# Laboratory for Nonlinear Dynamics in Optical Systems

The Laboratory for Nonlinear Dynamics in Optical Systems, under the direction of Prof. Rajarshi Roy, is located in the Institute for Research in Electronics and Applied Physics at the University of Maryland.

For information, please contact Prof. Roy, (301) 405-1636.

#### Research

The study of nonlinear dynamics and noise in optical devices and systems is relevant to very practical technological applications such as compact disk players, fiber optic communications, and the development of optical switching devices and laser arrays. At the same time, nonlinear phenomena that are observed in devices and systems of current interest may often be very interesting from a fundamental perspective.

An effort to understand nonlinear dynamical phenomena in laser systems, for example, may lead us to confront a very basic question; namely, under what conditions can we discern the influence of quantum fluctuations on the chaotic dynamics of a macroscopic system? Novel experimental schemes and techniques for analysis of data from nonlinear systems must be combined to approach this problem, and it is necessary to develop fully quantum mechanical models of nonlinear systems to predict the outcome of such experiments. If quantum noise does significantly influence the macroscopic dynamics of a nonlinear system under certain conditions of operation, it will definitely impact our ability to actively control the chaotic dynamics of these devices by deterministic techniques. The control and synchronization of chaotic devices is important technologically, since it may be possible to use chaotic lasers for encoding and decoding information-carrying signals.

The figure shows the parameter space of the 1D and 2D CML systems. (a) Parameter space of the 1D configuration (N = 256 elements). Blue corresponds to low entropy and periodicity; orange corresponds to high entropy and chaos. The dashed line indicates the critical coupling strength ε_{c}=0.54. There is a series of tongues containing profiles which are periodic in time and have spatial wavenumber K=1, K=2, and K=3 as indicated. (b) Parameter space of the 2D configuration (128 x 128 lattice). There is a prominent K=1 tongue, and two tongues with more complex spatial patterns that are not characterized by a wavenumber. (c) Experimental and numerical realizations of the 1D system. In (b), the incoherent region is highlighted in yellow. Labels A (coherence), B (chimera) and C (incoherence) show positions in the parameter space of a. (d) Experimental and numerical realizations of the 2D system. In E, the incoherent region is highlighted. ("Experimental Observation of Chimeras in Coupled-Map Lattices," A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hovel, I Omelchenko, and E. Scholl, Nature Physics 8, 658-661 (2012))

#### Publications

- "Harvesting Entropy and Quantifying the Transition from Noise to Chaos in a Photon-Counting Feedback Loop," Aaron Morgan Hagerstrom, Thomas Edward Murphy, and Rajarshi Roy, PNAS Early Edition 1-6 (2015).
- "Peak Variability and Optimal Performance in Cortical Networks at Criticality," Hongdian Yang, Woodrow L. Shew, Rajarshi Roy, and Dietmar Plenz,
*Criticality in Neural Systems*(John Wiley, 2014). - "Cluster Synchronization and Isolated Desynchronization in Complex Networks with Symmetries," L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, and Rajarshi Roy, Nature Commun. 5, 4079 (2014).
- "Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators," Caitlin R. S. Williams, Thomas E. Murphy, Rajarshi Roy, Francesco Sorrentino, Thomas Dahms, and Eckehard Schöll, Phys. Rev. Lett. 110, 064104 (2013).
- "Synchronization States and Multistability in a Ring of Periodic Oscillators: Experimentally Variable Coupling Delays," Caitlin R. S. Williams, Francesco Sorrentino, Thomas E. Murphy, and Rajarshi Roy, Chaos 23, 043117, 1-5 (2013).
- "Maximal Variability of Phase Synchrony in Cortical Networks with Neuronal Avalanches," H. Yang, W. L. Shew, Rajarshi Roy, and D. Plenz, J. Neurosci. 32, 1061-2072 (2012). (doi: 10.1523/JNEUROSCI.2771-11.2012)
- "Experimental Observation of Chimeras in Coupled-Map Lattices," A. M. Hagerstrom, T. E. Murphy, R. Roy, P. Hovel, I. Omelchenko, and E. Scholl, Nature Phys. 8, 658-661 (2012). (doi: 10.1038/nphys2372)
- "Scalable Parallel Physical Random Number Generator Based on a Superluminescent LED," Xiaowen Li, Adam B. Cohen, Thomas E. Murphy, and Rajarshi Roy, Optics Lett. 36 [6], 1020 (2011). (doi: 10.1364/OL.36.001020)
- "Information Capacity and Transmission Are Maximized in Balanced Cortical Networks with Neuronal Avalanches," Woodrow L. Shew, Hongidan Yang, Shan Yu, Rajarshi Roy, and Dietmar Plenz, J. Neuroscience 31 [1], 55-63 (2011). (doi: 10.1523/JNEUROSCI.4637-10.2011)
- "Robustness of Optimal Synchronization in Real Networks," Bhargava Ravoori, Adam B. Cohen, Jie Sun, Adilson E. Motter, Thomas E. Murphy, and Rajarshi Roy, Phys. Rev. Lett. 107, 034201 (2011). (doi: 10.1103/PhysRevLett.107.034102)
- "Crowd Synchrony and Quorum Sensing in Delay-Coupled Lasers," Jordi Zamora-Munt, C. Masoller, Jordi Garcia-Ojalvo, and Rajarshi Roy, Phys. Rev. Lett. 105, 264101 (2010). (doi: 10.1103/PhysRevLett.105.264101)
- "Fast Physical Random Number Generator Using Amplified Spontaneous Emission," Caitlin R. S. Williams, Julia C. Salevan, Xiaowen Li, Rajarshi Roy, and Thomas E. Murphy, Optics Express 18 [23], 23584 (2010). (doi: 10.1364/OE.18.023584)
- "Dynamic Synchronization of a Time-Evolving Optical Network of Chaotic Oscillators," Adam B. Cohen, Bhargava Ravoori, Francesco Sorrentino, Thomas E. Murphy, Edward Ott, and Rajarshi Roy, Chaos 20, 043142 (2010). (doi: 10.1063/1.3530425)
- "Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators," Thomas E. Murphy, Adam B. Cohen, Bhargava Ravoori, Karl R. B. Schmitt, Anurag V. Setty, Francesco Sorrentino, Caitlin R. S. Williams, Edward Ott, and Rajarshi Roy, Phil. Trans. R. Soc. A 368, 343-366 (2010). (doi: 10.1098/rsta.2009.0225)
- "Neuronal Avalanches Imply Maximum Dynamic Range in Cortical Networks at Criticality," Woodrow L. Shew, Hongdian Yang, Thomas Petermann, Rajarshi Roy, and Dietmar Plenz, J. Neuroscience 29 [49], 15595 (2009). (doi: 10.1523/?JNEUROSCI.3864-09.2009)
- "Adaptive Synchronization of Coupled Chaotic Oscillators," Bhargava Ravoori, Adam B. Cohen, Anurag V. Setty, Francesco Sorrentino, Thomas E. Murphy, Edward Ott, and Rajarshi Roy, Phys. Rev. E 80, 056205 (2009). (doi: 10.1103/PhysRevE.80.056205)
- "Chaotic Lasers: The World's Fastest Dice," Thomas E. Musphy and Rajarshi Roy, Nature Photonics 2, 714 (2008). (doi: 10.1038/nphoton.2008.239)
- "Local Conditional Lyapunov Exponent Characterization of Consistency of Dynamical Response of the Driven Lorenz System," Atsushi Uchida, Kazuyuki Yoshimura, Peter David, Shigeru Yoshimori, and Rajarshi Roy, Phys. Rev. E 78, 036203 (2008). (doi: 10.1103/PhysRevE.78.036203)
- "Using Synchronization for Prediction of High-Dimensional Chaotic Dynamics," Adam B. Cohen, Bhargava Ravoori, Thomas E. Murphy, and Rajarshi Roy, Phys. Rev. Lett. 101, 154102 (2008). (doi: 10.1103/PhysRevLett.101.154102)
- "Effect of Multiple Time Delays on Intensity Fluctuation Dynamics in Fiber Ring Lasers," Anthony L. Franz, Rajarshi Roy, Leah B. Shaw, and I. B. Schwartz, Phys. Rev. E 78, 016208 (2008). (doi: 10.1103/PhysRevE.78.016208)
- "Isochronal Synchrony and Bidirectional Communication with Delay-Coupled Nonlinear Oscillators," Brian B. Zhou and Rajarshi Roy, Phys. Rev. E 75, 026205 (2007). (doi: 10.1103/PhysRevE.75.026205)
- "Dual Synchronization of Chaos in Mackey-Glass Electronic Circuits with Time-Delayed Feedback," S. Sano, A. Uchida, S. Yoshimori, and R. Roy, Phys. Rev. E 75, 016207 (2007). (doi: 10.1103/PhysRevE.75.016207)
- "Dual Synchronization of Chaos in Mackey-Glass Electronic Circuits with Time-Delayed Feedback," S. Sano, A. Uchida, S. Yoshimori, and R. Roy, Phys. Rev. E 75, 016207 (2007). (doi: 10.1103/PhysRevE.75.016207)
- "Localized Excitations in Arrays of Synchronized Laser Oscillators," Fabien Rogister and Rajarshi Roy, Phys. Rev. Lett. 98, 104101 (2007). (doi: 10.1103/PhysRevLett.98.104101)
- "Changing Dynamical Complexity with Time Delay in Coupled Fiber Laser Oscillators," Anthony L. Franz, Rajarshi Roy, Leah Shaw, and Ira B. Schwartz, Phys. Rev. Lett. 99, 053905 (2007). (doi: 10.1103/PhysRevLett.99.053905)
- "Localized Excitations in Arrays of Synchronized Laser Oscillators," Fabien Rogister and Rajarshi Roy, Phys. Rev. Lett. 98, 104101 (2007). (doi: 10.1103/PhysRevLett.98.104101)
- "Changing Dynamical Complexity with Time Delay in Coupled Fiber Laser Oscillators," Anthony L. Franz, Rajarshi Roy, Leah Shaw, and Ira B. Schwartz, Phys. Rev. Lett. 99, 053905 (2007). (doi: 10.1103/PhysRevLett.99.053905)
- "Controlling Optical Chaos, Spatio-Temporal Dynamics, and Patterns," L. Illing, D. Gauthier, and Rajarshi Roy, Advances in Atomic, Molecular, Optical Phys. 54, 615-697 (2007). (doi: 10.1016/S1049-250X(06)54010-8)
- "Laser Beams with Embedded Vortices: Tools for Atom Optics," N. Chattrapibon, E. Rogers, D. Cofield, Rajarshi Roy and W.T. Hill III, J. Opt. Soc. Am. B23, 94–103 (2006). (doi: 10.1364/JOSAB.23.000094)
- "Observation of Chaotic Itinerancy in the Light and Carrier Dynamics of a Semiconductor Laser with Optical Feedback," Will Ray, Wing-Shun Lam, Parvez N. Guzdar, and Rajarshi Roy, Phys. Rev. E 73, 026219 (2006). (doi: 10.1103/PhysRevE.73.026219)
- "Synchronization and Time Shifts of Dynamical Patterns for Mutually Delay-Coupled Fiber Ring Lasers," Leah B. Shaw, I. B. Schwartz, Elizabeth Rogers, and Rajarshi Roy, Chaos 16, 015111 (2006). (doi: 10.1063/1.2150407)
- "Synchronization and Symmetry Breaking in Mutually Coupled Fiber Lasers," Elizabeth A.Rogers-Dakin, Jordi Garcia-Ojalvo, David J.DeShazer, and Rajarshi Roy, Phys Rev E 73, 045201(R) (2006). (doi: 10.1103/PhysRevE.73.045201)
- "Synchronization of Unidirectionally Coupled Mackey-Glass Analog Circuits with Frequency Bandwidth Limitations," Min-Young Kim, C. Sramek, A. Uchida, and Rajarshi Roy, Phys. Rev. E74, 016211 (2006). (doi: 10.1103/PhysRevE.74.016211)
- "Scaling Behavior of Laser Population Dynamics with Time-Delayed Coupling: Theory and Experiment," M-Y. Kim, Rajarshi Roy, J. L. Aron, T.W. Carr, and I.B. Schwartz, Phys. Rev. Lett. 94, 088101 (2005). (doi: 10.1103/PhysRevLett.94.088101)
- "Measurement of Hurst Exponents for Semiconductor Laser Phase Dynamics," Wing-Shun Lam, Will Ray, Parvez N. Guzdar, and Rajarshi Roy, Phys. Rev. Lett. 94, 010602 (2005). (doi: 10.1103/PhysRevLett.94.010602)
- "Spatiotemporal Chaos Synchronization in a Large Array of Locally Coupled Nonidentical Lasers," F. Rogister and Rajarshi Roy, Laser Physics 15, 313–319 (2005).
- "Synchronization and Communication with Chaotic Laser Systems," A. Uchida, J. Garcia-Ojalvo, F. Rogister, and Rajarshi Roy, pp. 203–341, Chapter 5, Progress in Optics, Vol. 48, ed. E. Wolf (North Holland) (2005). (doi: 10.1016/S0079-6638(05)48005-1)
- "Communications Technology: Chaos Down the Line," Rajarshi Roy, News and Views, article, Nature 438, 298-299 (2005). (doi: 10.1038/438298b)
- "Power-Law Spatial Correlations in Arrays of Locally Coupled Lasers," F. Rogister, K. Scott Thornburg, Jr., L. Fabiny, M. Moeller, and Rajarshi Roy, Phys. Rev. Lett. 92, 093905 (2004). (doi: 10.1103/PhysRevLett.92.093905)
- "Phase Synchronization in a Modulated Chaotic Laser Array," D. J. DeShazer, R. Breban, E. Ott, and Rajarshi Roy, Intl. J. Bif. Chaos 14, 3205 (2004). (doi: 10.1142/S0218127404011302)
- "Generalized Synchronization of Chaos: Experiments on a Two-Mode Microchip Laser with Optoelectronic Feedback," R. McAllister, A. Uchida, R. Meucci, and Rajarshi Roy, Physica D195, 244-262 (2004). (doi: 10.1016/j.physd.2004.03.017)
- "Stochastic Bursting Due to Frequency Drift in an Injected Fiber Laser," Jordi Garcia-Ojalvo, David J. DeShazer, Brian P. Tighe, and Rajarshi Roy, J. Optics B, Semiclassical and Quantum Optics 6, S780–S785 (2004). (doi: 10.1088/1464-4266/6/8/024)
- "Experimental Observation of Noise-Induced Synchronization of Bursting Dynamical Systems," David J. DeShazer, Brian P. Tighe, Juergen Kurths, and Rajarshi Roy, IEEE Jour. Sel. Top. Quant. Elect. 10, 906-910 (2004). (Invited paper). (doi: 10.1109/JSTQE.2004.837212)
- "Generalized Synchronization of Spatiotemporal Chaos in a Liquid Crystal Spatial Light Modulator," E. Rogers, R. Kalra, R. Schroll, A. Uchida, D.P. Lathrop, and Rajarshi Roy, Phys. Rev. Lett. 93, 084101 (2004). (doi: 10.1103/PhysRevLett.93.084101)
- "Consistency of Nonlinear System Response to Complex Drive Signals," A. Uchida, R. McAllister, and Rajarshi Roy, Phys. Rev. Lett. 93, 244102 (2004). (doi: 10.1103/PhysRevLett.93.244102)
- "Measuring Intense Rotation and Dissipation in Turbulent Flows," Benjamin W. Zeff, Daniel D. Lanterman, Ryan McAllister, Rajarshi Roy, Eric J. Kostelich, and Daniel P. Lathrop, Nature 421, 146 (2003). (doi: 10.1038/nature01334)
- "Competition Between Two Frequencies for Phase Synchronization of a Chaotic Laser," Ryan McAllister, Riccardo Meucci, David DeShazer, and Rajarshi Roy, Phys. Rev. E 67, 015202(R) (2003). (doi: 10.1103/PhysRevE.67.015202)
- "Hilbert Phase Analysis of the Dynamics of a Semiconductor Laser with Optical Feedback," Wing-Shun Lam, Parvez N. Guzdar, and Rajarshi Roy, Phys. Rev. E 67, 025604(R) (2003). (doi: 10.1103/PhysRevE.67.025604)
- "Bursting Dynamics of a Fiber Laser with an Injected Signal," David J. DeShazer, J. Garcia-Ojalvo, and Rajarshi Roy, Phys. Rev. E 67, 036602 (2003). (doi: 10.1103/PhysRevE.67.036602)
- "Effect of Spontaneous Emission Noise and Modulation on Semiconductor Lasers near Threshold with Optical Feedback," Wing-Shun Lam, Parvez N. Guzdar, and Rajarshi Roy, Int. J. Mod. Phys. B17, 4123-4138 (2003). (doi: 10.1142/S021797920302209X)
- "Generalized Synchronization of Chaos in Identical Systems with Hidden Degrees of Freedom", A. Uchida, R. McAllister, R. Meucci, and Rajarshi Roy, Phys. Rev. Lett. 91, 174101 (2003). (doi: 10.1103/PhysRevLett.91.174101)
- "Generation of Nondiffracting Bessel Beams by Use of a Spatial Light Modulator," N. Chattrapibon, E. Rogers, D. Cofield, W.T. Hill III, and Rajarshi Roy, Optics Letters 28, 2183 (2003). (doi: 10.1364/OL.28.002183)
- "Using GRENOUILLE to Characterize Asymmetric Femtosecond Pulses Undergoing Self- and Cross-Phase Modulation in a Polarization-Maintaining Optical Fiber," B. Khubchandani, A. Christian Silva, Parvez N. Guzdar, and Rajarshi Roy, Optics Express 11, 3063-3073 (2003). (doi: 10.1364/OE.11.003063)
- "Stochastic Modeling of Bursting Dynamics in an Injected Fiber Laser," J Garcia-Ojalvo, D. J. DeShazer, and R. Roy, Proceedings SPIE vol. 5111, pp. 126-134 (2003),
__Fluctuations and Noise in Photonics and Quantum Optics__, ed. by D. Abbott, J. H. Shapiro, and Y. Yamamoto. - "Communicating with Optical Spatiotemporal Chaos," J. Garcia-Ojalvo and Rajarshi Roy, Proc. SPIE, Int. Soc. Opt. Eng. 4646, 525 (2002). (doi: 10.1117/12.470556)
- "Communication with Dynamically Fluctuating States of Light Polarization," Gregory D. VanWiggeren, and Rajarshi Roy, Phys. Rev. Lett. 88, 097903 (2002). (doi: 10.1103/PhysRevLett.88.097903)
- "Chaotic Function Generator: Complex Dynamics and Its Control in a Loss-Modulated Nd:YAG Laser," R. Meucci, Ryan McAllister, and Rajarshi Roy, Phys. Rev. E 66, 026216 (2002). (doi: 10.1103/PhysRevE.66.026216)
- "Influence of Stochasticity on Multiple Four-Wave-Mixing Processes in an Optical Fiber," Bhaskar Khubchandani, Parvez N. Guzdar, and Rajarshi Roy, Phys. Rev. E 66, 066609 (2002). (doi: 10.1103/PhysRevE.66.066609)
- "Spatiotemporal Communication with Synchronized Optical Chaos," J. Garcia-Ojalvo and Rajarshi Roy, Phys. Rev. Lett. 86, 5204 (2001). (doi: 10.1103/PhysRevLett.86.5204)
- "Detecting Phase Synchronization in a Chaotic Laser Array," D. DeShazer, R. Breban, E. Ott, and R. Roy, Phys. Rev. Lett. 87, 044101 (2001). (doi: 10.1103/PhysRevLett.87.044101)
- "Parallel Communication with Optical Spatiotemporal Chaos," J. Garcia-Ojalvo and R. Roy, IEEE Trans. Circuits and Systems 48, 1491 (2001). (doi: 10.1109/TCSI.2001.972856)
- "Dynamics of Activated Escape and Its Observation in a Semiconductor Laser," J. Hales, A. Zhukov, R. Roy, and M. I. Dykman, Phys. Rev. Lett. 85, 78-81 (2000). (doi: 10.1103/PhysRevLett.85.78)
- "High-Speed Fiber-Optic Polarization Analyzer: Measurements of the Polarization Dynamics of an Erbium-Doped Fiber Ring Laser," G. D. VanWiggeren and R. Roy, Opt. Comm. 164, 107-120 (1999). (doi: 10.1016/S0030-4018(99)00163-7)
- "Transmission of Linearly Polarized Light through a Single-Mode Fiber with Random Fluctuations of Birefringence," G. D. VanWiggeren and R. Roy, Appl. Opt. 38, 3888 (1999). (doi: 10.1364/AO.38.003888)
- "Synchronization of Chaos in an Array of Three Lasers," J. R. Terry, K. Scott Thornburg, D. DeShazer, G. D. VanWiggeren, S. Zhu, P. Ashwin, and R. Roy, Phys. Rev. E 59, 4036 (1999). (doi: 10.1103/PhysRevE.59.4036)
- "Chaotic Communication Using Time-Delayed Optical Systems," G. D. VanWiggeren and R. Roy, Int. J. Bifur. Chaos 9 [11], 2129 (1999). (doi: 10.1142/S0218127499001565)
- "Blowout Bifurcation in a System of Coupled Chaotic Lasers," P. Ashwin, J. Terry, K. S. Thornburg, Jr., and R. Roy, Phys. Rev. E 58, 7186 (1998). (doi: 10.1103/PhysRevE.58.7186)
- "Polarization-Based Data Storage in Fibre Ring Lasers," J. García-Ojalvo and R. Roy, Quantum Semiclass. Opt.: J. European Opt. Soc. Part B 10, 723 (1998). (doi: 10.1088/1355-5111/10/6/005)
- "Optical Communication with Chaotic Waveforms," G. D. VanWiggeren and R. Roy, Phys. Rev. Lett. 81, 3547 (1998). (doi: 10.1103/PhysRevLett.81.3547)
- "Dynamical Evolution of Multiple Four-Wave Mixing Processes in an Optical Fiber," Darlene Hart, A. Judy, R. Roy, and J. W. Beletic, Phys. Rev. E 57, 4757 (1998). (doi: 10.1103/PhysRevE.57.4757)
- "Communication with Chaotic Lasers," G. D. VanWiggeren and R. Roy, Science 279, 1198 (1998). (doi: 10.1126/science.279.5354.1198)
- "Intracavity Chaotic Dynamics in Ring Lasers with an Injected Signal," J. García-Ojalvo and R. Roy, Phys. Lett. A 229, 362 (1997). (doi: 10.1016/S0375-9601(97)00198-9)
- "Fast Intracavity Polarization Dynamics of an Erbium-Doped Fiber Ring Laser: Inclusion of Stochastic Effects," Q. L. Williams, J. García-Ojalvo, and R. Roy, Phys. Rev. A 55, 2376 (1997). (doi: 10.1103/PhysRevA.55.2376)
- "Encoding and Decoding Messages with Chaotic Lasers," P. M. Alsing, A. Gavrielides, V. Kovanis, R. Roy, and K. S. Thornburg, Jr., Phys. Rev. E 56, 6302-6310 (1997). (doi: 10.1103/PhysRevE.56.6302)
- "Influence of Noise on Chaotic Laser Dynamics," C. Liu, R. Roy, H.D.I. Abarbanel, Z. Gills, and K. Nunes, Phys. Rev. E 55, 6483-6500 (1997). (doi: 10.1103/PhysRevE.55.6483)
- "Chaos and Coherence in Coupled Lasers," K. Scott Thornburg, M. Moeller, R. Roy, R. Li, T. Carr, and T. Erneux, Phys. Rev. E 55, 3865 (1997). (doi: 10.1103/PhysRevE.55.3865)