Automated correlation dimension analysis of optically injected solid state lasers.

Nonlinear lasers are excellent systems from which to obtain high signal-to-noise experimental data of nonlinear dynamical variables to be used to develop and demonstrate robust nonlinear dynamics analysis techniques. Here we investigate the dynamical complexity of such a system: an optically injected Nd:YVO(4) solid state laser. We show that a map of the correlation dimension as a function of the injection strength and frequency detuning, extracted from the laser output power time-series data, is an excellent mirror of the dynamics map generated from a theoretical model of the system. An automated computational protocol has been designed and implemented to achieve this. The correlation dimension map is also contrasted with prior research that mapped the peak intensity of the output power as an experimentally accessible measurand reflecting the dynamical state of the system [Valling et al., Phys. Rev. A 72, 033810 (2005)].

[1]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[2]  Silvano Donati,et al.  Introduction to the feature section on optical chaos and applications to cryptography , 2002 .

[3]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[4]  Albano,et al.  Filtered noise can mimic low-dimensional chaotic attractors. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Laurent Larger,et al.  Optical Cryptosystem Based on Synchronization of Hyperchaos Generated by a Delayed Feedback Tunable Laser Diode , 1998 .

[6]  Jean-Michel Lourtioz,et al.  Dynamic behaviors of semiconductor lasers under strong sinusoidal current modulation: modeling and experiments at 1.3 mu m , 1990 .

[7]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[8]  F Kannari,et al.  Experiments on chaos synchronization in two separate microchip lasers. , 1999, Optics letters.

[9]  Communication with Chaotic External Cavity Diode Lasers , 1999 .

[10]  S. Eriksson.  Dependence of the experimental stability diagram of an optically injected semiconductor laser on the laser current , 2002 .

[11]  A. Lindberg,et al.  Observations on the dynamics of semiconductor lasers subjected to external optical injection , 2002 .

[12]  Tadashi Nishikawa,et al.  Guiding of high-intensity femtosecond laser pulses in evacuated and gas-filled capillaries , 2003 .

[13]  K. H. Cameron,et al.  External cavity controlled single longitudinal mode laser transmitter module , 1981 .

[14]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[15]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[16]  Fan-Yi Lin,et al.  Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback , 2003 .

[17]  Louis M. Pecora,et al.  Synchronization in Chaotic Systems, Concepts and Applications , 2006 .

[18]  Numerical stability maps of an optically injected semiconductor laser , 2004 .

[19]  Daan Lenstra,et al.  The dynamical complexity of optically injected semiconductor lasers , 2005 .

[20]  Bernd Krauskopf,et al.  Experimental bifurcation diagram of a solid state laser with optical injection , 2007 .

[21]  Shuo Tang,et al.  Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback , 2001 .

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

[23]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[24]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[25]  K. Tai,et al.  Nonlinear dynamics induced by external optical injection in semiconductor lasers , 1997 .

[26]  Gerd Pfister,et al.  Comparison of algorithms calculating optimal embedding parameters for delay time coordinates , 1992 .

[27]  Angelo Corana,et al.  Most probable dimension value and most flat interval methods for automatic estimation of dimension from time series , 2004 .

[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]  M. Adams,et al.  Stability maps of injection-locked laser diodes using the largest Lyapunov exponent , 2003 .

[30]  J. D. Farmer,et al.  State space reconstruction in the presence of noise" Physica D , 1991 .

[31]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[32]  J P Toomey,et al.  Correlation dimension signature of wideband chaos synchronization of semiconductor lasers. , 2006, Optics letters.

[33]  M. Rosenstein,et al.  Reconstruction expansion as a geometry-based framework for choosing proper delay times , 1994 .

[34]  Vassilios Kovanis,et al.  Period‐doubling route to chaos in a semiconductor laser subject to optical injection , 1994 .

[35]  Influence of noise on chaotic laser dynamics , 1997 .

[36]  Jon Lawrence,et al.  Nonlinear dynamics of a laser diode with optical feedback systems subject to modulation , 2002 .

[37]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[38]  Maps of the dynamics of an optically injected solid-state laser (8 pages) , 2005 .

[39]  W. H. Steier,et al.  Locking of laser oscillators by light injection , 1966 .

[40]  Laurent Larger,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2005, Nature.

[41]  Thomas Fordell,et al.  Experimental and numerical intensity time series of an optically injected solid state laser , 2005 .

[42]  Meucci,et al.  Generation of chaotic dynamics by feedback on a laser. , 1986, Physical review. A, General physics.