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.
We analyze a laser system consisting of N closed three-level atoms confined in a single-mode cavity and derive the conditions for the onset of lasing without inversion or with inversion. We calculate the steady-state gain and lasing in the system and show that far above the lasing threshold, depending on the pumping and decay rates, the inversionless laser may operate in three different regimes, where the intensity of the laser depends linearly on N, is proportional to \ensuremath{\surd}N , or independent of N.
A model of three-level laser, in which the pumping excites the atoms from the lower lasing level, is considered. The statistical properties of the field are calculated using full quantum treatment. It is shown that apart from threshold there is additional critical value of the pump rate, at which the laser field behaves in a phase-transition-like manner: the photon number drops down, the Fano factor has a strong peak, the relative photon number variance grows enormously, and the second-order coherence function jumps to 2, which is typical for thermal light.
Dynamic properties of closed three-level laser systems are investigated. Two schemes of pumping---$\ensuremath{\Lambda}$ and V---are considered. It is shown that the nonlinear behavior of the photon number as a function of pump both near and far above threshold is crucially different for these two configurations. In particular, it is found that in the high pump regime laser can turn off in a phase-transition-like manner in both $\ensuremath{\Lambda}$ and V schemes.
We present a general theory that connects the pump process in multilevel lasers with the statistics of the laser field. The key ingredient in our approach is the derivation of an effective master equation that involves only the two laser levels and that contains a non-Markovian pump term. This pump term gives rise to a narrowing of the photon-number distribution in steady state. The qualitative features of this dynamic noise reduction can be inferred from the eigenvalues of the pump term, which are known analytically. As the mechanism that is responsible for the noise reduction, we identify a correlated excitation process in which the effective excitation rate from the lower to the upper laser level depends on the photon number. This correlated excitation process is very different from an excitation at equidistant times, such as in lasers with periodic external injection. We stress that our approach is general and the treatment nonlinear because we do not resort to approximations such as an adiabatic elimination of atomic variables or the linearization of a Fokker-Planck equation. It is therefore particularly relevant for the description of systems where the active medium consists of a few atoms only and where the field losses are not negligible on the time scale of the atomic relaxations. This would be the case in an ion-trap laser. For such a situation our results are substantially different from those obtained by a linearized treatment. \textcopyright{} 1996 The American Physical Society.
The quantum theory of the three-energy-level two-mode laser in which all the levels are being pumped is investigated and the master equation of the laser operation is obtained. It contains two variables,
n1, the photon number of the first mode, and
n2, the photon number of the second mode. There appear four terms in the master equation which represent two-photon processes between the two modes, the absorption of a photon from one mode, and emission of a photon to the other. They are absent in the single-mode case and in the two-mode case with pumping only to the upper level. The master equation can be represented by a diagram of probability in two dimensions which can be extended to infinity, and each arrow of it represents a term on the right-hand side of the master equation. By summing each variable (
n1 or
n2) of the master equation, two equations can be obtained. Each equation contains only one variable, and can be expressed by a diagram of probability flow in one dimension. By considering the correspondence between macroscopic equilibrium and microscopic detailed balance the equations of motion in the steady state are obtained. By introducing a parameter
H, the equation of motion is simplified and a formal solution can be deduced which is dependent on
H. It appears that the parameter
H cannot be fully determined, but some properties of it can be deduced which prove that the introduction of
H is reasonable. The operation characteristics of the laser under different conditions are discussed on the basis of the formal solution: among them are the threshold condition, the condition for one-mode operation, and the change of the photon-statistical distribution. We especially discuss the laser output power curves under two-mode operation above threshold. The curve of one mode, which oscillates first, shows a bending-down phenomenon as the excitation increases when the other mode goes beyond its threshold as demonstrated experimentally by Otsuka. This phenomenon is explained qualitatively and is attributed to the two-photon processes between the two modes.