Robust synchronization in fiber laser arrays.

Synchronization of coupled fiber lasers has been reported in recent experiments [Bruesselbach, Opt. Lett. 30, 1339 (2005); Minden, Proc. SPIE 5335, 89 (2004)]. While these results may lead to dramatic advances in laser technology, the mechanism by which these lasers synchronize is not understood. We analyze a recently proposed [Rogers, IEEE J. Quantum Electron. 41, 767 (2005)] iterated map model of fiber laser arrays to explore this phenomenon. In particular, we look at synchronous solutions of the maps when the gain fields are constant. Determining the stability of these solutions is analytically tractable for a number of different coupling schemes. We find that in the most symmetric physical configurations the most symmetric solution is either unstable or stable over insufficient parameter range to be practical. In contrast, a lower symmetry configuration yields surprisingly robust coherence. This coherence persists beyond the pumping threshold for which the gain fields become time dependent.

[1]  T. Maiman.  Stimulated Optical Radiation in Ruby , 1960, Nature.

[2]  Hans W. Bruesselbach,et al.  Self-organized coherence in fiber laser arrays. , 2005 .

[3]  Rajarshi Roy,et al.  Fast intracavity polarization dynamics of an erbium-doped fiber ring laser: Inclusion of stochastic effects , 1997 .

[4]  A Gavrielides,et al.  Extraction characteristics of a dual fiber compound cavity. , 2002, Optics express.

[5]  Gilmore J. Dunning,et al.  Self-organized coherence in fiber laser arrays , 2004, SPIE LASE.

[6]  Ira B. Schwartz,et al.  Bi-instability and the global role of unstable resonant orbits in a driven laser , 2000 .

[7]  Robert A. York,et al.  A new phase-shifterless beam-scanning technique using arrays of coupled oscillators , 1993 .

[8]  K. Wiesenfeld,et al.  LINEWIDTH CALCULATION FOR BARE 2D JOSEPHSON ARRAYS , 1997 .

[9]  Robert A. York,et al.  Nonlinear analysis of phase relationships in quasi-optical oscillator arrays , 1993 .

[10]  K. Wiesenfeld,et al.  Model for high-gain fiber laser arrays , 2005, IEEE Journal of Quantum Electronics.

[11]  C. B. Whan,et al.  Phase coherence and disorder in Josephson‐junction arrays , 1992 .

[12]  R. Roy,et al.  Fast polarization dynamics of an erbium-doped fiber ring laser. , 1996, Optics letters.

[13]  M. Golubitsky,et al.  The Symmetry Perspective , 2002 .

[14]  Andrew G. Glen,et al.  APPL , 2001 .

[15]  Chris Arney.  Sync: The Emerging Science of Spontaneous Order , 2007 .

[16]  Kurt Wiesenfeld,et al.  Synchronization in fiber laser arrays: theoretical study , 2005, Photonics North.

[17]  Wei-Ping Huang.  Coupled-mode theory for optical waveguides: an overview , 1994 .

[18]  J. Rogers,et al.  Synchronization by nonlinear frequency pulling. , 2004, Physical review letters.

[19]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[20]  David Pureur,et al.  Power scaling of fibre lasers with all-fibre interferometric cavity , 2002 .

[21]  H. Winful,et al.  Dynamics of phase-locked semiconductor laser arrays , 1988 .

[22]  Ira B. Schwartz,et al.  Subharmonic Hysteresis and Period Doubling Bifurcations for a Periodically Driven Laser , 1994, SIAM J. Appl. Math..

[23]  S. LaRochelle,et al.  A simple model describing both self-mode locking and sustained self-pulsing in ytterbium-doped ring fiber lasers , 2005, Journal of Lightwave Technology.

[24]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[25]  T F Morse,et al.  All-fiber coherent beam combining of fiber lasers. , 1999, Optics letters.

[26]  Steven H. Strogatz,et al.  Sync: The Emerging Science of Spontaneous Order , 2003 .

[27]  Henry D. I. Abarbanel,et al.  Synchronizing High-Dimensional Chaotic Optical Ring Dynamics , 1998 .

[28]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[29]  James Gary Eden,et al.  IEEE Journal of Quantum Electronics: Editorial , 2002 .

[30]  Robert M. Gray,et al.  Toeplitz And Circulant Matrices , 1977 .

[31]  Akira Shirakawa,et al.  Coherent addition of fiber lasers by use of a fiber coupler. , 2002, Optics express.

[32]  M. Golubitsky,et al.  The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space , 2002 .

[33]  P. Cheo,et al.  Self-organization in a multicore fiber laser array. , 2003, Optics letters.

[34]  F. Fontana,et al.  Maxwell-Bloch modelocking instabilities in erbium-doped fiber lasers , 1995 .

[35]  Thomas L. Paoli,et al.  OPTICAL COUPLING OF ADJACENT STRIPE‐GEOMETRY JUNCTION LASERS , 1970 .