Complexity in pulsed nonlinear laser systems interrogated by permutation entropy

Toomey, J. P.; Kane, D. M.; Ackemann, T.

doi:10.1364/oe.22.017840

Cited by 19 publications

(7 citation statements)

References 23 publications

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“…Situations of single-mode operation in the external cavity (corresponding to cw spatial solitons [53]) and multi-mode operation can be realized. Some self-pulsing was found in preliminary investigations [55,57,58]. The measurements reported in this letter demonstrate longterm mode-locking of solitons with an excellent phase coherence.…”

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confidence: 66%

Observation of Mode-Locked Spatial Laser Solitons

et al. 2017

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A stable nonlinear wave packet, self-localized in all three dimensions, is an intriguing and much sought after object in nonlinear science in general and in nonlinear photonics in particular. We report on the experimental observation of mode-locked spatial laser solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback from an external cavity. These spontaneously emerging and long-term stable spatiotemporal structures have a pulse length shorter than the cavity round-trip time and may pave the way to completely independent cavity light bullets. DOI: 10.1103/PhysRevLett.118.044102 Wave packets in general, and light wave packets in particular, do not remain confined to small regions in space or time, but have the natural tendency to broaden. In space this is due to diffraction and in time this is due to dispersion, at least in a medium. Although localization can be achieved by confining potentials (e.g., optical fibers and photonic crystals in optics), it was always the vision of researchers to obtain confinement by self-action. This is why the concept of solitary waves, or, more loosely speaking, of solitons, received a lot of attention over the last decades. A soliton is a wave packet in which the tendency to broaden is balanced by nonlinearities. Spatial and temporal solitons in one or two dimensions are known in many fields of science [1][2][3][4][5][6][7]. There was also early interest in three-dimensional (3D) self-localization, not least as a model for elementary particles [8]. However, early results [8] were discouraging as they indicated that stationary 3D localized states are not stable in a broad class of nonlinear wave equations. Significant interest continued in the theoretical and mathematical literature (e.g., Refs. [9][10][11][12][13][14][15]), but to our knowledge there is only evidence for 3D self-organized periodic patterns [16], but not for 3D self-localization.In optics, spatiotemporal localization of light, i.e., a "bullet" of light being confined in all three spatial dimensions (and time, because it is propagating), was considered as early as 1990 in the framework of a 3D nonlinear Schrödinger equation (NLSE) [17], but realized to be unstable due to the well-known blow-up experienced for cubic nonlinearities in more than one dimension [18,19]. There were several proposals of how to stabilize multidimensional solitons [19][20][21][22][23][24][25][26][27][28]. Spatiotemporal compression [29][30][31], metastable 2D spatiotemporal solitons [24,32], and metastable discrete light bullets [33,34] were observed in pioneering experiments, the latter constituting the closest realization of a stable light bullet up until now. However, these quasiconservative bullets are only stable over a few characteristic lengths and are long-term unstable due to losses and Raman shifts.This makes it attractive to look for solitons in dissipative optical systems in which losses are compensated by driving [5]. Indeed solitons can exist in two dimensions with a cubic nonlinearity within ...

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confidence: 66%

Observation of Mode-Locked Spatial Laser Solitons

et al. 2017

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“…This methodology is capable of identifying the presence of serial correlations in datasets, and by analyzing the statistics of the different symbols (ordinal patterns, OPs), it can capture subtle variations in temporally correlated data [35][36][37][38]. We unveiled serial correlations between consecutive spikes both, in the unforced laser (without modulation) and in the forced laser (with current modulation).…”

Section: Introductionmentioning

confidence: 99%

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback

Sorrentino¹,

Quintero-Quiroz²,

Aragoneses³

et al. 2015

Opt. Express

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Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

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“…We also compare the laser spikes with the neuronal spikes using OP analysis [38,40]. This is a popular technique to investigate complex signals, which has been extensively used to characterize the dynamical regimes of semiconductor lasers with optical feedback [41,[48][49][50][51][52][53][54][55][56][57]. A main advantage of this methodology is that, in its simplest implementation, it has only one parameter that is the size, D of the pattern, which determines the length of the temporal correlations studied: the D!…”

Section: Introductionmentioning

confidence: 99%

Comparing the dynamics of periodically forced lasers and neurons

2019

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Neuromorphic photonics is a new paradigm for ultra-fast neuro-inspired optical computing that can revolutionize information processing and artificial intelligence systems. To implement practical photonic neural networks is crucial to identify low-cost energy-efficient laser systems that can mimic neuronal activity. Here we study experimentally the spiking dynamics of a semiconductor laser with optical feedback under periodic modulation of the pump current, and compare with the dynamics of a neuron that is simulated with the stochastic FitzHugh-Nagumo model, with an applied periodic signal whose waveform is the same as that used to modulate the laser current. Sinusoidal and pulsedown waveforms are tested. We find that the laser response and the neuronal response to the periodic forcing, quantified in terms of the variation of the spike rate with the amplitude and with the frequency of the forcing signal, is qualitatively similar. We also compare the laser and neuron dynamics using symbolic time series analysis. The characterization of the statistical properties of the relative timing of the spikes in terms of ordinal patterns unveils similarities, and also some differences. Our results indicate that semiconductor lasers with optical feedback can be used as low-cost, energy-efficient photonic neurons, the building blocks of all-optical signal processing systems; however, the length of the external cavity prevents optical feedback on the chip.

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Complexity in pulsed nonlinear laser systems interrogated by permutation entropy

Cited by 19 publications

References 23 publications

Observation of Mode-Locked Spatial Laser Solitons

Observation of Mode-Locked Spatial Laser Solitons

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback

Comparing the dynamics of periodically forced lasers and neurons

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