Experimental control of pattern formation by photonic lattices

We study the control of modulational instability and pattern formation in a nonlinear dissipative feedback system with a periodic modulation of the material refractive index. We use a one-dimensional photonic lattice in a single-mirror feedback configuration and identify three mechanisms for pattern control: bandgap suppression of instability modes, periodicity induced pattern modes, and orientational pattern control.The authors acknowledge the support of the Conseil Régional de Lorraine, the bilateral FrenchAustralian Science and Technology program, and the Australian Research Council through Discovery projects

Will Health Literacy Research and Initiatives End the Confusion?

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Bifurcation to square-wave switching in orthogonally delay-coupled semiconductor lasers: Theory and experiment

We analyze the dynamics of two semiconductor lasers with so-called orthogonal time-delayed mutual coupling: the dominant TE (x) modes of each laser are rotated by 90∘ (therefore, TM polarization or y) before being coupled to the other laser. Although this laser system allows for steady-state emission in either one or in both polarization modes, it may also exhibit stable time-periodic dynamics including square waveforms. A theoretical mapping of the switching dynamics unveils the region in parameter space where one expects to observe long-term time-periodic mode switching. Detailed numerical simulations illustrate the role played by the coupling strength, the mode frequency detuning, or the mode gain to loss difference. We complement our theoretical study with several experiments and measurements. We present time series and intensity spectra associated with the characteristics of the square waves and other waveforms observed as a function of the strength of the delay coupling. The experimental observations are in very good agreement with the analysis and the numerical results.Peer ReviewedPostprint (published version

Stable microwave oscillations due to external-cavity-mode beating in laser diodes subject to optical feedback

Laser diodes subject to a delayed optical feedback may exhibit high-frequency oscillating intensities as a result of a beating between two external-cavity-modes ͑ECMs͒. We analyze the conditions for the stability of these microwave oscillations in the framework of the Lang-Kobayashi equations for a single-mode edgeemitting semiconductor laser ͓R. Lang and K. Kobayashi, IEEE J. Quantum Electron. QE-16, 347 ͑1980͔͒. We show that two different scenarios are possible. If the linewidth enhancement factor is relatively large (␣ϭ2 Ϫ5), the beating occurs between a stable ECM ͑mode͒ and an unstable ECM ͑antimode͒. The stability of the time-periodic solution is then limited in parameter space. But if the linewidth enhancement factor is sufficiently low (␣р␣ c Ӎ1), a beating between two stable modes is possible allowing stable high-frequency oscillating outputs

Deterministic polarization chaos from a laser diode

Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure

Stability of the nonlinear dynamics of an optically injected VCSEL

Automated protocols have been developed to characterize time series data in terms of stability. These techniques are applied to the output power time series of an optically injected vertical cavity surface emitting laser (VCSEL) subject to varying injection strength and optical frequency detuning between master and slave lasers. Dynamic maps, generated from high resolution, computer controlled experiments, identify regions of dynamic instability in the parameter space. © 2012 Optical Society of America

Nonlinear dynamics and chaos in an optomechanical beam

[EN] Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two-and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two-and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.This work was supported by the European Comission project PHENOMEN (H2020-EU-713450), the Spanish Severo Ochoa Excellence program and the MINECO project PHENTOM (FIS2015-70862-P). DNU, PDG and MFC gratefully acknowledge the support of a Ramon y Cajal postdoctoral fellowship (RYC-2014-15392), a Beatriu de Pinos postdoctoral fellowship (BP-DGR 2015 (B) and a Severo Ochoa studentship, respectively. We would like to acknowledge Jose C. Sabina de Lis, J.M. Plata Suarez, A. Trifonova and C. Masoller for fruitful discussions.Navarro-Urrios, D.; Capuj, NE.; Colombano, MF.; García, PD.; Sledzinska, M.; Alzina, F.; Griol Barres, A.... (2017). Nonlinear dynamics and chaos in an optomechanical beam. Nature Communications. 8. https://doi.org/10.1038/ncomms14965S8Strogatz, S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering Westview Press (2014).Lorenz, E. N. Deterministic nonperiodic ow. J. Atmos. Sci. 20, 130–141 (1963).Sparrow, C. The Lorenz Attractor: Bifurcations, Chaos and Strange Attractors Springer (1982).Aspelmeyer, M., Kippenberg, T. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391 (2014).Kippenberg, T., Rokhsari, H., Carmon, T., Scherer, A. & Vahala, K. Analysis of radiation-pressure induced mechanical oscillation of an optical microcavity. Phys. Rev. Lett. 95, 033901 (2005).Marquardt, F., Harris, J. G. E. & Girvin, S. M. Dynamical multistability induced by radiation pressure in high-finesse micromechanical optical cavities. Phys. Rev. Lett. 96, 103901 (2006).Krause, A. G. et al. Nonlinear radiation pressure dynamics in an optomechanical crystal. Phys. Rev. Lett. 115, 233601 (2015).Metzger, C. et al. Self-induced oscillations in an optomechanical system driven by bolometric backaction. Phys. Rev. Lett. 101, 133903 (2008).Bakemeier, L., Alvermann, A. & Fehske, H. Route to chaos in optomechanics. Phys. Rev. Lett. 114, 013601 (2015).Sciamanna, M. & Shore, K. A. Physics and applications of laser diode chaos. Nat. Photon. 9, 151–162 (2015).Williams, C. R. et al. Experimental observations of group synchrony in a system of chaotic optoelectronic oscillators. Phys. Rev. Lett. 110, 064104 (2013).Sciamanna, M. Optomechanics: vibrations copying optical chaos. Nat. Photon. 10, 366–368 (2016).Carmon, T., Cross, M. C. & Vahala, K. J. Chaotic quivering of micron-scaled on-chip resonators excited by centrifugal optical pressure. Phys. Rev. Lett. 98, 167203 (2007).Carmon, T., Rokhsari, H., Yang, L., Kippenberg, T. J. & Vahala, K. J. Temporal behavior of radiation-pressure-induced vibrations of an optical microcavity phonon mode. Phys. Rev. Lett. 94, 223902 (2005).Monifi, F. et al. Optomechanically induced stochastic resonance and chaos transfer between optical fields. Nat. Photon. 10, 399–405 (2016).Wu, J. et al. Dynamical chaos in chip-scale optomechanical oscillators. Preprint at https://arxiv.org/abs/1608.05071 (2016).Navarro-Urrios, D., Tredicucci, A. & Sotomayor-Torres, C. M. Coherent phonon generation in optomechanical crystals. SPIE Newsroom, doi:10.1117/2.1201507.006036 (2015).Navarro-Urrios, D. et al. A self-stabilized coherent phonon source driven by optical forces. Sci. Rep. 5, 15733 (2015).Johnson, T. J., Borselli, M. & Painter, O. Self-induced optical modulation of the transmission through a high-Q silicon microdisk resonator. Opt. Express 14, 817–831 (2006).Navarro-Urrios, D. et al. Self-sustained coherent phonon generation in optomechanical cavities. J. Opt. 18, 094006 (2016).Kemiktarak, U., Durand, M., Metcalfe, M. & Lawall, J. Mode competition and anomalous cooling in a multimode phonon laser. Phys. Rev. Lett. 113, 030802 (2014).Rosenstein, M. T., Collins, J. J. & De Luca, C. J. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117–134 (1993).Sprott, J. C. Chaos and Time-Series Analysis Vol. 69, Citeseer (2003).Grassberger, P. & Procaccia, I. Characterization of strange attractors. Phys. Rev. Lett. 50, 346–349 (1983).Hoppensteadt, F. C. & Izhikevich, E. M. Synchronization of MEMS resonators and mechanical neurocomputing. IEEE Trans. Circuits Syst. I, Reg. Papers 48, 133–138 (2001).Pennec, Y. et al. Band gaps and cavity modes in dual phononic and photonic strip waveguides. AIP Adv. 1, 041901 (2011).Gomis-Bresco, J. et al. A one-dimensional optomechanical crystal with a complete phononic band gap. Nat. Commun. 5, 4452 (2014).Johnson, S. G. et al. Perturbation theory for Maxwells equations with shifting material boundaries. Phys. Rev. E 65, 066611 (2002).Chan, J., Safavi-Naeini, A. H., Hill, J. T., Meenehan, S. & Painter, O. Optimized optomechanical crystal cavity with acoustic radiation shield. Appl. Phys. Lett. 101, 081115 (2012).Pennec, Y. et al. Modeling light-sound interaction in nanoscale cavities and waveguides. Nanophotonics 3, 413–440 (2014)

Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.Comment: Published in Nature Photonic

Reconfigurable chaos in electro-optomechanical system with negative Duffing resonators

Generating various laser sources is important in the communication systems. We propose an approach that uses a mechanical resonator coupled with the optical fibre system to produce periodic and chaotic optical signals. The resonator is structured in such a way that the nonlinear oscillation occurs conveniently. The mechanical apparatus in the configuration is the well known resonating system featured by the negative stiffness. The mechanical resonance is converted to reflected optical signal with the same dynamic properties as the mechanical oscillation, subsequently interacting with the optical signal within the optical fibre. The optical radiative force on the mechanical structure is also considered in the analysis. The coupled electro-optomechanical system has been analysed, and results show that the mechanical resonator has the capability to control the dynamics of the optical signal precisely. The system will have potential applications in tunable laser sources