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Dynamical properties induced by state-dependent delays in photonic systems.

Martínez-Llinàs J, Porte X, Soriano MC, Colet P, Fischer I - Nat Commun (2015)

Bottom Line: Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies.On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays.Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.

ABSTRACT
In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

No MeSH data available.


Related in: MedlinePlus

Dependence of the optical spectrum on the pump current of the laser.The frequency axis is centred to the value of the solitary laser frequency (194,350 GHz). FBG1 and FBG2 are detuned from the solitary laser frequency by −4±0.01 GHz and −11±0.01 GHz, respectively. The dashed horizontal line indicates the highest current for which the two spectral bands corresponding to the filters are separated by a gap larger than 10 dB. The relative amplitudes of the two spectral components are affected by the coupling ratio of the coupler at which the spectra are measured.
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f2: Dependence of the optical spectrum on the pump current of the laser.The frequency axis is centred to the value of the solitary laser frequency (194,350 GHz). FBG1 and FBG2 are detuned from the solitary laser frequency by −4±0.01 GHz and −11±0.01 GHz, respectively. The dashed horizontal line indicates the highest current for which the two spectral bands corresponding to the filters are separated by a gap larger than 10 dB. The relative amplitudes of the two spectral components are affected by the coupling ratio of the coupler at which the spectra are measured.

Mentions: Figure 2 exhibits optical spectra of the laser diode emission depending on the injection current. Since the feedback from the external reflectors reduces the threshold current of the laser, the optical spectra are depicted for pump currents ranging from 4% below the solitary laser threshold to 10% above. For currents below 1.08Ith, the two filters can be considered isolated, with a spectral gap >10 dB between them (indicated via a horizontal dashed line in Fig. 2). For pump currents above 1.08Ith, this gap gradually disappears and the dynamics resulting from these spectral signatures cannot be considered spectrally separated anymore. We note that the spectra close to threshold exhibit comparable spectral amplitudes and bandwidths in both filters and, therefore, one can expect similar contributions to the dynamics from both filters. Therefore, due to the chosen geometry, and for sufficiently low pump current, our system belongs to the class of systems described by the state-dependent delay equation 1.


Dynamical properties induced by state-dependent delays in photonic systems.

Martínez-Llinàs J, Porte X, Soriano MC, Colet P, Fischer I - Nat Commun (2015)

Dependence of the optical spectrum on the pump current of the laser.The frequency axis is centred to the value of the solitary laser frequency (194,350 GHz). FBG1 and FBG2 are detuned from the solitary laser frequency by −4±0.01 GHz and −11±0.01 GHz, respectively. The dashed horizontal line indicates the highest current for which the two spectral bands corresponding to the filters are separated by a gap larger than 10 dB. The relative amplitudes of the two spectral components are affected by the coupling ratio of the coupler at which the spectra are measured.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4557356&req=5

f2: Dependence of the optical spectrum on the pump current of the laser.The frequency axis is centred to the value of the solitary laser frequency (194,350 GHz). FBG1 and FBG2 are detuned from the solitary laser frequency by −4±0.01 GHz and −11±0.01 GHz, respectively. The dashed horizontal line indicates the highest current for which the two spectral bands corresponding to the filters are separated by a gap larger than 10 dB. The relative amplitudes of the two spectral components are affected by the coupling ratio of the coupler at which the spectra are measured.
Mentions: Figure 2 exhibits optical spectra of the laser diode emission depending on the injection current. Since the feedback from the external reflectors reduces the threshold current of the laser, the optical spectra are depicted for pump currents ranging from 4% below the solitary laser threshold to 10% above. For currents below 1.08Ith, the two filters can be considered isolated, with a spectral gap >10 dB between them (indicated via a horizontal dashed line in Fig. 2). For pump currents above 1.08Ith, this gap gradually disappears and the dynamics resulting from these spectral signatures cannot be considered spectrally separated anymore. We note that the spectra close to threshold exhibit comparable spectral amplitudes and bandwidths in both filters and, therefore, one can expect similar contributions to the dynamics from both filters. Therefore, due to the chosen geometry, and for sufficiently low pump current, our system belongs to the class of systems described by the state-dependent delay equation 1.

Bottom Line: Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies.On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays.Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

View Article: PubMed Central - PubMed

Affiliation: Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (UIB-CSIC), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.

ABSTRACT
In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

No MeSH data available.


Related in: MedlinePlus