pulses for the front and rear edges, and will reduce the energy-conversion efficiency.