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Physical Review A

Lasing without inversion in three-level systems: Self-pulsing in the cascade schemes

J. Mompart, C. Peters, R. Corbalán

Published Mar 1, 1998• 0 citations
Publisher

Abstract

Lasing without inversion (LWI) in specific models of closed three-level systems is analyzed in terms of nonlinear dynamics. From a linear stability analysis of the trivial nonlasing solution of the homogeneously broadened systems with on-resonance driving and laser fields, we find that, near lasing threshold, resonant closed $\ensuremath{\Lambda}$ and $V$ schemes yield continuous-wave LWI while resonant cascade schemes can give rise to self-pulsing LWI. The origin of this different behavior is discussed. For parameters of a real cascade system in atomic ${}^{138}\mathrm{Ba}$ we check numerically that the self-pulsing solution is stable in a broad range of nonzero detunings. It is shown that the self-pulsing emission can still be observed when the typical residual Doppler broadening of an atomic beam is taken into account.

DOI
10.1103/physreva.57.2163

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Lasing without inversion (LWI) in specific models of closed three-level systems is analyzed in terms of nonlinear dynamics. From a linear stability analysis of the trivial nonlasing solution of the homogeneously broadened systems with on-resonance driving and laser fields, we find that, near lasing threshold, resonant closed \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ and VVV schemes yield continuous-wave LWI while resonant cascade schemes can give rise to self-pulsing LWI. The origin of this different behavior is discussed. For parameters of a real cascade system in atomic 138Ba{}^{138}\mathrm{Ba}138Ba we check numerically that the self-pulsing solution is stable in a broad range of nonzero detunings. It is shown that the self-pulsing emission can still be observed when the typical residual Doppler broadening of an atomic beam is taken into account.
Lasing without inversion (LWI) in specific models of closed three-level systems is analyzed in terms of nonlinear dynamics. From a linear stability analysis of the trivial nonlasing solution of the homogeneously broadened systems with on-resonance driving and laser fields, we find that, near lasing threshold, resonant closed Λ and V schemes yield continuous-wave LWI while resonant cascade schemes can give rise to self-pulsing LWI. The origin of this different behavior is discussed. For parameters of a real cascade system in atomic 138Ba we check numerically that the self-pulsing solution is stable in a broad range of nonzero detunings. It is shown that the self-pulsing emission can still be observed when the typical residual Doppler broadening of an atomic beam is taken into account.
Lasing without inversion (LWI) is investigated from a nonlinear dynamics point of view for an atomic system with three coupled J = 0-1 transitions. The driving and generated fields couple two of these transitions defining a double- scheme. In addition, two incoherent pump fields are acting on the system. We find that LWI can occur not only in a continuous wave regime but also in a self-pulsing regime. A clear physical interpretation of the origin of this self-pulsing LWI is given. We obtain analytically the threshold driving field intensity needed to achieve both continuous wave and self-pulsing LWI emission. For large enough cavity losses, the system can reach either continuous wave or self-pulsing regimes by only changing the driving field intensity.
A way resulting in lasing without inversion (LWI) in an open resonant A-type system from a nonlinear dynamics viewpoint is investigated. The destabilization of the non-lasing solution can occur not only through pitchfork bifurcation, giving rise to continuous wave LWI, but also through Hopf bifurcation,giving rise to self-pulsing LWI. This is much different from that of the corresponding closed resonant A-type system in which the destabilization of the non-lasing solution can occur only through pitchfork bifurcation. The effects of the unsaturated gain coefficient, cavity loss coefficient, atomic injection and exit rates on the two bifurcations are discussed.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.
We characterize analytically the nature of the lasing solutions of a laser operating without population inversion. We consider models involving three-level media interacting with a strong driving field and a lasing field in the vicinity of the lasing threshold. We assess the influence of different relaxation and pumping schemes on the dynamics of these lasers. We use the atom-field detuning, the cavity detuning, and the linear gain as bifurcation parameters. Depending on their values, the stable lasing solution is shown to be cw or self-pulsing. We show that the optimal lasing operation is achieved if both the driving field frequency and the cavity frequency are out of resonance with the atomic frequencies. Physically, the lasing regimes arise from nonlinearly interacting sidebands induced in the lasing medium by atomic interference.