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Viktorov EA, Habruseva T, Hegarty SP, Huyet G, Kelleher B. Coherence and incoherence in an optical comb. PHYSICAL REVIEW LETTERS 2014; 112:224101. [PMID: 24949771 DOI: 10.1103/physrevlett.112.224101] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Indexed: 06/03/2023]
Abstract
We demonstrate a coexistence of coherent and incoherent modes in the optical comb generated by a passively mode-locked quantum dot laser. This is experimentally achieved by means of optical linewidth, radio frequency spectrum, and optical spectrum measurements and confirmed numerically by a delay-differential equation model showing excellent agreement with the experiment. We interpret the state as a chimera state.
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Affiliation(s)
- Evgeny A Viktorov
- National Research University of Information Technologies, Mechanics and Optics, 199034 St. Petersburg, Russia and Optique Nonlinéaire Théorique, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, B-1050 Bruxelles, Belgium
| | - Tatiana Habruseva
- Centre for Advanced Photonics and Process Analysis, and Department of Applied Physics and Instrumentation, Cork Institute of Technology, Cork, Ireland and Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork, Ireland and Aston University, Aston Triangle, B4 7ET Birmingham, United Kingdom
| | - Stephen P Hegarty
- Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork, Ireland
| | - Guillaume Huyet
- National Research University of Information Technologies, Mechanics and Optics, 199034 St. Petersburg, Russia and Centre for Advanced Photonics and Process Analysis, and Department of Applied Physics and Instrumentation, Cork Institute of Technology, Cork, Ireland and Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork, Ireland
| | - Bryan Kelleher
- Centre for Advanced Photonics and Process Analysis, and Department of Applied Physics and Instrumentation, Cork Institute of Technology, Cork, Ireland and Tyndall National Institute, University College Cork, Lee Maltings, Dyke Parade, Cork, Ireland
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Romanelli M, Wang L, Brunel M, Vallet M. Measuring the universal synchronization properties of driven oscillators across a Hopf instability. OPTICS EXPRESS 2014; 22:7364-7373. [PMID: 24718112 DOI: 10.1364/oe.22.007364] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
When a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal oscillations. Here we characterize these two synchronization regimes in a laser experiment, by measuring the spectrum of the phase fluctuations across the bifurcation. We find experimentally, and confirm numerically, that the low frequency phase noise of the driven oscillator is strongly suppressed in both regimes in the same way. Thus the long-term phase stability of the master oscillator is transferred to the driven one, even in the absence of phase-locking. The numerical study of a generic, minimal model suggests that such behavior is universal for any periodically driven oscillator near a Hopf bifurcation point.
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Kelleher B, Goulding D, Pascual BB, Hegarty SP, Huyet G. Bounded phase phenomena in the optically injected laser. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:046212. [PMID: 22680561 DOI: 10.1103/physreve.85.046212] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2011] [Revised: 02/03/2012] [Indexed: 06/01/2023]
Abstract
Two routes to phase-locking in the optically injected laser system are investigated both involving limit cycles where the phase of the slave laser is unlocked but is nevertheless bounded. We use an experimental phase-resolving technique to unambiguously demonstrate the phenomenon via explicit phasors for the slave laser electric field. Theoretical considerations show that for locking mechanisms involving Hopf bifurcations, such limit cycles of bounded phase are generic. For weakly damped devices, such as quantum well lasers, this can involve an excited resonance at the relaxation oscillation frequency. For highly damped devices there is no such excitation but the bounded phase behavior must persist. Phasor portraits for other regimes are also obtained including a chaotic regime.
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Affiliation(s)
- B Kelleher
- Centre for Applied Photonics and Process Analysis, Cork Institute of Technology, Cork, Ireland
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Thévenin J, Romanelli M, Vallet M, Brunel M, Erneux T. Resonance assisted synchronization of coupled oscillators: frequency locking without phase locking. PHYSICAL REVIEW LETTERS 2011; 107:104101. [PMID: 21981505 DOI: 10.1103/physrevlett.107.104101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2011] [Indexed: 05/31/2023]
Abstract
Frequency locking without phase locking of two coupled nonlinear oscillators is experimentally demonstrated. This synchronization regime is found for two coupled laser modes, beyond the phase-locking range fixed by Adler's equation, because of a resonance mechanism. Specifically, we show that the amplitudes of the two modes exhibit strong fluctuations that produce average frequency synchronization, even if the instantaneous phases are unlocked. The experimental results are in good agreement with a theoretical model.
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Affiliation(s)
- J Thévenin
- Institut de Physique de Rennes, Université Rennes I-CNRS UMR 6251,Campus de Beaulieu, 35042 Rennes Cedex, France
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Krauskopf B, Graaf WAVD, Lenstra D. Bifurcations of relaxation oscillations in an optically injected diode laser. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/1355-5111/9/5/011] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Ellmer P, Jung C. Irregular phase slipping in a model for a laser with injected signal. CHAOS (WOODBURY, N.Y.) 1997; 7:341-349. [PMID: 12779661 DOI: 10.1063/1.166230] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In a model for a single mode laser with injected signal we find irregular pulsing of the output signal. During the turbulent time intervals the relative phase between the internal and the external field slips by an integer multiple of 2pi, where the multiplicity varies irregularly from pulse to pulse. Between the pulses, in the laminar time intervals, the relative phase is locked. We compare this behavior with the results of various other laser models. By the investigation of this interesting mechanism for the creation of phase chaos in a driven oscillator, we learn which properties are responsible for the irregular interruption of the phase locking. (c) 1997 American Institute of Physics.
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Affiliation(s)
- P. Ellmer
- Fachbereich Physik der Universitat Bremen, 28359 Bremen, Germany
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Erneux T, Kovanis V, Gavrielides A, Alsing PM. Mechanism for period-doubling bifurcation in a semiconductor laser subject to optical injection. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:4372-4380. [PMID: 9913411 DOI: 10.1103/physreva.53.4372] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Torre MS, Ranea-Sandoval HF, Buceta RC. Normal-form theory for a laser model with periodic signal and noise injection. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:3427-3437. [PMID: 9911293 DOI: 10.1103/physreva.50.3427] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Zeghlache H, Zehnlé V. Theoretical study of a laser with injected signal. I. Analytical results on the dynamics. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:6015-6027. [PMID: 9908858 DOI: 10.1103/physreva.46.6015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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