Lévy flights for light in ordered lasers

Rocha, Erick G.; Santos, Emanuel P.; Santos, Bruno J.; Albuquerque, Samuel; Pincheira, Pablo I. R.; Argolo, C.; Moura, André L.

doi:10.1103/physreva.101.023820

Cited by 15 publications

(10 citation statements)

References 32 publications

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“…where β (0 < β ⩽ 1) is a dimensionless parameter introduced to consider that an ion relaxing at the transition |2> → |1> does not necessarily create a photon at the random medium (for example due to nonradiative relaxations), and τ 21 is the relaxation time of the photons out of the random medium, which in a conventional laser is linked to the mirrors reflectivity [25]. This approach is based on that introduced by Noginov et al for RLs [26], which has been describing quite well the experimental observations [27] including parametric effects [28,29].…”

Section: Theoretical Considerations and Numerical Resultsmentioning

confidence: 99%

Gain clamping in random lasers

Santos¹,

Silva²,

Silva³

et al. 2021

Laser Phys. Lett.

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Random lasers (RLs) rely on obtaining laser emission in disordered systems with gain. The characterization of the RLs are performed by the observations of bandwidth narrowing, increasing in the slope efficiency, time shortening of the upper level of the RL transition, intensity and spectral fluctuations, and even photon statistics transitions when increasing the optical gain. However, the gain clamping, which is a known phenomenon in conventional lasers, i.e. lasers with well-defined cavity, was never investigated in RLs. Here we realize an experimental-theoretical investigation of the gain clamping in RLs, and demonstrate that it can be used as an alternative tool to characterize the transition from spontaneous emission to the RL regime.

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Section: Theoretical Considerations and Numerical Resultsmentioning

confidence: 99%

Gain clamping in random lasers

Santos¹,

Silva²,

Silva³

et al. 2021

Laser Phys. Lett.

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show abstract

“…In [41], a plot of the interspike intervals and the interevent intervals distributions indicates that neurons and neural network activities are characterized by a non-Gaussian heavy-tail interval distribution, thereby providing a solid reason as to why it makes sense to consider Lévy noise in the study of neural systems. Lévy noise has also been extensively used to model many other complex systems, including lasers [42], quantum dots [43], cardiac dynamics [38], molecular motor [44], economics [45,46], and social systems [47], where changes are often abrupt [48,49]. Furthermore, several studies on stochastic systems have departed from Gaussian to Lévy processes and compared their effects.…”

Section: Introductionmentioning

confidence: 99%

Lévy noise-induced self-induced stochastic resonance in a memristive neuron

Yamakou

Tran

2021

Nonlinear Dyn

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All previous studies on self-induced stochastic resonance (SISR) in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the deterministic timescale and mean escape timescale of an $$\alpha $$ α -stable Lévy process (with value increasing as a power $$\sigma ^{-\alpha }$$ σ - α of the noise amplitude $$\sigma $$ σ , unlike the mean escape timescale of a Gaussian process which increases as in Kramers’ law) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could guide hardware implementations of neuromorphic silicon circuits operating in noisy regimes.

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“…In [69], a plot of interspike intervals and interevent intervals distributions indicates that neurons and neural network activities are characterized by a non-Gaussian heavy-tail interval distribution, thereby providing a solid reason as to why it makes sense to consider Lévy noise in the study of neural systems. Lévy noise has also been extensively used to model many other complex systems, including lasers [66], quantum dots [55], cardiac dynamics [60], molecular motor [41], economics [74,2], and social systems [63], where changes are often abrupt [14,87].…”

Section: Introductionmentioning

confidence: 99%

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

Yamakou

Tran

2021

Preprint

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Self-induced stochastic resonance (SISR) is a subtle resonance mechanism requiring a nontrivial scaling limit between the stochastic and the deterministic timescales of an excitable system, leading to the emergence of a limit cycle behavior which is absent without noise. All previous studies on SISR in neural systems have only considered the idealized Gaussian white noise. Moreover, these studies have ignored one electrophysiological aspect of the nerve cell: its memristive properties. In this paper, first, we show that in the excitable regime, the asymptotic matching of the mean escape timescale of an α-stable Lévy process (with value increasing as a power σ-α of the noise amplitude σ, unlike the mean escape timescale of a Gaussian process with the value increasing as in Kramers' law) and the deterministic timescale (controlled by the singular parameter) can also induce a strong SISR. In addition, it is shown that the degree of SISR induced by Lévy noise is not always higher than that of Gaussian noise. Second, we show that, for both types of noises, the two memristive properties of the neuron have opposite effects on the degree of SISR: the stronger the feedback gain parameter that controls the modulation of the membrane potential with the magnetic flux and the weaker the feedback gain parameter that controls the saturation of the magnetic flux, the higher the degree of SISR. Finally, we show that, for both types of noises, the degree of SISR in the memristive neuron is always higher than in the non-memristive neuron. Our results could find applications in designing neuromorphic circuits operating in noisy regimes.

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Lévy flights for light in ordered lasers

Cited by 15 publications

References 32 publications

Gain clamping in random lasers

Gain clamping in random lasers

Lévy noise-induced self-induced stochastic resonance in a memristive neuron

Lévy Noise-induced Self-induced Stochastic Resonance in a Memristive Neuron

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