Bifurcations of an optically pumped three-level laser model

Abstract We study the bifurcations in a sixth-order model of a resonant, homogeneously broadened, three-level, optically pumped laser. Standard analytical and numerical techniques are used to obtain a complete unfolding of the model's equilibrium bifurcations in its four-dimensional parameter space. Regions of stationary, periodic and potentially chaotic behaviour are then readily identified. Turning to two specific cases, we study the principal global bifurcations in a two-parameter plane and show their origin in special degenerate bifurcation points of codimension two. The different relative dispositions of the principal homoclinic and heteroclinic connections in these two examples result in different local bifurcation behaviours and chaotic dynamics, which we illustrate in detail.

[1]  Hübner,et al.  Homoclinic and heteroclinic chaos in a single-mode laser. , 1988, Physical review letters.

[2]  T. Bedford,et al.  New directions in dynamical systems , 2008 .

[3]  F. Laguarta,et al.  Lorenz-like dynamics in Doppler broadened coherently pumped lasers , 1989 .

[4]  W. Klische,et al.  On observability of Lorenz instabilities in lasers , 1984 .

[5]  Edgar Knobloch,et al.  Bifurcations in a model of magnetoconvection , 1983 .

[6]  N. Lawandy,et al.  Limitations on coherently pumped molecular systems for studying two-level laser instabilities , 1987 .

[7]  Colin Sparrow,et al.  Local and global behavior near homoclinic orbits , 1984 .

[8]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[9]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[10]  M. Siegrist,et al.  Two-mode optical pumping of a laser , 1984 .

[11]  Knut H. Alfsen,et al.  Systematics of the Lorenz Model at σ = 10 , 1985 .

[12]  R. Harrison,et al.  Theoretical analysis of instabilities in optically pumped molecular lasers , 1986 .

[13]  L. P. Šil'nikov,et al.  A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE , 1970 .

[14]  R. Temkin,et al.  Dispersion in a laser-pumped molecular laser , 1980 .

[15]  F. Laguarta,et al.  Influence of pump coherence on the dynamic behavior of a laser , 1988 .

[16]  I. Koryukin,et al.  Bifurcations and chaos in the three-level model of a laser with coherent optical pumping , 1988 .

[17]  C. Sparrow.  The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[18]  James A. Yorke,et al.  Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model , 1979 .

[19]  Hübner,et al.  Dimensions and entropies of chaotic intensity pulsations in a single-mode far-infrared NH3 laser. , 1989, Physical review. A, General physics.

[20]  C. Weiss.  Observation of instabilities and chaos in optically pumped far-infrared lasers , 1985 .

[21]  Milan Kubíček,et al.  Periodic and aperiodic regimes in coupled dissipative chemical oscillators , 1986 .

[22]  Colin Sparrow,et al.  T-points: A codimension two heteroclinic bifurcation , 1986 .

[23]  Harrison,et al.  Local bifurcations of a three-level optically pumped laser. , 1989, Physical review. A, General physics.

[24]  Richard J. Temkin,et al.  Interaction of two laser fields with a three-level molecular system , 1977 .

[25]  Harrison,et al.  Regular and chaotic dynamics of optically pumped molecular lasers. , 1989, Physical review. A, General physics.

[26]  Weiss,et al.  Evidence for Lorenz-type chaos in a laser. , 1986, Physical review letters.

[27]  Hermann Haken,et al.  Analogy between higher instabilities in fluids and lasers , 1975 .

[28]  Weiss,et al.  Instabilities and routes to chaos in a homogeneously broadened 1- and 2-mode ring laser. , 1985, Physical review. A, General physics.

[29]  Harrison,et al.  Gain, dispersion, and emission characteristics of three-level molecular laser amplifier and oscillator systems. , 1987, Physical review. A, General physics.

[30]  Harrison,et al.  Origin of chaotic relaxation oscillations in an optically pumped molecular laser. , 1987, Physical review letters.

[31]  M. Siegrist,et al.  The conditions for Lorenz chaos in an optically-pumped far-infrared laser , 1986 .

[32]  N. Lawandy,et al.  Instabilities in a three-level coherently pumped laser , 1987 .