untitled

Nonlinear Dynamics and Chaos
in Electronic and Laser Systems:
PROJECTS

Mutually coupled semiconductor laser with orthogonal optical injection (Davis, Dube, Mabuza, and Trimmer, Summer 2007; Lee, McKay, and Mooneyham, Summer 2008 )

Abstracts of talks to be given at Annual Meeting of the Optical Society of America (OSA 2008), Frontiers in Optics 2008 / Laser Science XXIV, Rochester, New York, October 2008.0

"Dynamics of Diode Lasers with Mutual Coupling by Rotated Optical Injection" B. Mooneyham, K. Lee, J. McKay, D.W. Sukow, Washington and Lee University, Lexington, VA 24450. Orthogonal optical injection in a system of mutually-coupled edge-emitting lasers can produce polarization-modulated square waves with a tunable duty cycle. The asymmetry in these square waves can be varied using system parameters such as pump current, alignment, and coupling strength. Experimental results and numerical simulations will be reported. Supported by NSF CAREER award #0239413.

"Theoretical Analysis of Mutually-Coupled Diode Laser Systems" K. Lee, J. McKay, B. Mooneyham, D.W. Sukow, Washington and Lee University, Lexington, VA 24450. A semiclassical, delay-differential model describes the dynamics of a system of two diode lasers with mutual coupling via orthogonal optical injection. Numerical simulations reproduce square waves, and analytical expressions predict properties of steady states, in agreement with experimental observations. Supported by NSF CAREER award #0239413.

Two edge-emitting lasers coupled through polarization-rotated optical injection exhibit square-wave oscillations provided the roundtrip time from laser to laser and back is sufficiently large. If the mutual coupling between the lasers is relatively weak, the two plateaus of the square-waves exhibit different durations even though the total period remains close to the roundtrip time. This asymmetry progressively disappears as the feedback strength is increased. The experimental observations are confirmed by numerical simulations. The simulations also reveal that the square-wave regimes appear through a series of complex bifurcations and that a sufficiently large roundtrip time is needed.

“Asymmetric Square Waves in Mutually-Coupled Semiconductor Lasers,” David W. Sukow, Athanasios Gavrielides, Thomas Erneux, Josiah Davis, Makhosazana Dube, Saneliso Mabuza, and Russell Trimmer, Proceedings of the SPIE: Semiconductor Lasers and Laser Dynamics III, vol. 6997 (2008).

Polarization self-modulation in edge-emitting diode lasers (Amonette, Burner, McLachlan, and Miller, Summer 2005; Burner, Fall 2006; Bunting, Winter 2007; Davis, Dube, Mabuza, and Trimmer, Summer 2007)

The square-wave response of edge-emitting diode lasers subject to a delayed polarization-rotated optical feedback is studied in detail. Specifically, the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. Square-wave self-modulated polarization intensities oscillating in antiphase are observed experimentally. We find numerically that these oscillations naturally appear for a broad range of values of parameters provided the feedback is sufficiently strong and the differential losses in the normally-unsupported polarization mode are small. We then investigate the laser equations analytically and find that the square-wave oscillations are the result of a bifurcation phenomenon.

“Square-wave self-modulation in diode lasers with polarization-rotated optical feedback,” Athanasios Gavrielides, Thomas Erneux, David W. Sukow, Guinevere Burner, Taylor McLachlan, John Miller, and Jake Amonette, Optics Letters , vol. 31 no. 13, pp. 2006 - 2008 (2006). Available in pdf format

The square-wave response of edge-emitting diode lasers subject to a delayed polarization-rotated optical feedback is studied experimentally and theoretically. Square-wave self-modulated polarization intensities of a period close to twice the delay τ of the feedback gradually appear through a sequence of bifurcations starting with a Hopf bifurcation (Gavrielides et al, Proc. SPIE 6115, to appear, 2006). In Gavrielides et al (submitted, 2006), squarewave solutions were determined analytically from the laser equations in the limit of large τ . A condition on the laser parameters was derived explaining why square-wave oscillations are preferentially observed for sufficiently large feedback strength. In this paper, we concentrate on the relaxation oscillations that always appear at each intensity jump between the plateaus of the square-wave. We show analytically that if the feedback strength is progressively decreased, a bifurcation to sustained relaxation oscillations is possible for one of the two plateaus.

“Square-wave oscillations in edge-emitting diode lasers with polarization-rotated optical feedback,” Athanasios Gavrielides, Thomas Erneux, David W. Sukow, Guinevere Burner, Taylor McLachlan, John Miller, and Jake Amonette, Proceedings of the SPIE: Semiconductor Lasers and Laser Dynamics II, vol. 6184, pp. 255-261 (2006).

The response of a diode laser resulting from an incoherent delayed optical feedback is considered from numerical and experimental perspectives. We concentrate on a class of solutions that appear as regular square waveforms. A two-field model is used and the bifurcation diagram of these square-wave regimes is studied. Conditions under which they typically appear are determined. The roles of various parameters are examined, particularly with regard to the gains and losses of the two polarization modes. Numerical results are in close agreement with experiments.

“Square waveforms in edge-emitting diode laser subject to polarization-rotated optical feedback,” Athanasios Gavrielides, David W. Sukow, Guinevere Burner, Taylor McLachlan, John Miller, Jake Amonette, and Thomas Erneux, Proceedings of the SPIE: Physics and Simulation of Optoelectronic Devices XIV vol. 6115, pp. 60 - 69 (2006).

Synchronized chaos in semiconductor lasers (Amonette, Burner, McLachlan, and Miller, Summer 2005; Baracco, Blackburn, Parmenter, and Sexton, Summer 2004; Blackburn and Spain, Winter 2004; Babcock, Bennett, Blackburn, and Spain, Summer 2003)

Abstract from article in Physical Review A

Identity synchronization is observed experimentally and numerically in the chaotic dynamics of a system of two unidirectionally-coupled semiconductor lasers. The transmitter and receiver lasers are subjected to polarization-rotated optical feedback and injection, respectively. Numerical and analytical results show that identity synchronization requires parameter matching through a relationship between the injection and feedback strengths, and linewidth enhancement factors of the lasers. Inverse synchronization is also observed experimentally.

“Identity synchronization in diode lasers with unidirectional feedback and injection of rotated optical fields,” David W. Sukow, Athanasios Gavrielides, Taylor McLachlan, Guinevere Burner, Jake Amonette, and John Miller, Physical Review A, vol. 74, 023812 (2006). Available in pdf format

“Two-field description of chaos synchronization in diode lasers with incoherent optical feedback and injection,” David W. Sukow, Athanasios Gavrielides, Thomas Erneux, Michael J. Baracco, Zachary A. Parmenter, and Karen L. Blackburn, Physical Review A , vol. 72 , 043818 (2005). Available in pdf format

This study investigates chaos synchronization of two semiconductor lasers with polarization-rotated optical feedback and unidirectional injection, from experimental and theoretical perspectives. The transmitter laser is driven into chaos using delayed optical feedback, with the polarization state of the feedback beam made to be orthogonal to the natural laser mode. A similarly rotated beam is injected into an isolated receiver laser. We demonstrate successful experimental chaos synchronization. Particular attention is given to the form of synchronization, noting that both positive and inverse synchronization with a lag characteristic of driving synchronization is observed experimentally. These observations do not agree with the predictions of the incoherent optoelectronic feedback model. Progress in reconciling these results with an expanded model is discussed.

"Polarization dynamics in semiconductor lasers with incoherent optical feedback," David W. Sukow, Athanasios Gavrielides, Thomas Erneux, Michael J. Baracco, Zachary A. Parmenter, and Karen L. Blackburn, Proceedings of the SPIE: Physics and Simulation of Optoelectronic Devices XIII vol. 5722, pp 256 - 266 (2005). Available in pdf format

. (653k) Copyright 2005 Society of Photo-Optical Instrumentation Engineers. This paper will be published in Proceedings of the SPIE: Physics and Simulation of Optoelectonic Devices XIII, vol. 5722 and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

We demonstrate experimental chaos synchronization between two chaotic semiconductor lasers subjected to polarizaiton-rotated optical feedback and unidirectional injection. This system allows high-quality synchronization to be obtained between dissimilar lasers in a wide range of chaotic operating regimes. Another features of this system is its operation at high characteristic frequencies, taking advantage of the all-optical implementation. Time series and rf spectra showing synchronization are confirmed by high correlation coefficients in excess of 0.85.

“Experimental synchronization of chaos in diode lasers with polarization-rotated feedback and injection,” David W. Sukow, Karen L. Blackburn, Allison R. Spain, Katherine J. Babcock, Jake V. Bennett, and Athanasios Gavrielides, Optics Letters , vol. 29 no. 20, pp. 2393 - 2395 (2004). Available in pdf format

Bifurcations in a semiconductor laser subject to delayed incoherent feedback (Hicks, Winter 2002)

Abstract from article:

We examine experimentally and numerically the bifurcation sequence and route into chaos of a semiconductor laser subject to delayed incoherent feedback. We show that the sequence of bifurcations follows a three frequency scenario in which the steady state of the laser destabilizes by a Hopf bifurcation at the relaxation frequency of the laser. Specifically, we show experimentally and numerically that the Hopf bifurcation can be supercritical or subcritical depending on the length of the delay and the pumping of the laser above threshold. This is followed by a torus bifurcation at the external cavity frequency and further by a tertiary bifurcation at a significantly lower frequency.

Read the publication in Optics Communciations (preprint)

. (6007k) "Bifurcations in a semiconductor laser subject to delayed incoherent feedback," J.M Saucedo Solorio, D.W. Sukow, D.R. Hicks, and A. Gavrielides, Optics Communications, vol. 214 no. 1-6, pp. 327 – 334 (2002). Copyright ©2002 Elsevier Science B.V.

High-Frequency Oscillations from a Semiconductor Laser with Two Delayed Optical Feedbacks (Wright and Hegg, Summer 2001)

Abstract from proposal:

We propose to study the phenomenon of stable, high-frequency oscillations present in semiconductor diode lasers subject to delayed optical feedback from two distant reflectors. Recent experiments have discovered the existence of such oscillations, but they have not been characterized carefully, nor are they completely understood theoretically. Therefore, we will examine these oscillations experimentally, with the goal of unambiguously identifying their dynamical origins. Offering theoretical guidance is recent work that analyzes similar dynamics in a slightly simpler system; this analysis suggests that the oscillations originate from a novel dynamical state of the laser: a "mixed" state that is a combination of two external cavity modes. The proposed study will contribute mainly to fundamental understanding of laser dynamics in delayed feedback systems. However, given the technological importance of diode lasers, such understanding may also contribute to improved performance in communication and data storage applications.

Read the publication in Optics Letters

:(105k) "Mixed external cavity mode dynamics in a semiconductor laser," David W. Sukow, Michael C. Hegg, Jennifer L. Wright, and Athanasios Gavrielides, Optics Letters, vol. 27, no. 10, pp. 827 – 829 (2002.. Copyright ©2002 Optical Society of America, Inc.

Read the publication in the SPIE Conference Proceedings

(1073k): "Mixed-mode dynamics in a semiconductor laser with two optical feedbacks," David W. Sukow, Athanasios Gavrielides, Michael C. Hegg, and Jennifer L. Wright, to appear in Proceedings of the SPIE: Physics and Simulation of Optoelectonic Devices X, vol. 4646, (2002). Copyright 2002 Society of Photo-Optical Instrumentation Engineers. This paper will be published in Proceedings of the SPIE: Physics and Simulation of Optoelectonic Devices X, vol. 4646 and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Circuit analog of a semiconductor laser with delayed optical feedback (Klotz and Silverman, Summer 2000)

We study the nonlinear dynamical behavior of a semiconductor laser subject to delayed optoelectronic feedback. We perform this study by designing a simple electronic circuit whose behavior is governed by the same equations that govern the laser system. The circuit offers important experimental advantages, since it operates with much slower speeds, and has easily tunable parameters. Furthermore, it can be investigated systematically using automated data acquisition and control of system parameters. The dynamics we observe are in good agreement with numerical and theoretical predictions. We also model certain unavoidable limitations of the real laser system by adding a filter to the idealized circuit. The filter induces some changes to the global dynamics, but does not affect the fundamental oscillation frequency of the system.