Periodic Pulse Train Research Articles

Microwave probing of relaxation oscillations related to terahertz power detection in superconducting hot electron bolometers

Relaxation oscillations related to terahertz (THz) power detection in superconducting niobium nitride hot electron bolometers (HEBs) have been studied using microwaves as a probe. The reflected microwave signal, which is related to the impedance changes of the HEB irradiated by an incident THz signal, can be used to characterize relaxation oscillations. The frequency of relaxation oscillation switching between the superconducting and resistive states increases linearly with incident THz power but nonlinearly with bias voltage or bath temperature. The observed strong periodic pulse trains of relaxation oscillations have a maximum duty cycle of ∼50%. These strong switching pulses indicate that DC Joule heating, THz radiation or thermal energy is absorbed in the bi-stable region of the HEB intermittently. In addition to relaxation oscillations, we also see weaker oscillations when the device is in the resistive state, which we call intrinsic oscillations. These have a constant frequency at the order of 10 kHz which is independent of external stimuli. The weak periodic pulse trains at a constant frequency can be divided into mainly two types—one is the pulse train with a small duty cycle and the other is the quasi-square wave. Measurement of these oscillations in HEBs has some practical applications. Digital THz power measurement with frequencies below and above the gap frequency can be made based on the linearity between relaxation oscillation frequency and incident THz power. The relaxation oscillation frequency can be used to estimate the maximum speed of a THz direct detection system especially for a multi-pixel HEB array. In particular, extra noise induced by relaxation oscillations and intrinsic oscillations can be determined for the HEB operating as a THz direct detector.

On Mode-Spacing Division of a Frequency Comb by Temporal Phase Modulation

Mode-spacing division of a phase-coherent optical frequency comb is numerically investigated using temporal phase modulation of a periodic optical pulse train. Different schemes, including Talbot and random phase modulations, are investigated and compared, i.e., concerning the tunability of mode-spacing division factors and the robustness to potential practical deviations on the modulation phase profiles. Talbot phase modulation provides a versatile technique for mode-spacing division of a frequency comb; however, the approach is found to be sensitive to phase deviations under certain design parameters. The results show the difficulty in obtaining experimentally the frequency shift by half mode spacing that is predicted by theory for odd division factors. In contrast, generalized random phase modulation methods, proposed here for the first time, utilize random 0-π or multilevel phase profiles to provide interesting alternative methods for implementation of mode-spacing division of a frequency comb. The use of random 0-π phase modulation simplifies the practical implementation of the scheme as it requires inducing only 0 and π phase shifts. The use of random multilevel phase modulation generalizes the approach by using multiple levels of random phase shifts. Both random phase modulation approaches enable successful mode-spacing division by any designed division factor, and they show a relatively lower sensitivity to phase deviations in the modulation functions.

Investigation of Architectures for Models of Neural Responses to Electrical Brain Stimulation.

Electrical brain stimulation is used clinically to target pathological regions of the brain for treatment of diseases, such as Parkinson's disease, epilepsy and depression. Conventional treatments involve chronic implants that disrupt activity through a fixed periodic train of pulses or bursts of pulses applied to the affected region. However, stimulating one region of the brain necessarily affects other structurally and/or functionally connected areas. Understanding how connected regions of the brain are affected by stimulation at the implant site could improve treatment efficacy by informing optimal placement and stimulation patterns. In this study, we build predictive input-output models from intracranial recordings obtained from 10 epilepsy patients implanted with electrodes. Specific contacts within each subject were electrically stimulated (inputs), and evoked responses were simultaneously captured from all contacts (outputs). From these data, we constructed and compared four different dynamical models that contain causal linear and nonlinear components. All model architectures successfully predicted evoked responses to stimulation with single pulses and sequences of pulses. Results suggest that a linear time-invariant model in series with a quadratic non-linearity best captures the relationship between stimulation amplitudes and evoked responses.

Hong-Ou-Mandel heat noise in the quantum Hall regime

We investigate heat current fluctuations induced by a periodic train of Lorentzian-shaped pulses, carrying an integer number of electronic charges, in a Hong-Ou-Mandel interferometer implemented in a quantum Hall bar in the Laughlin sequence. We demonstrate that the noise in this collisional experiment cannot be reproduced in a setup with a single drive, in contrast to what is observed in the charge noise case. Nevertheless, the simultaneous collision of two identical levitons always leads to a total suppression even for the Hong-Ou-Mandel heat noise at all filling factors, despite the presence of emergent anyonic quasi-particle excitations in the fractional regime. Interestingly, the strong correlations characterizing the fractional phase are responsible for a remarkable oscillating pattern in the HOM heat noise, which is completely absent in the integer case. These oscillations can be related to the recently predicted crystallization of levitons in the fractional quantum Hall regime.

Synchronization of pancreatic islets by periodic or non-periodic muscarinic agonist pulse trains.

Pulsatile insulin secretion into the portal vein from the many pancreatic islets of Langerhans is critical for efficient glucose homeostasis. The islets are themselves endogenous oscillators, but since they are not physically coupled it is not obvious how their oscillations are synchronized across the pancreas. It has been proposed that synchronization of islets is achieved through periodic activity of intrapancreatic ganglia, and indeed there are data supporting this proposal. Postganglionic nerves are cholinergic, and their product, acetylcholine, can influence islet β-cells through actions on M3 muscarinic receptors which are coupled to Gq type G-proteins. In addition, the neurons secrete several peptide hormones that act on β-cell receptors. The data supporting synchronization via intrapancreatic ganglia are, however, limited. In particular, it has not been shown that trains of muscarinic pulses are effective at synchronizing islets in vitro. Also, if as has been suggested, there is a ganglionic pacemaker driving islets to a preferred frequency, no neural circuitry for this pacemaker has been identified. In this study, both points are addressed using a microfluidic system that allows for the pulsed application of the muscarinic agonist carbachol. We find that murine islets are entrained and synchronized over a wide range of frequencies when the carbachol pulsing is periodic, adding support to the hypothesis that ganglia can synchronize islets in vivo. We also find that islet synchronization is very effective even if the carbachol pulses are applied at random times. This suggests that a neural pacemaker is not needed; all that is required is that islets receive occasional coordinated input from postganglionic neurons. The endogenous rhythmic activity of the islets then sets the frequency of the islet population rhythm, while the input from ganglia acts only to keep the islet oscillators in phase.

Evolution of Amplitude Fluctuation in Fractional Temporal Talbot Effect

Temporal Talbot phenomena occur when a periodic optical pulse train propagates through a dispersive medium with a proper dispersion amount, which includes integer and fractional orders depending on the dispersion amount. The fractional temporal Talbot (FTT) effect has attracted great interest because of its potentials in repetition rate multiplication of optical pulse train and passive amplification of short pulses. In this paper, we investigate the evolution of amplitude fluctuation in FTT systems from the viewpoint of the frequency-dependent fading of pulse train envelope. It is found that the envelope frequency response of FTT is different from that of integer orders since there is waveform-to-waveform phase profile in the output pulse train in FTT systems. The noise reduction phenomenon in FTT systems is analyzed based on the derived frequency response. A closed-form expression of the noise reduction ratio is derived for the first time based on the analysis of the noise power spectral density. With the given model, we are able to predict the fluctuation suppression effect in FTT systems more precisely.

Improved Algorithm of Radar Pulse Repetition Interval Deinterleaving Based on Pulse Correlation

In the electromagnetic space, a single channel radar receiver will often intercept several periodic pulse trains radiating from the surrounding emitters simultaneously. The aim of radar pulse deinterleaving is to sort out the pulses coming from different emitters. Most traditional pulse repetition interval (PRI) deinterleaving methods are easy to sort out the pulses with small PRI fluctuations but difficult in dealing with relatively bigger fluctuation or staggered PRIs. In addition, this searching procedure can easily cause pulse omission phenomenon and even generate false pulses. In this paper, we propose an improved histogram method for PRI deinterleaving based on pulse correlation to overcome the above-mentioned shortcomings. After calculating the multi-level time difference histogram, we introduce the mean filter and interquartile range algorithm to optimize the estimated PRI values. Our method extracts the pulse pairs based on pulse correlation directly instead of searching for the pulses and then determines whether the PRI is staggered or not. The experiments on simulation data show that our method can achieve better performance on both the pulse trains of jittered PRIs and the staggered PRIs.

Cavity-assisted modulation instability lasing of a fiber ring laser

We report on the experimental evidences of cavity-assisted modulation instability (CAMI) lasing of fiber lasers. We first reviewed the theory of CAMI. We then presented experimental evidences of CAMI lasing of fiber lasers with either an anomalous or a normal dispersion cavity. It is shown that even in a fiber laser without any mode-locking element in cavity, if the orientation of the intracavity polarization controller is changed, a CW emission could be suddenly converted into a stable periodic pulse train emission. Moreover, the repetition rate of the pulse train can be adjusted over a wide range from the fundamental cavity repetition frequency to hundreds of GHz by changing the cavity detuning. We point out that the CAMI lasing should be a general effect of lasers with a nonlinear cavity.

Variational Renormalization Group for Dissipative Spin-Cavity Systems: Periodic Pulses of Nonclassical Photons from Mesoscopic Spin Ensembles.

Mesoscopic spin ensembles coupled to a cavity offer the exciting prospect of observing complex nonclassical phenomena that pool the microscopic features from a few spins with those of macroscopic spin ensembles. Here, we demonstrate how the collective interactions in an ensemble of as many as a hundred spins can be harnessed to obtain a periodic pulse train of nonclassical light. To unravel the full quantum dynamics and photon statistics, we develop a time-adaptive variational renormalization group method that accurately captures the underlying Lindbladian dynamics of the mesoscopic spin-cavity system.

Improved Neural Coding of ITD with Bilateral Cochlear Implants by Introducing Short Inter-pulse Intervals.

Bilateral cochlear implant (CI) users have poor perceptual sensitivity to interaural time differences (ITDs), which limits their ability to localize sounds and understand speech in noisy environments. This is especially true for high-rate (> 300pps) periodic pulse trains, which are used as carriers in CI processors. Here, we investigate a novel stimulation strategy in which extra pulses are added to high-rate periodic pulse trains to introduce short inter-pulse intervals (SIPIs). We hypothesized that SIPIs can improve neural ITD sensitivity similarly to the effect observed by randomly jittering IPIs (Hancock et al., J. Neurophysiol. 108:714-28, 2012). To test this hypothesis, we measured ITD sensitivity of single units in the inferior colliculus (IC) of unanesthetized rabbits with bilateral CIs. Introducing SIPIs into high-rate pulse trains significantly increased firing rates for ~ 60% of IC neurons, and the extra spikes tended to be synchronized to the SIPIs. The additional firings produced by SIPIs uncovered latent ITD sensitivity that was comparable to that observed with low-rate pulse trains. In some neurons, high spontaneous firing rates masked the ITD sensitivity introduced by SIPIs. ITD sensitivity in these neurons could be revealed by emphasizing stimulus-synchronized spikes with a coincidence detection analysis. Overall, these results with SIPIs are consistent with the effects observed previously with jittered pulse trains, with the added benefit of retaining control over the timing and number of SIPIs. A novel CI processing strategy could incorporate SIPIs by inserting them at selected times to high-rate pulse train carriers. Such a strategy could potentially improve ITD perception without degrading speech intelligibility and thereby improve outcomes for bilateral CI users.

Crystallization of levitons in the fractional quantum Hall regime

Using a periodic train of Lorentzian voltage pulses, which generates soliton-like electronic excitations called Levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in non-linear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in nowadays electron quantum optics experiments.

Modulated wave formation in myocardial cells under electromagnetic radiation

We exclusively analyze the onset and condition of formation of modulated waves in a diffusive FitzHugh–Nagumo model for myocardial cell excitations. The cells are connected through gap junction coupling. An additive magnetic flux variable is used to describe the effect of electromagnetic induction, while electromagnetic radiation is imposed on the magnetic flux variable as a periodic forcing. We used the discrete multiple scale expansion and obtained, from the model equations, a single differential-difference amplitude nonlinear equation. We performed the linear stability analysis of this equation and found that instability features are importantly influenced by the induced electromagnetic gain. We present the unstable and stable regions of modulational instability (MI). The resulting analytic predictions are confirmed by numerical experiments of the generic equations. The results reveal that due to MI, an initial steady state that consisted of a plane wave with low amplitude evolves into a modulated localized wave patterns, soliton-like in shape, with features of synchronization. Furthermore, the formation of periodic pulse train with breathing motion presents a disappearing pattern in the presence of electromagnetic radiation. This could provide guidance and better understanding of sudden heart failure exposed to heavily electromagnetic radiation.

Self-Induced Faraday Instability Laser.

We predict the onset of self-induced parametric or Faraday instabilities in a laser, spontaneously caused by the presence of pump depletion, which leads to a periodic gain landscape for light propagating in the cavity. As a result of the instability, continuous wave oscillation becomes unstable even in the normal dispersion regime of the cavity, and a periodic train of pulses with ultrahigh repetition rate is generated. Application to the case of Raman fiber lasers is described, in good quantitative agreement between our conceptual analysis and numerical modeling.

Nonlinear periodic wavetrains in thin liquid films falling on a uniformly heated horizontal plate

A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e., rivulet structures) to modulated nonlinear wavetrain structures. Some of these structures have been observed experimentally; however, conditions under which they form are still not well understood. In this work, we examine profiles of nonlinear wave patterns formed by a thin liquid film falling on a uniformly heated horizontal plate. For this purpose, the Benney model is considered assuming a uniform temperature distribution along the film propagation on the horizontal surface. It is shown that for strong surface tension but a relatively small Biot number, spatially localized periodic-wave structures can be analytically obtained by solving the governing equation under appropriate conditions. In the regime of weak nonlinearity, a multiple-scale expansion combined with the reductive perturbation method leads to a complex Ginzburg-Landau equation: the solutions of which are modulated periodic pulse trains which amplitude and width and period are expressed in terms of characteristic parameters of the model.

Optomechanical frequency combs

We study the formation of frequency combs in a single-mode optomechanical cavity. The comb is composed of equidistant spectral lines centered at the pump laser frequency and located at different harmonics of the mechanical resonator. We investigate the classical nonlinear dynamics of such system and find analytically the onset of parametric instability resulting in the breakdown of a stationary continuous wave intracavity field into a periodic train of pulses, which in the Fourier domain gives rise to a broadband frequency comb. Different dynamical regimes, including a stationary state, frequency comb generation and chaos, and their dependence on the system parameters, are studied both analytically and numerically. Interestingly, the comb generation is found to be more robust in the poor cavity limit, where optical loss is equal or larger than the mechanical resonance frequency. Our results show that optomechanical resonators open exciting opportunities for microwave photonics as compact and robust sources of frequency combs with megahertz line spacing.

Resonant optical pulses on a continuous-wave background in two-level active media

We present exact N-soliton optical pulses riding on a continuous-wave (c.w.) beam that propagate through and interact with a two-level active optical medium. Their representation is derived via an appropriate generalization of the inverse scattering transform for the corresponding Maxwell-Bloch equations. We describe the single-soliton solutions in detail and classify them into several distinct families. In addition to the analogues of traveling-wave soliton pulses that arise in the absence of a c.w. beam, we obtain breather-like structures, periodic pulse-trains and rogue-wave–type (i.e., rational) pulses, whose existence is directly due to the presence of the c.w. beam. These soliton solutions are the analogues for Maxwell-Bloch systems of the four classical solution types of the focusing nonlinear Schrödinger equation with non-zero background, although the physical behavior of the corresponding solutions is quite different.

Pseudorandom dynamics of frequency combs in free-running quantum cascade lasers

Recent research has shown that free-running quantum cascade lasers are capable of producing frequency combs in midinfrared and THz regions of the spectrum. Unlike familiar frequency combs originating from mode-locked lasers, these do not require any additional optical elements inside the cavity and have temporal characteristics that are dramatically different from the periodic pulse train of conventional combs. Frequency combs from quantum cascade lasers are characterized by the absence of sharp pulses and strong frequency modulation, periodic with the cavity round trip time but lacking any periodicity within that period. To explicate for this seemingly perplexing behavior, we develop a model of the gain medium using optical Bloch equations that account for hole burning in spectral, spatial, and temporal domains. With this model, we confirm that the most efficient mode of operation of a free-running quantum cascade laser is indeed a pseudorandom frequency-modulated field with nearly constant intensity. We show that the optimum modulation period is commensurate with the gain recovery time of the laser medium and the optimum modulation amplitude is comparable to the gain bandwidth, behavior that has been observed in the experiments.

Storage and retrieval of time-entangled soliton trains in a three-level atom system coupled to an optical cavity

The storage and subsequent retrieval of coherent pulse trains in the quantum memory (i.e. cavity-dark state) of three-level Λ atoms, are considered for an optical medium in which adiabatic photon transfer occurs under the condition of quantum impedance matching. The underlying mechanism is based on intracavity Electromagnetically-Induced Transparency, by which properties of a cavity filled with three-level Λ-type atoms are manipulated by an external control field. Under the impedance matching condition, we derive analytic expressions that suggest a complete transfer of an input field into the cavity-dark state by varying the mixing angle in a specific way, and its subsequent retrieval at a desired time. We illustrate the scheme by demonstrating the complete transfer and retrieval of a Gaussian, a single hyperbolic-secant and a periodic train of time-entangled hyperbolic-secant input photon pulses in the atom–cavity system. For the time-entangled hyperbolic-secant input field, a total controllability of the periodic evolution of the dark state population is made possible by changing the Rabi frequency of the classical driving field, thus allowing to alternately store and retrieve high-intensity photons from the optically dense Electromagnetically-Induced transparent medium. Such multiplexed photon states, which are expected to allow sharing quantum information among many users, are currently of very high demand for applications in long-distance and multiplexed quantum communication.

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow.

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa etal. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

Asymptotic behavior of a rotational population distribution in a molecular quantum-kicked rotor with ideal quantum resonance

We performed a mathematical analysis of the time-dependent dynamics of a quantum-kicked rotor implemented in a diatomic molecule under the condition of ideal quantum resonance. We examined a model system featuring a diatomic molecule in a periodic train of terahertz pulses, regarding the molecule as a rigid rotor with the state-dependent transition moment and including the effect of the magnetic quantum number M. We derived the explicit expression for the asymptotic distribution of a rotational population by making the transition matrix correspondent with a sequence of ultraspherical polynomials. The mathematical results obtained were validated by numerical simulations.