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Physical Review A

Nonlinear theory of noninversion lasers of an open three-level system

Shi-Yao Zhu, De-Zhong Wang, Jin-Yue Gao

Published Feb 1, 1997• 28 citations
Publisher

Abstract

A nonlinear theory of a noninversion laser of an open three-level system based on electromagnetically induced transparency is given. In this noninversion laser model, a nonselective pumping mechanism is used for obtaining lasing gain such that the population in the lower lasing level is always larger than a half of the total population no matter whether the driving field is on or off. In the lasing region, there is no direct pumping to the upper level. The conditions for the existence of a nontrivial and stable laser field are obtained. The dependence of the laser intensity on the intensity of the driving field and the ratio of the two decay rates from the upper level has been obtained, and the ways to obtain a large laser field have been studied.

DOI
10.1103/physreva.55.1339

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A nonlinear theory of a noninversion laser of an open three-level system based on electromagnetically induced transparency is given. In this noninversion laser model, a nonselective pumping mechanism is used for obtaining lasing gain such that the population in the lower lasing level is always larger than a half of the total population no matter whether the driving field is on or off. In the lasing region, there is no direct pumping to the upper level. The conditions for the existence of a nontrivial and stable laser field are obtained. The dependence of the laser intensity on the intensity of the driving field and the ratio of the two decay rates from the upper level has been obtained, and the ways to obtain a large laser field have been studied.
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.
We give a exact nonlinear analytical solution of the steady state in an open V type noninversion lasing system pumped by the two color fields,discuss the conditions of producing lasing without inversion in the limit cases of the strong driving field,and analyze the effect of nonlinearities on the gain,dispersion,population differences between levels and pumping rate threshold of the pumping field in the frequency up conversion regime by the numerical calculation results from the nonlinear analytical solution,study finally the stability of the steady state of the system.
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.
Summary form only given.The behavior of a laser intensity as a function of a pump rate is studied. We consider a three-level lasing scheme with two different types of pumping. In the first case, the lower lasing level is depleted to the ground state, and then the pumping is used to excite the atom from the ground state to the upper lasing level. In the second case the pumping is used to excite the atom directly from the lower lasing level to one of the excited states, which is then depleted to the upper lasing level. We refer these two types of pumping as type 1 and type 2, respectively. It is shown that although these two schemes are equivalent mathematically, i.e., they are formally described by the same set of equations, physically their dynamical properties are completely different. It is noted that the pumping of the type 1 does not affect either of lasing levels directly, whereas the pumping of the type 2 does connect the lower lasing level with one of the excited states. It is this difference of the two ways of pumping which is responsible for the crucial difference in the dynamic behavior of the lasing schemes of types 1 and 2.