Periodic Pulse Train Research Articles

Spatiotemporal Bragg gratings forming inside a nonlinear dispersive medium.

We show that a spatiotemporal Bragg grating can be created inside a nonlinear dispersive medium (such as silica fibers) by launching a periodic train of pump pulses that travel as fundamental solitons. We develop a theoretical model and use it to find the band structure of such gratings. We study the interaction of a probe pulse with the Bragg grating, both within and outside of momentum gaps. We also show that a photonic analog of the Anderson localization is possible when a disorder is introduced into a spatiotemporal Bragg grating.

Generation of Soliton Frequency Combs in NEMS.

In this study, we present an innovative approach leveraging combination internal resonances within a NEMS platform to generate mechanical soliton frequency combs (FCs) spanning a broad spectrum. In the time domain, the FCs take the form of a periodic train of narrow pulses, a highly coveted phenomenon within the realm of nonlinear wave-matter interactions. Our method relies on an intricate interaction among multiple vibration modes of a bracket-nanocantilever enabled by the strong nonlinearity of the electrostatic field. Through numerical simulation and experimental validation, we demonstrate that by amplifying the motions of the NEMS with the external electrostatic forcing tuned to excite the superharmonic resonance of order-n of the fundamental mode and exploiting combination internal resonances, we can generate multiple stable localized mechanical wave packets with different lobe sizes embodying soliton states I and II. This represents a significant breakthrough with profound implications for quantum computing and metrology.

Cnoidal waves and their soliton limits in single mode fiber lasers

Cnoidal waves are a type of nonlinear periodic wave solutions of the nonlinear dynamic equations. They are well known in fluid dynamics, but it is not the case in optics. In this paper we show both experimentally and numerically that cnoidal waves could be formed in a fiber laser either in the net normal or net anomalous cavity dispersion regime, especially because, as the pump power is increased, the formed cnoidal waves could eventually evolve into a train of bright (in the net anomalous cavity dispersion regime) or dark (in the net normal cavity dispersion regime) solitons. Numerical simulations of the laser operation based on the extended nonlinear Schrödinger equation (NLSE) have well reproduced the experimental observations. The result not only explains why solitons can still be formed in a fiber laser even without mode locking but also suggests a new effective way of automatic stable periodic pulse train generation in lasers with a nonlinear cavity.

A numerical study of a single isolated human ventricular cell response to a periodic pulse stimulus current using the Rogers–McCulloch model

Among the primary causes of cardiac arrhythmias are abnormalities in the generation of action potentials (APs) by the cardiac cells, which may be induced by alterations in the electrophysiological properties of the cells as well as the stimuli delivered to them. Through numerical simulations using the phenomenological model of Rogers–McCulloch, this study examined how external stimuli modulate the electrical activity of a single isolated human ventricular cell functioning under normal conditions. First, we investigated how the initial conditions of the two model state variables affect how the cell responds to a single rectangular current pulse. This allows for the determination of a critical curve, which separates the initial conditions that allow for AP activation from those that inhibit it. This critical curve can be used to predict AP activation not only when the cell is stimulated by a single current pulse but also by a periodic stimulus. Then, we examined the cell response to a periodic train of rectangular current pulses, with a focus on the effects of the stimulus pacing length and amplitude. Our findings demonstrated that, despite not considering any alteration in the dynamics of ionic currents through the cell membrane, the Rogers–McCulloch model was capable of reproducing some of the most common activation patterns that have been widely identified in several clinical, experimental, and numerical studies. Depending on the stimulus properties, the following activation patterns were identified: (1) AP activation in synchrony with the stimulus, with one AP activation per pulse; (2) quasi-periodic and periodic Wenckebach-like patterns, in which successive AP activations are interrupted by a skipped beat; (3) completely irregular patterns; (4) abnormal potential oscillations that interrupt the repolarization of a previously activated AP, followed or not by a skipped beat; and (5) abnormal potential oscillations that completely inhibit cell repolarization.

Two-quantum magnetic resonance driven by a periodic RF pulse train

We theoretically investigate two-quantum magnetic resonance at the end sublevels of the ground state with a total angular momentum F g =1 in application to 87Rb atoms. In this work, the effect of the elliptically polarized light on the shift of the resonance frequency is studied. Two schemes are compared: when the RF field is harmonic and when a periodic RF pulse train is used. We demonstrate that the latter approach provides a significantly smaller shift, which can be helpful in reducing the heading error in optically pumped magnetometers.

Optical Time-Mapped Spectrograms (I): From the Time-Lens Fourier Transformer to the Talbot-Based Design

The short-time Fourier transform (STFT), or spectrogram (SP), is the prime method for joint time-frequency signal analysis and processing. Real-time implementation of this powerful tool over instantaneous bandwidths above the GHz range remains challenging. We propose here a universal analog optical processing approach to obtain the STFT of a high-speed temporal waveform (typically, a microwave signal) in a continuous and real-time manner, and with no gaps in the signal acquisition and analysis. The proposed method is based on a photonics time-mapped Fourier transformer, involving temporal modulation of the signal under test (SUT) with a chirped optical pulse (i.e., a time lens) followed by group-velocity dispersion, in which consecutive, overlapping chirped pulses (or time lenses) are utilized for realization of a continuous and gap-free STFT analysis. We derive the design conditions and performance trade-offs of this general scheme, especially concerning its instantaneous bandwidth, time-frequency resolutions and processing speed (number of FTs per second). Moreover, we also show that a previous, simpler time-mapped STFT design based on Talbot effects, in which the SUT is directly sampled with unchirped pulses before dispersion, can be interpreted and evaluated as a particular case of the time-lens STFT scheme introduced here. This suggests a way of implementing an array of overlapping time lenses by simply sampling the SUT with a suitable periodic train of short pulses. The time-lens STFT scheme offers a remarkable versatility to tailor the specifications of the obtained SP, whereas the Talbot design is particularly interesting for SP analysis with enhanced time resolution and ultrahigh processing speed. Our findings are validated through numerical simulations. The proposed method would enable performing the STFT of signals over instantaneous bandwidths above a few tens of GHz, with MHz frequency resolutions and processing speeds exceeding hundreds of millions of FTs per second using realistic fiber-optics technologies.

A 4–8 GHz Galactic Center Search for Periodic Technosignatures

Radio searches for extraterrestrial intelligence have mainly targeted the discovery of narrowband continuous-wave beacons and artificially dispersed broadband bursts. Periodic pulse trains, in comparison to the above technosignature morphologies, offer an energetically efficient means of interstellar transmission. A rotating beacon at the Galactic Center (GC), in particular, would be highly advantageous for galaxy-wide communications. Here, we present blipss, a CPU-based open-source software that uses a fast folding algorithm (FFA) to uncover channel-wide periodic signals in radio dynamic spectra. Running blipss on 4.5 hr of 4–8 GHz data gathered with the Robert C. Byrd Green Bank Telescope, we searched the central of our galaxy for kHz-wide signals with periods between 11 and 100 s and duty cycles (δ) between 10% and 50%. Our searches, to our knowledge, constitute the first FFA exploration for periodic alien technosignatures. We report a nondetection of channel-wide periodic signals in our data. Thus, we constrain the abundance of 4–8 GHz extraterrestrial transmitters of kHz-wide periodic pulsed signals to fewer than one in about 600,000 stars at the GC above a 7σ equivalent isotropic radiated power of ≈2 × 1018 W at δ ≃ 10%. From an astrophysics standpoint, blipss, with its utilization of a per-channel FFA, can enable the discovery of signals with exotic radio frequency sweeps departing from the standard cold plasma dispersion law.

Chaotic Bloch oscillations in dissipative optical systems driven by a periodic train of coherent pulses

We study the response of an optical system with the Kerr nonlinearity demonstrating Bloch oscillations to a periodic train of coherent pulses. It has been found out that the intensity of the field excited in the system by pulses resonantly depends on the train period. It is demonstrated numerically and analytically that the response of the system is stronger when the period of the driving pulses is commensurate with the period of the Bloch oscillations. Moreover, large enough pulses are capable to induce the instabilities which eventually lead to onset of chaotic Bloch oscillations of the wave-function envelope bouncing both in time and space. The analysis reveals that these instabilities are associated with period-doubling bifurcations. A cascade of such bifurcations with increase of the pulse amplitude triggers the chaotic behavior.

Thermoelectric study of the time-dependent resonant level model

We study the non-interacting time-dependent resonant level model mimicking a driven quantum dot connected through leads to two electronic reservoirs held at different temperatures and electrochemical potentials. Using a scattering approach, we provide analytical formulas of the time-dependent particle currents, heat currents, and input driving power under the wideband limit approximation. We also derive Landauer formulas for the corresponding time-integrated quantities when the perturbation applied on the dot is of finite duration. Then, we focus on the case of a single square pulse, benchmark our analytical results against numerical ones that are valid beyond the wideband limit, and perform numerical simulations for a smooth square pulse and a periodic square pulse train. Finally, we discuss whether the efficiency of the device in a stationary Seebeck configuration can be enhanced by driving the dot potential. We find numerically that the transient increase of the efficiency observed in some cases is eventually canceled out at long times.

Soliton trains induced by femtosecond laser filamentations in transparent materials with saturable nonlinearity

Femtosecond laser inscriptions in optical media current offer the most reliable optical technology for processing of transparent materials, among which is the laser micromachining technology. In this process, the nonlinearity of the transparent medium can be either intrinsic or induced by multiphoton ionization processes. In this work, a generic model is proposed to describe the dynamics of femtosecond laser inscription in transparent materials characterized by a saturable nonlinearity. The model takes into account multiphoton ionization processes that can induce an electron plasma of inhomogeneous density and electron diffusions. The mathematical model is represented by a one-dimensional complex Ginzburg–Landau equation with a generalized saturable nonlinearity term in addition to the residual nonlinearity related to multiphoton ionization processes, coupled to a rate equation for time evolution of the electron plasma density. Dynamical properties of the model are investigated focusing on the nonlinear regime, where the model equations are transformed into a set of coupled first-order nonlinear ordinary differential equations, which are solved numerically with the help of a sixth-order Runge–Kutta algorithm with a fixed time step. Simulations reveal that upon propagation, spatiotemporal profiles of the optical field and of the plasma density are periodic pulse trains, the repetition rates and amplitudes of which are increased with an increase of both the multiphoton ionization order and the saturable nonlinearity. When electron diffusions are taken into account, the system dynamics remains qualitatively unchanged; however, the electron plasma density gets strongly depleted, leaving almost unchanged the amplitude of pulses composing the femtosecond laser soliton crystals.

Bandwidth Compressed Time-Mapped Spectrogram Analysis Based on Temporal Talbot Effect and Temporal Magnification

A method to provide bandwidth compressed time-mapped spectrogram analysis based on temporal Talbot effect and temporal magnification is proposed and numerically demonstrated in this paper. The signal under test (SUT) is firstly sampled by a periodic pulse train, then passes through a dispersive medium under the Talbot condition and the spectrogram of the SUT is mapped to the time domain, so-called time-mapped spectrogram (TM-SP). Subsequently, a temporal magnification technique is implemented to stretch the time axis and compress the spectrum bandwidth, so that the effect of detection bandwidth on the frequency resolution is alleviated. Though the TM-SP cannot be acquired in a continuous way, the SUT is analyzed with ultrahigh frame rate in the temporal aperture. Additionally, a method to improve acquisition frame rate is proposed. The proposed bandwidth compressed TM-SP analysis is compared with the dispersion-based Fourier transform, and the related tradeoffs are provided in detail. The bandwidth compressed TM-SP analysis with a frequency resolution of 0.1 GHz, a measurable frequency range of 4.85 GHz, an analysis period of 0.1 ns, and an observation period of 4 ns is achieved by simulation.

Periodic Wave Trains in Nonlinear Media: Talbot Revivals, Akhmediev Breathers, and Asymmetry Breaking

We study theoretically and observe experimentally the evolution of periodic wave trains by utilizing surface gravity water wave packets. Our experimental system enables us to observe both the amplitude and the phase of these wave packets. For low steepness waves, the propagation dynamics is in the linear regime, and these waves unfold a Talbot carpet. By increasing the steepness of the waves and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, where the higher frequency periodic patterns at the fractional Talbot distance disappear. Further increase in the wave steepness leads to deviations from the Akhmediev breather solution and to asymmetric breaking of the wave function. Unlike the periodic revival that occurs in the linear regime, here the wave crests exhibit self acceleration, followed by self deceleration at half the Talbot distance, thus completing a smooth transition of the periodic pulse train by half a period. Such phenomena can be theoretically modeled by using the Dysthe equation.

Amplification and Generation of Frequency-Modulated Soliton Pulses in Nonuniform Active Fiber Configurations

We report on the theoretical and numerical analysis of the nonlinear Schrödinger equation describing the dynamical evolution of frequency-modulated (FM) optical signals propagating through the fiber configuration comprising active fibers with the anomalous dispersion nonuniformly distributed over the fiber length. In our consideration, a single active fiber section including segments with initially increasing and then decreasing dispersion is used for amplification and compression of an external FM pulse resulting in an increase of ~6 orders of magnitude in the pulse peak power and a 100-fold narrowing of the pulse duration down to a few picoseconds. Moreover, we demonstrate that, with a ~1 mW weakly modulated continuous wave input signal, the fiber configuration comprising two active fiber sections with different dispersion profiles is able to generate a strongly periodic pulse train, resulting in a pulse repetition rate >100 GHz, a pulse duration ~0.5 ps, and peak power up to ~1 kW. An evolution of optical signals governed by modulation instability in both fiber configurations is explored.

Konsonanzempfinden und Periodizitätsanalyse im auditorischen System

Since ancient times, regular pulses of the air beating against the ear have been regarded as the cause of pitch. Until the time of Leonhard Euler, theorists plotted point sequences to represent these regular pulses of the air. Two parallel point sequences symbolized an interval. The number of coinciding points of both point sequences determined the degree of consonance or dissonance. This so called “coincidence theory of consonance” lost its importance with the rise of modern science. Georg Simon Ohm introduced Jean Baptiste Joseph Fourier’s theorem to acoustics which allowed precise spectral analysis and calculation of any vibration. A tone was no longer described by a sequence of points symbolizing pulses of the air but by sine or cosine functions and their sums. Spectral analysis led to considerations in the frequency-domain. Combining it with the phenomenon of roughness, Hermann von Helmholtz developed a consonance theory based on the disturbance of harmony by roughness. Today, his idea forms the basis of the concept of sensory consonance. In contrast to computations in the frequency domain, however, sound is neuronally processed in the time domain. A single tone, for example, is neuronally represented by a periodic pulse train. Musical intervals produce firing patterns in the auditory nerve with regularities depending on the vibration ratio of the fundamental pitches. A mathematical model can be described that makes it possible to define a value to calculate the degree of these regularities for each vibration ratio. It turns out that this value, called Generalized coincidence function (Allgemeine Koinzidenzfunktion) is quite similar to the degree of tonal fusion as described by Carl Stumpf. This finding makes it probable that tonal fusion is a consequence of certain properties of the neuronal periodicity detection mechanism. Together with the roughness of intervals, this neuronal mechanism may be regarded as the basis of consonance and dissonance.

Ultrashort pulse generation from continuous-wave driven degenerate optical parametric oscillators

Degenerate <inline-formula><tex-math notation="LaTeX">$\chi ^{(2)}$</tex-math></inline-formula> optical parametric oscillators (OPOs) pumped by continuous-wave (cw) lasers in bulk or integrated format represent a promising platform for the study of classical as well as quantum phenomena, enabling interesting applications such as squeezing and random number generation. When subjected to phase modulation, such devices can generate ultrashort output pulses. In this report, we study pulse generation and spectral broadening in degenerate OPOs with intracavity electro-optic modulator (EOM). We numerically investigate ultrashort pulse generation from a cw-driven degenerate OPO based on MgO:PPLN as the nonlinear gain medium. The phase sensitive gain provided by the quadratic nonlinear medium in a detuned cavity and the inherent self-phase-locking of the degenerate field with that of the pump govern the signal amplification. Using high-performance computing tools, we study the full intracavity complex field evolution over 10000 round trips, as the OPO reaches the steady state. Taking advantage of the high nonlinear gain and low threshold of degenerate OPO, and using an intracavity EOM synchronized to the free-spectral-range of the cavity in combination with spectral filtering, we show that a stable, uniform, and periodic train of picosecond pulses of <inline-formula><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula>5 ps duration with FWHM spectral bandwidth of 0.4 THz can be generated. The results of our theoretical model are valid for <inline-formula><tex-math notation="LaTeX">$\chi ^{(2)}$</tex-math></inline-formula> OPOs in bulk and integrated format.

Ultra-fast full-field optical characterization of CW lasers based on optical frequency comb, wavelength-to-time mapping and phase-diversity.

Optical frequency comb (OFC), a periodic optical pulse train in time domain, has been widely employed to measure optical frequency due to its equidistant modes in the frequency domain. Here, we propose and demonstrate a novel optical spectrum analyzer for CW lasers based on stretching the OFC in a dispersive element and mapping the frequency comb into the time domain. The optical spectrum analyzer also provides instantaneous full-field (wavelength, amplitude and phase) optical characterization capability by combining with optical phase-diversity technology. Experimental results show that we successfully trace the evolution of modulated lasers with a measurement speed of ∼51 MHz (related to the pulse repetition of the OFC) and a high spectral resolution of ∼21 pm. Thanks to the use of wavelength-to-time mapping and OFC, the single channel measurement range of the proposed system can reach ∼10 nm, which breaks the restriction of the bandwidth of photodetector.

Josephson-Based Scheme for the Detection of Microwave Photons

We propose a scheme for the detection of microwave-induced photons through a current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero-voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the signal-to-noise ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.

Cyclostationary Approach to the Analysis of the Power in Electric Circuits under Periodic Excitations

This paper proposes a cyclostationary based approach to power analysis carried out for electric circuits under arbitrary periodic excitation. Instantaneous power is considered to be a particular case of the two-dimensional cross correlation function (CCF) of the voltage across, and current through, an element in the electric circuit. The cyclostationary notation is used for deriving the frequency domain counterpart of CCF—voltage–current cross spectrum correlation function (CSCF). Not only does the latter exhibit the complete representation of voltage–current interaction in the element, but it can be systematically exploited for evaluating all commonly used power measures, including instantaneous power, in the form of Fourier series expansion. Simulation examples, which are given for the parallel resonant circuit excited by the periodic currents expressed as a finite sum of sinusoids and periodic train of pulses with distorted edges, numerically illustrate the components of voltage–current CSCF and the characteristics derived from it. In addition, the generalization of Tellegen’s theorem, suggested in the paper, leads to the immediate formulation of the power conservation law for each CSCF component separately.

Temporal analog of Fabry-P\xe9rot resonator via coherent population trapping

Ramsey spectroscopy via coherent population trapping (CPT) is essential in precision measurements. The conventional CPT-Ramsey fringes contain numbers of almost identical oscillations and so that it is difficult to identify the central fringe. Here we experimentally demonstrate a temporal analog of Fabry–Pérot resonator via double-Λ CPT of laser-cooled 87Rb atoms. By inserting a periodic CPT pulse train between the two CPT-Ramsey pulses, due to the constructive interference of spin coherence, the transmission spectrum appears as a comb of equidistant peaks in frequency domain and thus the central Ramsey fringe can be easily identified. From the five-level Bloch equations for our double-Λ system, we find that the multi-pulse CPT interference can be regarded as a temporal analog of Fabry–Pérot resonator. Because of the small amplitude difference between the two Landé g factors, each peak splits into two when the external magnetic field is not too weak. This splitting is exactly linear with the magnetic field strength and thus can be used for measuring a magnetic field without involving magneto-sensitive transitions.

Optimal control for suppressing wave-packet spreading with strong nonresonant laser pulses

We use nonlinear optimal control simulation to systematically examine how to suppress wave-packet spreading with strong nonresonant near-infrared (NIR) laser pulses through a case study of a vibrational wave packet in the $B$ state of ${\mathrm{I}}_{2}$. As the degree of spreading of the vibrational wave packet is controllable by adjusting the pump pulse shape, the vibrational wave packet may be regarded as a prototype system to study spreading suppression by using nonresonant laser pulses. We quantitatively define spreading suppression in terms of the probability of finding the wave packet in the analytically defined, initially excited state at every vibrational period. From optimal control simulation and simulation by using model Gaussian pulse trains that mimic optimal pulses, we conclude that a simple periodic NIR pulse train without highly tuned temporal widths, amplitudes, or irradiation timings can almost perfectly stop the wave-packet spreading over a long control period, provided that the degree of spreading is not too large.