Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Stability properties of a resonant cascade laser

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

Published Feb 1, 1994• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.1243

Related papers

Cascade laser dynamics

Ramon A. Vilaseca, Germán J. de Valcárcel, V. Espinosa +1 more

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.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 1, 1993•1 citation

Stationary emission and stability of a detuned cascade laser

Eugenio Roldán, Germán J. de Valcárcel, Ramon A. Vilaseca +1 more

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.

Journal of Modern Optics•Jan 1, 1997•8 citations

Effects of Atomic Coherence and Injected Classical Field on Chaotic Dynamics of Non-degenerate Cascade Two-Photon Lasers

Yajun Zhang, Huang Hong-Bin, Peng Yang +1 more

Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations.

Communications in Theoretical Physics•Aug 1, 2007•0 citations

Nonlinear dynamics of double-cavity optical bistability of a three-level ladder system

H. Aswath Babu, Harshawardhan Wanare

We present nonlinear dynamical features of two-photon double-cavity optical bistability exhibited by a three-level ladder system in the mean-field limit at low input light levels. The system exhibits a hump-like feature in the lower branch of the bistable response, wherein a region of instability develops. The system displays a range of dynamical features varying from normal stable switching to periodic self-pulsing and chaos. The inclusion of two competing cooperative atom-field couplings leads to such rich, nonlinear dynamical behavior. We provide a domain map that clearly delineates the various regions of stability, as well as bifurcation diagrams with associated supporting evidence that identifies the period-doubling route to chaos.

arXiv:1009.1550•Physical Review A•Mar 18, 2011•12 citations

Two-photon laser dynamics

Germán J. de Valcárcel, Eugenio Roldán, Javier F. Urchueguía +1 more

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.

Physical Review A•Nov 1, 1995•22 citations

Nonlinear dynamics of a class-A two-photon laser with injected signal

Javier F. Urchueguía, V. Espinosa, Eugenio Roldán +1 more

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.

Journal of Modern Optics•Nov 1, 1996•7 citations
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 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.
Based on the cascade two-photon laser dynamic equation derived with the technique of quantum Langevin operators with the considerations of coherently prepared three-level atoms and the classical field injected into the cavity, we numerically study the effects of atomic coherence and classical field on the chaotic dynamics of a two-photon laser. Lyapunov exponent and bifurcation diagram calculations show that the Lorenz chaos and hyperchaos can be induced or inhibited by the atomic coherence and the classical field via crisis or Hopf bifurcations.
We present nonlinear dynamical features of two-photon double-cavity optical bistability exhibited by a three-level ladder system in the mean-field limit at low input light levels. The system exhibits a hump-like feature in the lower branch of the bistable response, wherein a region of instability develops. The system displays a range of dynamical features varying from normal stable switching to periodic self-pulsing and chaos. The inclusion of two competing cooperative atom-field couplings leads to such rich, nonlinear dynamical behavior. We provide a domain map that clearly delineates the various regions of stability, as well as bifurcation diagrams with associated supporting evidence that identifies the period-doubling route to chaos.
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.
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.