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Physical Review A

Line selection in off-resonantly pumped multilevel systems

M.‐A. Dupertuis, M. R. Siegrist

Published Jul 1, 1987• 7 citations
Publisher

Abstract

In weakly, off-resonantly pumped multilevel systems gain is usually observed at the transition frequencies (line-center lines) and at the pump-offset-dependent frequencies (Raman lines). Modes developing at these frequencies are subject to strong mutual competition due to several coupling mechanisms. A general six-level system is investigated in this paper. Line competition effects are studied in particular in the simplified basic four-level cases comprising parallel, cascade, and V-\ensuremath{\Lambda} subsystems. We predict the type of transitions which survive and ultimately remain active. A comparison with experimental results using far-infrared lasers is made.

DOI
10.1103/physreva.36.669

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In weakly, off-resonantly pumped multilevel systems gain is usually observed at the transition frequencies (line-center lines) and at the pump-offset-dependent frequencies (Raman lines). Modes developing at these frequencies are subject to strong mutual competition due to several coupling mechanisms. A general six-level system is investigated in this paper. Line competition effects are studied in particular in the simplified basic four-level cases comprising parallel, cascade, and V-\ensuremath{\Lambda} subsystems. We predict the type of transitions which survive and ultimately remain active. A comparison with experimental results using far-infrared lasers is made.
For some time already it has been known that off-resonantly pumped far infrared (FIR) lasers oscillate on the Raman line [1]. This feature has led to important applications such as the realisation of widely tunable CH3F lasers (150–1200 μm) [2]. Only recently it has been shown [3] that mode competition is responsible for the fact that Raman oscillation (R) dominates line centre oscillation (LC) in a three-level system. The same considerations are valid in the equivalent situation of a single refilling transition (|0 > → |1> in Fig. 1). In certain experiments [4–7] Λ and V transitions (Fig. 1) appear in combination. For this case LC and R oscillations have been observed to exist simultaneously in one of the FIR transitions [5].
We examine the problem of line competition in an off-resonantly pumped three-level loop configuration that is encountered in four-wave mixing. Population and coherence pulsations play a key role during the competition. Analytical results in the small-signal-gain region provide some insight into the start-up of the loop oscillation. The general problem with saturating fields and strong line competition is solved numerically. We show that in the asymptotic regime of oscillation all the lines may survive, although some of them remain quite weak. We show also that our results are compatible with recent experiments.
Aid or competition between two laser modes oscillating on different transitions of a three-level medium are studied following the method of Lamb. An arbitrary amount of Doppler broadening is allowed for. The "electric-quadrupole" term generated by back-to-back transitions of the two modes but having vanishing electric dipole moment is found to have little effect on the oscillation intensities in typically observed circumstances. This fact justifies, in part, the rate-equation approximation commonly used in multilevel analysis. For a bidirectional ring cascade configuration, however, this coherence term can be important because of constructive interference familiar from two-photon, Doppler-free spectroscopy. The ordinary (i.e., hole-burning) cross-saturation terms for cascade transitions produce mutual mode aid, rather than competition as in the competitive cases. A curious consequence of this difference is greater accuracy in the third-order theory of cascade transitions than in that of competitive transitions, as a result of partial cancellation of errors incurred through neglect of higher orders. The treatment is generalized to multilevel media (four or more levels) with numerical illustration and discussion of the method's relationship to laser oscillation involving diatomic molecules.
We present a theoretical analysis of the influence of the collimation of a strong pump beam on a small-signal-gain line shape in a three-level \ensuremath{\Lambda}-type molecular system in the regime of high pump intensity when saturation and Stark (Autler-Townes) splitting of the levels of the pumping transition take place. The cases of homogeneous and Doppler-broadened pumping transitions have been considered. A significant offset, an asymmetric deformation, and a narrowing of the gain line, i.e., a spectrum focusing, have been obtained and explained as a result of the nonlinear (dispersion) and the active (gain) wave guiding of the small signal in the field of the strong pump beam.
A theoretical investigation of collisional contributions to the gain line shape of coherently driven three-level systems is presented. The theory differs from previous work in that it includes, in addition to the usual thermal-bath mechanisms, direct collisional coupling between optically active states. It is shown that for stronger coupling between the stimulated levels than between the pump and two-quantum levels (i) the small signal gain g obtained with off-resonant pumping is greater than that obtained with resonant pumping, (ii) the unsaturated gain profile becomes asymmetric in proportion to the degree of pump detuning, and (iii) the unsaturated gain asymmetry is translated into the emission profiles gI obtained with nonzero values of stimulated intensities I. These results may be of particular importance in the case of optically pumped submillimeter lasers which exhibit large differences in the thermalization rates of the pump (V-V) and stimulated (R-R) transitions.