Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems

Martínez-Llinàs, Jade; Colet, Pere; Erneux, Thomas

doi:10.1103/physreve.89.042908

Cited by 11 publications

(10 citation statements)

References 38 publications

(61 reference statements)

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“…The coexistence of in-and out-of-phase Hopf bifurcation points for the same s 0 that appears with negative feedback (χ n < 0) it is not allowed with positive feedback (χ n > 0) as it was recently demonstrated in Ref. [26]. Second, several in-phase Hopf bifurcations or several out-of phase solutions may appear for the same value of s 0 with different periods.…”

Section: Onset Of Periodic Solutionsmentioning

confidence: 73%

“…The dynamics can be described in terms of x i , proportional to the ac voltage applied to the MZI, and y i (t) = t t 0 x i (t )dt , leading to a system of four delay differential equations [26],…”

Section: Modelmentioning

confidence: 99%

“…We note that in the stability analysis done in Ref. [26] δ was neglected because it was a small parameter. However, here we keep it because it will be necessary to determine the frequency of a slow oscillation as we will see below.…”

Section: Onset Of Periodic Solutionsmentioning

confidence: 99%

“…The case of negative feedback has been considered in Ref. [26]. Here we focus on the case of positive feedback.…”

Section: Onset Of Periodic Solutionsmentioning

confidence: 99%

“…In this situation square waves are in general asymmetric in the sense that the duty cycle differs from half the period. We have recently studied the generation of symmetric square-wave pulses in a model for two mutually delay-coupled OEOs with offset phases in the range for negative feedback [26]. We showed that multiple in-phase square waves with different periods can coexist when the ratio between the self-feedback and the cross-feedback delay times satisfies a rational relationship involving two odd numbers.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators

2015

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We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in-and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple inand out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques.

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Section: Onset Of Periodic Solutionsmentioning

confidence: 73%

Section: Modelmentioning

confidence: 99%

Section: Onset Of Periodic Solutionsmentioning

confidence: 99%

“…The case of negative feedback has been considered in Ref. [26]. Here we focus on the case of positive feedback.…”

Section: Onset Of Periodic Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators

2015

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Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

Oden

Lavrov

Chembo

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

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Doublet structure in the optical spectrum of a semiconductor laser with optoelectronic feedback in a square-wave regime

Islam

Kovalev

Iachkula

et al. 2022

Applied Physics Letters

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We observe an optical spectrum consisting of a doublet in the output of a semiconductor laser diode with optoelectronic feedback in a dynamical regime in which a self-sustained square-wave modulation is observed, depending on injection current and feedback strength. The doublet frequency splitting is strongly correlated with the duty cycle of the square wave; both parameters as well as the relative magnitude of the peaks are observed to vary with the feedback level. A rate equation model reproduces the spectral doublets. The appearance of the doublet is attributed to active medium gain saturation and refractive index dependence on the carrier density.

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Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems

Cited by 11 publications

References 38 publications

Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators

Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

Doublet structure in the optical spectrum of a semiconductor laser with optoelectronic feedback in a square-wave regime

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