Do Optomechanical Metasurfaces Run Out of Time?

Artificially structured metasurfaces make use of specific configurations of subwavelength resonators to efficiently manipulate electromagnetic waves. Additionally, optomechanical metasurfaces have the desired property that their actual configuration may be tuned by adjusting the power of a pump beam, as resonators move to balance pump-induced electromagnetic forces with forces due to elastic filaments or substrates. Although the reconfiguration time of optomechanical metasurfaces crucially determines their performance, the transient dynamics of unit cells from one equilibrium state to another is not understood. Here, we make use of tools from nonlinear dynamics to analyze the transient dynamics of generic optomechanical metasurfaces based on a damped-resonator model with one configuration parameter. We show that the reconfiguration time of optomechanical metasurfaces is not only limited by the elastic properties of the unit cell but also by the nonlinear dependence of equilibrium states on the pump power. For example, when switching is enabled by hysteresis phenomena, the reconfiguration time is seen to increase by over an order of magnitude. To illustrate these results, we analyze the nonlinear dynamics of a bilayer cross-wire metasurface whose optical activity is tuned by an electromagnetic torque. Moreover, we provide a lower bound for the configuration time of generic optomechanical metasurfaces. This lower bound shows that optomechanical metasurfaces cannot be faster than state-of-the-art switches at reasonable powers, even at optical frequencies.

Reducing the phase sensitivity of laser-based optical reservoir computing systems.

Optical implementations of reservoir computing systems are very promising because of their high processing speeds and the possibility to process several tasks in parallel. These systems can be implemented using semiconductor lasers subject to optical delayed feedback and optical injection. While the amount of the feedback/injection can be easily controlled, it is much more difficult to control the optical feedback/injection phase. We present extensive numerical investigations of the influence of the feedback/injection phases on laser-based reservoir computing systems with feedback. We show that a change in the phase can lead to a strong reduction in the reservoir computing system performance. We introduce a new readout layer design that -at least for some tasks- reduces this sensitivity to changes in the phase. It consists in optimizing the readout weights from a coherent combination of the reservoir's readout signal and its delayed version rather than only from the reservoir's readout signal as is usually done.

Relaxation and square-wave oscillations in a semiconductor laser with polarization rotated optical feedback.

The rate equations for a laser with a polarization rotated optical feedback are investigated both numerically and analytically. The frequency detuning between the polarization modes is now taken into account and we review all earlier studies in order to motivate the range of values of the fixed parameters. We find that two basic Hopf bifurcations leading to either stable sustained relaxation or square-wave oscillations appear in the detuning versus feedback rate diagram. We also identify two key parameters describing the differences between the total gains of the two polarization modes and discuss their effects on the periodic square-waves.

Fast photonic information processing using semiconductor lasers with delayed optical feedback: role of phase dynamics.

Semiconductor lasers subject to delayed optical feedback have recently shown great potential in solving computationally hard tasks. By optically implementing a neuro-inspired computational scheme, called reservoir computing, based on the transient response to optical data injection, high processing speeds have been demonstrated. While previous efforts have focused on signal bandwidths limited by the semiconductor laser's relaxation oscillation frequency, we demonstrate numerically that the much faster phase response makes significantly higher processing speeds attainable. Moreover, this also leads to shorter external cavity lengths facilitating future on-chip implementations. We numerically benchmark our system on a chaotic time-series prediction task considering two different feedback configurations. The results show that a prediction error below 4% can be obtained when the data is processed at 0.25 GSamples/s. In addition, our insight into the phase dynamics of optical injection in a semiconductor laser also provides a clear understanding of the system performance at different pump current levels, even below solitary laser threshold. Considering spontaneous emission noise and noise in the readout layer, we obtain good prediction performance at fast processing speeds for realistic values of the noise strength.

All-optical controlled switching between time-periodic square waves in diode lasers with delayed feedback.

We investigate the square-wave (SW) self-modulation output of an edge-emitting diode laser subject to polarization rotated optical feedback in detail, both experimentally and theoretically. Our experimental results show that the 2τ-periodic SW, where τ is the delay of the feedback, coexists with other SW oscillations of shorter periods. We have found that these new SWs are specific harmonics of the fundamental one and their periods are P(n)≃2τ/(1+2n), where n is an integer. Numerical simulations and analytical studies of laser rate equations confirm the multistability of SW solutions. By adding a weak conventional optical feedback, we show that the switching between the different periodic SWs can be easily controlled. The delay of this feedback control is the key parameter determining the harmonic that is stabilized. Numerical simulations corroborate the effectiveness of our experimental control scheme.

Fast phase response and chaos bandwidth enhancement in semiconductor lasers subject to optical feedback and injection.

We numerically show the quantitative relation between the chaos bandwidth enhancement and fast phase dynamics in semiconductor lasers with optical feedback and optical injection. The injection increases the coupling between the intensity and the phase leading to a competition between the relaxation oscillation (RO) frequency and the intrinsic response frequency of the phase. For large feedback strengths, it is found that the chaos bandwidth is determined by the intrinsic phase response frequency. For smaller feedback strengths, the system is not chaotic and its bandwidth is determined by the RO frequency.

Controlling Cherenkov radiation with transformation-optical metamaterials.

In high energy physics, unknown particles are identified by determining their mass from the Cherenkov radiation cone that is emitted as they pass through the detector apparatus. However, at higher particle momentum, the angle of the Cherenkov cone saturates to a value independent of the mass of the generating particle, making it difficult to effectively distinguish between different particles. Here, we show how the geometric formalism of transformation optics can be applied to describe the Cherenkov cone in an arbitrary anisotropic medium. On the basis of these results, we propose a specific anisotropic metamaterial to control Cherenkov radiation, leading to enhanced sensitivity for particle identification at higher momentum.

A general model for toxin-antitoxin module dynamics can explain persister cell formation in E. coli.

Toxin-Antitoxin modules are small operons involved in stress response and persister cell formation that encode a "toxin" and its corresponding neutralizing "antitoxin". Regulation of these modules involves a complex mechanism known as conditional cooperativity, which is supposed to prevent unwanted toxin activation. Here we develop mathematical models for their regulation, based on published molecular and structural data, and parameterized using experimental data for F-plasmid ccdAB, bacteriophage P1 phd/doc and E. coli relBE. We show that the level of free toxin in the cell is mainly controlled through toxin sequestration in toxin-antitoxin complexes of various stoichiometry rather than by gene regulation. If the toxin translation rate exceeds twice the antitoxin translation rate, toxins accumulate in all cells. Conditional cooperativity and increasing the number of binding sites on the operator serves to reduce the metabolic burden of the cell by reducing the total amounts of proteins produced. Combining conditional cooperativity and bridging of antitoxins by toxins when bound to their operator sites allows creation of persister cells through rare, extreme stochastic spikes in the free toxin level. The amplitude of these spikes determines the duration of the persister state. Finally, increases in the antitoxin degradation rate and decreases in the bacterial growth rate cause a rise in the amount of persisters during nutritional stress.

Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback.

We report on an integrated approach to obtain multiwavelength emission from semiconductor ring lasers with filtered optical feedback. The filtered feedback is realized on-chip employing two arrayed-waveguide gratings to split/recombine light into different wavelength channels. Through experimental observations and numerical simulations, we find that the effective gain of the different modes is the key parameter which has to be balanced in order to achieve multiwavelength emission. This can be achieved by tuning the injection current in each amplifier.

Square-wave oscillations in semiconductor ring lasers with delayed optical feedback.

We analyze experimentally and theoretically the effects of delayed optical cross-feedback in semiconductor ring lasers. We show that under appropriate conditions, feeding of only one directional mode back into the counter-propagating mode leads to square-wave oscillations. In this regime, the laser switches regularly between the two counter-propagating modes with a period close to twice the roundtrip time in the external feedback loop. We find that these oscillations are robust and appear for a wide range of parameters as long as a small asymmetry in the linear coupling between both modes is present. We show that by increasing the feedback strength or the injection current, the square-wave oscillations gradually disappear. Due to noise, mode-hopping between stable lasing in one directional mode and square wave oscillations is observed in this transition region.

Fast random bits generation based on a single chaotic semiconductor ring laser.

The use of the postprocessing method consisting of bitwise Exclusive-OR and least significant bits extraction to generate random bit sequences typically requires two distinct chaotic outputs. While the two signals are, in general, generated using two separated devices, e.g. two Fabry-Perot lasers, a single semiconductor ring laser can be used as an alternative due to its circular symmetry which facilitates lasing in two counterpropagating mode directions. We consider a chaotic semiconductor ring laser and investigate both numerically and experimentally its characteristics for fast random bit generation. In particular, we show that by sampling each directional mode's output signal using a 8-bit analog-digital converter and through Exclusive-OR operation applied to the two resulting signals (after throwing away 4 most significant bits), we can achieve fast random bit-streams with a bit rate 4 × 10 = 40 Gbit/s, passing the statistical randomness tests. To optimize the system performance, we also study the dependence of randomness on the main system parameters and on noise.

Loss of time-delay signature in chaotic semiconductor ring lasers.

We investigate the possibility of concealing the time-delay signatures in semiconductor ring lasers (SRLs) with external feedback. Through the autocorrelation and delayed mutual information, we report different scenarios leading to simultaneous time-delay concealment both in the intensity and the phase dynamics of such systems. In particular, the fact that such delay signatures can be eliminated in a SRL subject to short feedback constitutes a step toward the possibility of implementing secure communication schemes and random number generators on chip.

Characterization of a low-speckle laser line generator.

The goal of our investigation is to design a low-speckle laser line generator based on partial spatially coherent laser light. Low speckle is achieved by exploiting a regime of strongly reduced spatial coherence of a broad-area vertical-cavity surface-emitting laser, which is used as the line generator's light source. A comparative experimental study of different optical configurations is conducted, leading to the design of an optimal optical system. The results of our study are also valid for other sources of partial spatially coherent emission.

Optical injection in semiconductor ring lasers: backfire dynamics.

We report on directional mode switching in semiconductor ring lasers through optical injection co-propagating with the lasing mode. The understanding of this novel feature in ring lasers is based on the particular structure of a two-dimensional asymptotic phase space. Our theoretical results are verified numerically and experimentally.

Monostable multivibrators as novel artificial neurons.

Retriggerable and non-retriggerable monostable multivibrators are simple timers with a single characteristic, their period. Motivated by the fact that monostable multivibrators are implementable in large quantities as counters in digital programmable hardware, we set out to investigate their applicability as building blocks of artificial neural networks. We derive the nonlinear input-output firing rate relations for single multivibrator neurons as well as the equilibrium firing rate of large recurrent networks. We show that in rate-encoded monostable multivibrators networks the synaptic weights are tunable as the period ratio of connected units, and thus reconfigurable at run time in a counter-based digital implementation. This is illustrated with the task of handwritten digit recognition. Furthermore, we show in a task-independent manner that networks of monostable multivibrators are capable of nonlinear separation, when operating directly on pulse streams. Our research implies that pulse-coupled neural networks with excitable neurons showing a delayed response can perform computations even when working solely with suprathreshold pulses.

Bistability in a system of two species interacting through mutualism as well as competition: Chemostat vs. Lotka-Volterra equations.

We theoretically study the dynamics of two interacting microbial species in the chemostat. These species are competitors for a common resource, as well as mutualists due to cross-feeding. In line with previous studies (Assaneo, et al., 2013; Holland, et al., 2010; Iwata, et al., 2011), we demonstrate that this system has a rich repertoire of dynamical behavior, including bistability. Standard Lotka-Volterra equations are not capable to describe this particular system, as these account for only one type of interaction (mutualistic or competitive). We show here that the different steady state solutions can be well captured by an extended Lotka-Volterra model, which better describe the density-dependent interaction (mutualism at low density and competition at high density). This two-variable model provides a more intuitive description of the dynamical behavior than the chemostat equations.

Integrated culturing, modeling and transcriptomics uncovers complex interactions and emergent behavior in a three-species synthetic gut community.

The composition of the human gut microbiome is well resolved, but predictive understanding of its dynamics is still lacking. Here, we followed a bottom-up strategy to explore human gut community dynamics: we established a synthetic community composed of three representative human gut isolates (Roseburia intestinalis L1-82, Faecalibacterium prausnitzii A2-165 and Blautia hydrogenotrophica S5a33) and explored their interactions under well-controlled conditions in vitro. Systematic mono- and pair-wise fermentation experiments confirmed competition for fructose and cross-feeding of formate. We quantified with a mechanistic model how well tri-culture dynamics was predicted from mono-culture data. With the model as reference, we demonstrated that strains grown in co-culture behaved differently than those in mono-culture and confirmed their altered behavior at the transcriptional level. In addition, we showed with replicate tri-cultures and simulations that dominance in tri-culture sensitively depends on the initial conditions. Our work has important implications for gut microbial community modeling as well as for ecological interaction detection from batch cultures.

Computational Methods to Model Persistence.

Bacterial persister cells are dormant cells, tolerant to multiple antibiotics, that are involved in several chronic infections. Toxin-antitoxin modules play a significant role in the generation of such persister cells. Toxin-antitoxin modules are small genetic elements, omnipresent in the genomes of bacteria, which code for an intracellular toxin and its neutralizing antitoxin. In the past decade, mathematical modeling has become an important tool to study the regulation of toxin-antitoxin modules and their relation to the emergence of persister cells. Here, we provide an overview of several numerical methods to simulate toxin-antitoxin modules. We cover both deterministic modeling using ordinary differential equations and stochastic modeling using stochastic differential equations and the Gillespie method. Several characteristics of toxin-antitoxin modules such as protein production and degradation, negative autoregulation through DNA binding, toxin-antitoxin complex formation and conditional cooperativity are gradually integrated in these models. Finally, by including growth rate modulation, we link toxin-antitoxin module expression to the generation of persister cells.

Nonlinear lattice model for spatially guided solitons in nonlinear photonic crystals.

Numerical simulations have shown the existence of transversely localized guided modes in nonlinear two-dimensional photonic crystals. These soliton-like Bloch waves induce their own waveguide in a photonic crystal without the presence of a linear defect. By applying a Green's function method which is limited to within a strip perpendicular to the propagation direction, we are able to describe these Bloch modes by a nonlinear lattice model that includes the long-range site-to-site interaction between the scattered fields and the non-local nonlinear response of the photonic crystal. The advantages of this semi-analytical approach are discussed and a comparison with a rigorous numerical analysis is given in different configurations. Both monoatomic and diatomic nonlinear photonic crystals are considered.

Ghost stochastic resonance in vertical-cavity surface-emitting lasers: experiment and theory.

We study the polarization response of a vertical-cavity surface-emitting laser, driven simultaneously by noise and two (or more) weak periodic signals. In the bistable regime, we observe experimentally the occurrence of stochastic resonance at a frequency that is absent in the input driving signal. The presence of this so-called ghost resonance is confirmed theoretically.