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Journal of Modern Optics

Stationary emission and stability of a detuned cascade laser

Eugenio Roldán, Germán J. de Valcárcel, Ramon A. Vilaseca, V. Espinosa

Published Jan 1, 1997• 8 citations
Publisher

Abstract

The stationary emission and stability of a three-level cascade laser in which two fields of different frequencies can be simultaneously amplified is investigated under conditions of cavity detuning. Different monomode and bimode solutions are found and analysed for the effects of different pitchfork and Hopf bifurcations. At moderate cavity detunings, features different from those observed in other classes of lasers are found, such as for instance a decrease in the instability threshold when detuning is introduced. Particular attention is paid to the case of resonance of the two-photon transition, which allows us to study the continuous evolution, when detuning is increased, of a resonant cascade laser towards a pure two-photon laser. In particular, this establishes the origin of some features which are characteristic of two-photon lasers.

DOI
10.1080/09500349708232901

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The stationary emission and stability of a three-level cascade laser in which two fields of different frequencies can be simultaneously amplified is investigated under conditions of cavity detuning. Different monomode and bimode solutions are found and analysed for the effects of different pitchfork and Hopf bifurcations. At moderate cavity detunings, features different from those observed in other classes of lasers are found, such as for instance a decrease in the instability threshold when detuning is introduced. Particular attention is paid to the case of resonance of the two-photon transition, which allows us to study the continuous evolution, when detuning is increased, of a resonant cascade laser towards a pure two-photon laser. In particular, this establishes the origin of some features which are characteristic of two-photon lasers.
The emission of a resonant nondegenerate cascade laser in which up to two fields can be simultaneously amplified inside a cavity is theoretically investigated. Each field is resonantly coupled with one of the transitions of a ladder three-level atomic system, in conditions of homogeneous broadening. General analytical expressions for zero-, one-, and two-field solutions are given. Cooperative emission between both fields is found. Through the linear stability analysis of these solutions we obtain phase diagrams showing their respective domains of stability. Together with the existence of Hopf bifurcations associated with one-photon processes, which coincide with those of a Lorenz-Haken laser, a genuine Hopf bifurcation due to two-photon processes has been found. This last bifurcation does not require the ``bad cavity'' nor the ``Lorenz threshold'' conditions. The stability of the orbits that bifurcate from these critical points is analytically investigated. For this we have rewritten one of the standard criteria in a useful and straightforward way. Finally, the dynamic regimes exhibited by the system well above the instability thresholds is numerically investigated revealing transitions to chaos via quasiperiodicity.
The behavior of a cascade laser in which two fields are simultaneously amplified is theoretically investigated. Each field is coupled with one of the transitions of a ladder three- level atomic or molecular system in conditions of homogeneous broadening. Steady-state as well as dynamic solutions are considered. Cooperative emission of both fields is found in steady state regime. Single-field solutions can loose stability through two different types of Hopf bifurcations. One of them can appear below the Lorenz-Haken second laser threshold, and the `bad cavity' condition is not necessarily required. In the unstable regimes transitions to chaos via the quasiperiodicity road are found. The influence of cavity detuning and the passage from cascade to two-photon laser are considered.
The dynamics of a two-photon laser with injected signal (TPLIS) in the limit of high quality cavity (class-A laser) is analysed by explicitly considering the underlying multi-level structure of the amplifying medium. A three-level cascade system is considered which retains the basic physics of the microscopic lasing processes. In this way the usual two-photon laser equations are consistently modified by the appearance of different dynamic frequency shifts dependent on the two-photon population inversion and on the laser intensity (ac-Stark shift). Although the basic instability scenarios are not qualitatively modified with respect to the effective two-level TPLIS, from the quantitative point of view, population-induced shifts heavily affect the threshold of appearance of instabilities.
We performed a comprehensive study of the temporal dynamics of a two-photon laser with resonant injected signal in the high-Q cavity limit (class-A laser). The stationary solutions as well as their stability are completely characterized. In particular it is shown that tristable behaviour is possible, in contrast with two-photon optical bistability. It is also shown that there are two independent Hopf bifurcations, the sub- or supercritical character of which is analytically determined. The dynamics of the system far from the bifurcation points is classified through a numerical study.
We study theoretically the polarization dynamics of a new type of quantum oscillator that is based on the two-photon stimulated emission process in the presence of a magnetic field of arbitrary orientation. Both cases of cascade (small intermediate-state atomic detuning) and two-photon (large atomic detuning) lasers are considered. The primary goal of this work is to investigate the origin of recently observed polarization instabilities in a two-photon laser (Pfister et al 2001 Phys. Rev. Lett. 86 4512) using a highly simplified model. It is found that the two-photon laser can emit linearly polarized radiation with its plane of polarization orthogonal to the direction of the magnetic field at small magnetic field strengths. It can also emit elliptically polarized radiation over a large range of magnetic field strengths and orientations. When the magnetic field deviates from a direction perpendicular to the laser cavity axis periodic instabilities can appear through a Hopf bifurcation. This dynamic regime could have contributed to the polarization instabilities observed in the experiment.
Degenerate as well as nondegenerate three-level two-photon laser (TPL) models are derived. In the limit of equal cavity losses for both fields, it is shown that the nondegenerate model reduces to the degenerate one. We also demonstrate the isomorphism existing between our degenerate TPL model and that of a dressed-state TPL. All these models contain ac-Stark and population-induced shifts at difference from effective Hamiltonian models. The influence of the parameters that control these shifts on the nonlinear dynamics of a TPL is investigated. In particular, the stability of the periodic orbits that arise at the Hopf bifurcation of the system and the extension of the self-pulsing domains of the system are studied, revealing the role played by the detuning and ac-Stark parameters.