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Physical Review A

Optical bistability and lasing without inversion in a system of driven two-level atoms with incoherent injection

Guo Qin Ge, Ying Wu, Xueli Luo, Zaiguang Li

Published Aug 1, 1995• 14 citations
Publisher

Abstract

We have studied a laser system in which initially incoherent atoms are injected into a cavity and directly driven by a coherent pump field. Here we show that such a system can display optical bistability in the absence of population inversion. Two disconnected branches of the solutions are obtained for lasing action. They correspond to the inversion branch and inversionless branch, respectively. Also, a mechanism is proposed here to produce higher-power lasing by the inversionless laser.

DOI
10.1103/physreva.52.1783

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Atomic coherence and bistable lasers without inversion

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We examine a model of a driven two-level system with injected coherent atoms. We find a set of lasing phase diagrams for the resonant excitations. We show that the laser field in the system is related to the initial preparation of atoms, and that when the degree of this coherence is changed, the system exhibits bistability in the inversionless region. We also discuss the crucial role of atomic coherence in achieving lasing action. \textcopyright{} 1996 The American Physical Society.

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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.

Conference on Lasers and Electro-Optics•Aug 29, 2005•1 citation

Lasing without inversion in three-level systems without external coherent driving

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We have studied an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity. This system generates two laser fields, one of them without population inversion. Both ladder and V-type three-level schemes are considered with a ratio $R={\ensuremath{\omega}}_{\ensuremath{\alpha}}/{\ensuremath{\omega}}_{\ensuremath{\beta}}$ of inversionless laser frequency ${\ensuremath{\omega}}_{\ensuremath{\alpha}}$ to ordinary laser frequency ${\ensuremath{\omega}}_{\ensuremath{\beta}}$ of $R=0.67$ and $R=1.88,$ respectively. Dual-wavelength lasing extends up to Doppler-broadening values for optical transitions of atoms in a vapor cell. Some considerations for the practical realization of this dual-wavelength laser are discussed.

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Chinese Journal of Quantum Electronics•Jan 1, 2007•0 citations
We have studied a laser system in which initially incoherent atoms are injected into a cavity and directly driven by a coherent pump field. Here we show that such a system can display optical bistability in the absence of population inversion. Two disconnected branches of the solutions are obtained for lasing action. They correspond to the inversion branch and inversionless branch, respectively. Also, a mechanism is proposed here to produce higher-power lasing by the inversionless laser.
Introduction Usage has reserved the expression optical bistability mostly for coherently driven passive systems. An atomic system is called passive when there is no population inversion. This is the case, for example, of a system at thermal equilibrium. On the contrary, the laser that we have described in Chapter 1 is a driven active system, because a population inversion is created. The laser equations we have studied so far describe an incoherently driven laser. However, nothing prevents driving a lasing cavity with a coherent field emitted by another laser. This is realized in a whole class of lasers that are used mainly as frequency converters. In optical bistability (OB), the driving field is usually a coherent field. Thus we have to account for two differences between the laser and the optically bistable system: (1) In OB, there is no inversion of population: 〈| A 2 |〉>〈| B 2 |〉, in the notation of Chapter 1. Hence, in the absence of interaction with a field, the population difference D relaxes toward a negative value. (2) The pumping is coherent, meaning that an external laser field is added to the cavity field. Using the single-mode equations (1.48)–(1.50), we have to change the sign of D and D a (which amounts to keeping D defined in (1.34) as it is but changing P into – P and A into – A ) and to add a source term in the equation for the complex field amplitude.
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 have studied an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity. This system generates two laser fields, one of them without population inversion. Both ladder and V-type three-level schemes are considered with a ratio $R={\ensuremath{\omega}}_{\ensuremath{\alpha}}/{\ensuremath{\omega}}_{\ensuremath{\beta}}$ of inversionless laser frequency ${\ensuremath{\omega}}_{\ensuremath{\alpha}}$ to ordinary laser frequency ${\ensuremath{\omega}}_{\ensuremath{\beta}}$ of R=0.67R=0.67R=0.67 and R=1.88,R=1.88,R=1.88, respectively. Dual-wavelength lasing extends up to Doppler-broadening values for optical transitions of atoms in a vapor cell. Some considerations for the practical realization of this dual-wavelength laser are discussed.
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
Theoretical model of an open four-level atomic system driven by two fields was presented. The density matrix equations of motion were obtained by the electric dipole and the rotating wave approximations. Under resonance of corresponding fields, the physical mechanism of lasing without inversion (LWI) was discussed and its linear analytical solution was obtained. By numerical results, we studied the effects of the spontaneous decay rates between atomic levels, incoherent pump rate, the injection rates, and the exit rate on the gain without inversion and the population difference of the system. The difference between the linear and nonlinear gain and the population difference of the system were discussed. A LWI gain was got during the region of the spontaneous decay rates between atomic levels. The LWI gain can obtain by adjusting suitably incoherent pump rate, the atomic injection ratio and the exit rate. The curves of the linear gain and the nonlinear gain were similar with the Rabi frequencies of the driving fields. The curves of the linear population difference and the nonlinear population difference were similar too. The linear stable value of the gain was larger than the nonlinear stable value of the gain.