Order parameters for class-B lasers with a long time delayed feedback

Abstract A local dynamics for class-B laser systems with optoelectronic feedback is considered in the case of a very long time delay. We determine the conditions for the bifurcation of infinite dimension. It is shown that the (ordinary) delay system can be described by a systematically derived complex Ginzburg–Landau equation without delay terms. The complicated quasi-periodic dynamics near equilibrium can be demonstrated analytically on the basis of space–time representation.

[1]  Haken,et al.  Traveling waves and pulses in a two-dimensional large-aspect-ratio system. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[2]  Moses,et al.  Spatially and temporally modulated traveling-wave pattern in convecting binary mixtures. , 1988, Physical review letters.

[3]  H. Haken,et al.  Travelling wave dynamics in a nonlinear interferometer with spatial field transformer in feedback , 1999 .

[4]  Sergey A. Kaschenko,et al.  Normalization in the Systems with Small Diffusion , 1996 .

[5]  Hermann Haken,et al.  The oscillatory instability of a spatially homogeneous state in large aspect ratio systems of fluid dynamics , 1988 .

[6]  L. Keefe.  Properties of Ginzburg-Landau attractors associated with their Lyapunov vectors and spectra , 1989 .

[7]  Giacomelli,et al.  Relationship between delayed and spatially extended dynamical systems. , 1996, Physical review letters.

[8]  H. Haken.  Generalized Ginzburg-Landau equations for phase transition-like phenomena in lasers, nonlinear optics, hydrodynamics and chemical reactions , 1975 .

[9]  Hermann Haken,et al.  Theory of quasiperiodicity in model of lasers with delayed optoelectronic feedback , 1999 .

[10]  Hermann Haken,et al.  Laser light dynamics , 1985 .

[11]  K. Otsuka,et al.  Coexistence of two attractors in lasers with delayed incoherent optical feedback , 1993 .

[12]  E. Grigorieva,et al.  Parametric transverse patterns in broad aperture lasers , 1998 .

[13]  T. Paoli,et al.  Frequency stabilization and narrowing of optical pulses from CW GaAs injection lasers , 1970 .

[14]  Meucci,et al.  Dynamics of a CO2 laser with delayed feedback: The short-delay regime. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[15]  L. Tuckerman,et al.  Bifurcation analysis of the Eckhaus instability , 1990 .

[16]  C. Fletcher.  Computational techniques for fluid dynamics , 1992 .

[17]  Wischert,et al.  Delay-induced instabilities in nonlinear feedback systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  T. Erneux,et al.  Stabilizing or destabilizing lasers by continuous delayed feedback , 1995 .

[19]  H. Haken,et al.  Two-dimensional traveling wave patterns in nonequilibrium systems , 1989 .

[20]  Yoshiki Kuramoto,et al.  On the Formation of Dissipative Structures in Reaction-Diffusion Systems Reductive Perturbation Approach , 1975 .

[21]  Antonio Politi,et al.  Multiple scale analysis of delayed dynamical systems , 1998 .

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

[23]  G. Sell,et al.  The Hopf Bifurcation and Its Applications , 1976 .

[24]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[25]  E. Grigorieva,et al.  Regular and Chaotic Pulsations in Laser Diode with Delayed Feedback , 1993 .

[26]  Y. Pomeau,et al.  Order within chaos , 1986 .

[27]  Meucci,et al.  Defects and spacelike properties of delayed dynamical systems. , 1994, Physical review letters.

[28]  Complex temporal structures in models of a laser with optoelectronic delayed feedback , 1993 .

[29]  L. M. Chanin,et al.  PRESSURE-DEPENDENT BREAKDOWN POTENTIALS IN PENNING MIXTURES , 1965 .

[30]  J. Hale,et al.  Stability of Motion. , 1964 .

[31]  H. Haken,et al.  Modulated traveling waves in nonequilibrium systems: The ‘blinking state’ , 1989 .

[32]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[33]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[34]  K. Ikeda,et al.  High-dimensional chaotic behavior in systems with time-delayed feedback , 1987 .