Frequency Chirp Research Articles

Dynamics of high-contrast grating vertical-cavity surface-emitting laser with lateral optical feedback by a heterostructure interface.

We investigate the dynamics of high-contrast grating vertical-cavity surface-emitting laser (HCG-VCSEL) with a lateral optical feedback cavity. The lateral optical feedback is realized by the reflection at the heterostructure interface between two different HCGs. The lateral optical feedback cavity possesses slow light which can be tuned by changing HCG parameters, and can control the dynamics of the HCG-VCSEL. The optical feedback can enhance the -3-dB bandwidth and enlarge the eye openings of diagrams of the HCG-VCSEL, and can also reduce the frequency chirp. The HCG-VCSEL with a lateral optical feedback cavity can achieve a -3-dB bandwidth of 37.7 GHz at 12 mA and eye diagrams at 60 Gbps (non-return to zero format) and 50 GBaud (4-level pulse amplitude modulation format) with sufficient openings.

Single-Lane 54-Gbit/s PAM-4/8 Signal Transmissions Using 10G-Class Directly Modulated Lasers Enabled by Low-Complexity Nonlinear Digital Equalization

This work presents the use of a directly modulated laser (DML) in time- and wavelength division multiplexed passive optical networks (TWDM-PONs), in which an EDFA-based booster amplification and an SOA-based pre-amplification are utilized to improve the optical power budget. We experimentally demonstrate the C-band optically amplified data transmissions and compare the performance of the non-return-to-zero on-off keying (NRZ-OOK), four and eight-level pulse amplitude modulation (PAM-4/PAM-8) using a 10-G class DML. With optical amplification, the uplink and downlink power budgets of about 28 dB and 35 dB, respectively, are achieved for the PAM-4 54-Gbit/s signals at the hard-decision forward error correction (HD-FEC) limit of 3.8x10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> after transmissions over a 25-km single-mode fiber link. To mitigate waveform distortions caused by the limited bandwidth, nonlinear dynamics, memory effects, and strong laser frequency chirp of the DML, especially during multi-level signal modulations, artificial neural network-based machine learning equalizers and low-complexity Volterra nonlinear equalizers are applied, which operate at the signal baud rate. The bit error ratio performance in conjunction with an enhanced power budget through the use of a low-complexity nonlinear equalizer can justify the validity of using a DML in the next-generation PONs.

Experiments on an FM Mode-Locked Laser as an Arbitrary Optical Function Generator

We describe experimentally that an FM mode-locked laser can generate various optical pulses such as Gaussian, secant hyperbolic (sech), double-sided exponential, rectangular, parabolic, triangular, and Nyquist pulses like an optical function generator. The experiments were carried out by employing a 10 GHz actively FM mode-locked erbium fiber laser, where a specific filter was installed in the laser cavity. The specific filter was characterized by the Fourier transformed spectrum <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega )$ </tex-math></inline-formula> of an output pulse <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a(t)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A(\omega $ </tex-math></inline-formula> + <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n\Omega _{m})$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n=- \infty \sim + \infty $ </tex-math></inline-formula> . Here, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega _{m}$ </tex-math></inline-formula> is the angular modulation frequency. We employed a software-controlled liquid crystal on silicon (LCoS) optical filter, which can control the amplitude and the phase of the input signal as a function of optical frequency. Therefore, we were able to generate various optical pulses by simply changing the filter shape using the software. The filter resolution was 10 GHz. The generated optical pulses agreed well with the theory, where the spectral profile even below −40 dB coincided well with the theoretical profile. We proved experimentally from the product of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \nu \Delta \tau $ </tex-math></inline-formula> at −3 dB that the output pulses have none of the frequency chirp that would inevitably occur with conventional FM mode-locking. It was not possible to generate an asymmetric single-sided pulse as we pointed out theoretically. We were also able to generate parabolic and triangular intensity pulses as we predicted in a previous paper. Finally, we compared the possibilities of generating various pulses with AM and FM mode-locking techniques.

CHIRP AUDITORY STEADY -STATE RESPONSE AS A HEARING SCREENING TOOL IN HIGH- RISK INFANTS

Background:Newborn hearing screening with automated procedures usually uses broad band stimuli, such as click. Studies using the Auditory Steady-State Response (ASSR) that used specific frequency chirps named narrow band CE-chirps have shown obvious diagnostic results. Objective:To assess the value of the binaural multi-frequency chirp ASSR as a hearing screening tool. To compare chirp ASSR and click ABR as a tool for early diagnosis of hearing loss in infants with risk factors for hearing loss.Methodology: Two groups of infants were studied, group I (28 infants with risk factors) with one or more risk factor for permanent hearing loss, group II (ten infants without risk factors). Their age ranges from one to six months. Assessment of middle ear pressure using immittancemetry, and hearing threshold estimation using Click ABR and Chirp ASSR were done. Results: When comparing hearing threshold of [group (I) infants with risk factors], and [group (II) infants without risk factors] it was found that there was no statistically significant difference when hearing was evaluated by using click ABR or Chirp ASSR.By comparing average ASSR (Average thresholds of1000, 2000 and 4000 HZ) threshold with ABR threshold, there was no statistically significant difference. There was high positive correlation between ABR threshold and average ASSR. Conclusion: Chirp ASSR can be used for assessment of hearing thresholds in infants with the same accuracy of Click ABR thresholds, with more advantage perceived by ASSR in the form of frequency specific threshold estimation. The binaural multi-frequency chirp ASSR can be used as a hearing screening tool.

Enhancement of electron–positron pairs in combined potential wells with linear chirp frequency

Effect of linear chirp frequency on the process of electron–positron pairs production from vacuum is investigated by the computational quantum field theory. With appropriate chirp parameters, the number of electrons created under combined potential wells can be increased by two or three times. In the low frequency region, frequency modulation excites interference effect and multiphoton processes, which promotes the generation of electron–positron pairs. In the high frequency region, high frequency suppression inhibits the generation of electron–positron pairs. In addition, for a single potential well, the number of created electron–positron pairs can be enhanced by several orders of magnitude in the low frequency region.

Engineering dissipative chirped solitons in the cardiac tissue under electromagnetic induction

This work deals with the engineering dissipative chirped solitary waves in the cardiac tissue under electromagnetic induction. Employing the a two-dimensional Ginzburg-Landau (GL) equation describing the spatiotemporal evolution of transmembrane potential in cardiac cells under magnetic flow effect, we use the phase imprint technique to reduce the model equation into a derivative GL equation (alias chirping model equation) that allow us to investigate the dynamics of dissipative chirp solitary wave propagating through a cardiac tissue. The baseband modulational instability (MI) of the chirping model is investigated and the analytical expression of the MI growth rate is derived. In the baseband MI regime, we use the approximative solitonlike solution of the chirping model to investigate the dynamics of transmembrane potential in cardiac cells. We show that the frequency chirp associated to the solitary wave is directly proportional to the wave amplitude and the nonlinear chirping parameter can be used to modulate the chirping amplitude. Also, our results show that the approximate solution of the chirping model can be used to generate bright (dissipative) solitons, dark solitons, breather solitons and first-order rogue wave in the cardiac cell under electromagnetic induction. Our theoretical results are confirmed by numerical simulations. The results of this work can motivate the investigations of qualitative new phenomena in the presence of large dissipation.

Generation of high performance optical chirped pulse for distributed strain sensing application with high strain accuracy and larger measurement range.

A photonic approach for generating low frequency drifting noise, arbitrary and large frequency chirping rate (FCR) optical pulses based on the Kerr effect in the nonlinear optical fiber is theoretically analyzed and experimentally demonstrated. Due to the Kerr effect-induced sinusoidal phase modulation in the nonlinear fiber, high order Kerr pulse with a large chirping rate is generated. In the concept-proof experiments, the FCR of the mth Kerr pulse has been significantly improved by a factor of 2m+1. In addition, dynamic strain measurement along with a random fiber grating array (RFGA) sensor by using different order Kerr pulse is carried out for demonstrating a large strain measurement range with lower uncertainty sensing capability. Benefiting from the use of a single laser source and large FCR Kerr pulse, the system exhibits a 3.9 µɛ static strain measurable range, 0.24 µɛ measurement uncertainty by using -4th order Kerr pulse that has an FCR up to 0.8 GHz/ns. Note that the FCR of the chirped pulse could be further enhanced by using larger FCR chirped pulse seed or choosing higher order Kerr pulses.

Comparison of different laser pulse envelopes with frequency chirp for efficient electron acceleration in vacuum

In the present manuscript, we have investigated the effect of chirped laser pulse envelope to study electron acceleration in vacuum. For this purpose, we have chosen two different pulse shapes, i.e trapezoidal pulse envelope and Sin4 pulse envelope. Electron has been injected axially to the front of the tested envelopes. In all calculations, the front end of each pulse is presumed to have caught up with the electron at t = 0 at the coordinate origin. The relativistic Newton-Lorentz equations of motion of electron in the field of the laser pulse have been analytically and numerically solved. By optimizing laser and frequency chirp parameters, the energy gain of the order of GeV is obtained, and it has been noticed that under the similar range of phases (0 to 2π) and laser intensity parameter (a0 = 3), trapezoidal pulse envelope shows better result than Sin4 pulse envelope on effective electron acceleration in vacuum.

Imprint of the temporal envelope of ultra-short laser pulses on the longitudinal momentum spectrum of e+e− pairs

The effect of the temporal pulse shape of intense pulses on the momentum distribution of ${e}^{+}{e}^{\ensuremath{-}}$ pairs is studied using the quantum kinetic equation. Two closely resembling temporal envelopes, namely, Gaussian and Sauter, keeping all the other pulse parameters the same, are considered to this end. Contrary to the common perception which can be gauged from the interchangeable use of these temporal profiles, the longitudinal momentum spectrum of the pairs created by the two pulses is found to differ significantly in all the temporal regimes. For the pulses having a few cycles of oscillations, the temporal profile of the pulse is revealed in the oscillatory interference pattern riding over the otherwise smooth longitudinal momentum spectrum at asymptotic times. The onset of the oscillation due to the quantum interference of reflection amplitudes from the scattering potential due to the pulses having a temporal structure of multiple barriers takes place for fewer-cycle oscillations for the Gaussian pulse compared to that for the Sauter pulse. Furthermore, the oscillation amplitude for the same number of oscillations within the pulse duration is larger for the Gaussian pulse. The presence of the carrier-envelope phase and the frequency chirping is found to magnify these differences. In the absence of any appreciable interference effect for the pulses having less than five oscillations, the longitudinal momentum spectrum has a higher peak value for the Sauter pulse at asymptotic times. On the other hand, before the transient stage of evolution, the peak of the spectrum shows the opposite trend.

Long distance high resolution FMCW laser ranging with phase noise compensation and 2D signal processing.

A long distance high resolution frequency-modulated continuous wave (FMCW) laser rangefinder with phase noise compensation and two-dimensional (2D) data processing skills is developed. Range-finding ladar consists of a continuously chirped laser source, an auxiliary reference interferometer, and a monostatic optical transceiver for target illumination and return photon collection. To extend the range unambiguity and lower the electronic processing bandwidth, a two-step laser frequency chirping scheme is adopted, where a long pulse width, small frequency bandwidth laser chirping signal are used in step 1 for coarse distance estimation, and a short pulse width and large frequency bandwidth laser chirping signal are applied afterwards for step 2 high resolution distance realization. An auxiliary reference interferometer is to record the phase noise originated from the laser source to compensate for phase errors induced in the target return photons. The 2D data processing skill helps to coherently sum up all the phase noise removed echo photons to achieve high resolution range peak extraction with high detection sensitivity. Experimental demonstration shows that the proposed FMCW ladar at 1550 nm wavelength with a laser chirping bandwidth of 10 GHz and electronic processing bandwidth of 200 MHz can measure a corner cube test target in an outdoor atmospheric environment, and the measurement results are 12013.905 m with a 2.4 cm range resolution under strong return photon levels and 12013.920 m with a 2.5 cm range resolution under weak return photon levels.

Direct Observation of Coherent Longitudinal and Shear Acoustic Phonons in TaAs Using Ultrafast X-Ray Diffraction.

Using femtosecond time-resolved x-ray diffraction, we investigated optically excited coherent acoustic phonons in the Weyl semimetal TaAs. The low symmetry of the (112) surface probed in our experiment enables the simultaneous excitation of longitudinal and shear acoustic modes, whose dispersion closely matches our simulations. We observed an asymmetry in the spectral line shape of the longitudinal mode that is notably absent from the shear mode, suggesting a time-dependent frequency chirp that is likely driven by photoinduced carrier diffusion. We argue on the basis of symmetry that these acoustic deformations can transiently alter the electronic structure near the Weyl points and support this with model calculations. Our study underscores the benefit of using off-axis crystal orientations when optically exciting acoustic deformations in topological semimetals, allowing one to transiently change their crystal and electronic structures.

Laser wakefield and direct laser acceleration of electron by chirped laser pulses

Chirped laser pulses are investigated theoretically for laser wakefield (LW) and direct laser (DL) acceleration of electrons in the plasma-bubble regime. Chirping of laser pulse with a suitable frequency allows a better trapping of electron in bubble regime which enforces a strong betatron resonance inside the plasma bubble. Linear and non-linear effects of frequency chirp determine electron acceleration, de-phasing, beam quality in terms of energy spread and high energy from the direct laser field and its plasma wake in bubble regime. Gaussian chirped laser pulse exhibit high energy to the electrons compared with linear and other non-linear chirped pulses in plasma-bubble regime. The investigation with chirped laser pulse opens new dimension to hybrid LW-DL acceleration mechanism in bubble regime.

Comparing frequency-chirp sensitivity in the inferior colliculus to basic response properties using novel stimuli

Most neurons in the central nucleus of the inferior colliculus (ICC) are sensitive to the direction of phase-curvature of Schroeder-phase (SCHR) stimuli. This phase-curvature controls the direction and velocity of frequency chirps within the fundamental SCHR period. Differences in responses to different SCHR stimuli may originate from an underlying sensitivity to frequency chirp direction or velocity. However, known ICC sensitivities, such as those to frequency or envelope periodicity and duty cycle, may also contribute to the observed effect. To parse these confounding SCHR stimulus features, we designed novel frequency-chirping stimuli to isolate the influences of periodicity, duty cycle, and frequency-chirp direction or velocity on ICC neuron responses. Extracellular, single-unit recordings of chirp responses were made in awake rabbit ICC. Simultaneously, basic response properties were characterized using methods such as frequency response maps, modulation transfer functions, and spectro-temporal receptive fields. By comparing basic response properties across chirp-sensitive neurons (comprising 80% of ICC neurons), we can outline the shared characteristics among them. Our goal is to determine whether frequency-chirp sensitivity in ICC neurons is independent of other established feature sensitivities. Frequency-chirp-sensitive neurons are interesting, because they may play a unique role in encoding sounds with complex phase, including speech. [Work supported by NIDCD-R01-001641.]

A survey of pedestal magnetic fluctuations using gyrokinetics and a global reduced model for microtearing stability

This article presents a global reduced model for slab-like microtearing modes (MTMs) in the H-mode pedestal, which reproduces distinctive features of experimentally observed magnetic fluctuations, such as chirping and discrete frequency bands at noncontiguous mode numbers. Our model, importantly, includes the global variation of the diamagnetic frequencies, which is necessary to reproduce the experimental observations. The key insight underlying this model is that MTM instability is enabled by the alignment of a rational surface with the peak in the profile of the diamagnetic frequency. Conversely, MTMs are strongly stabilized for toroidal mode numbers for which these quantities are misaligned. This property explains the discrete fluctuation bands in several DIII-D and JET discharges, which we survey using our reduced model in conjunction with global gyrokinetic simulations. A fast yet accurate reduced model for MTMs enables rapid interpretation of magnetic fluctuation data from a wide range of experimental conditions to help assess the role of MTM in the pedestal.

The model of particles modes. I. A paradigm for phase synchronization in tokamak turbulence

Superthermal energetic particles may alter the kinetic and resonant nature of zonal flows by leading to new types of instabilities. Here, we study the effects induced by superthermal energetic ions on trapped-ion modes (TIM) by using a reduced Hamiltonian gyrokinetic model, where both fast scales (cyclotron and bounce or transit motions) are gyro-averaged. In particular, we analyze the enhancement of resonant processes induced by energetic ions associated with nonlinear phase synchronization, in an extended version of the TIM model including circulating ions. Once an energetic particle mode is driven unstable, a rich nonlinear dynamics is observed, which encompasses a frequency chirping associated with a synchronization process driven by TIM and a transition scenario. An equivalence with the classic Kuramoto model—the paradigm describing the synchronization of a system of coupled oscillators—explains much of this phenomenology.

New chirped gray and kink self–similar waves in presence of quintic nonlinearity and self–steepening effect

We demonstrate new types of chirped self-similar waves for a generalized derivative nonlinear Schrödinger equation with varying dispersion, self–steepening effect, cubic–quintic nonlinearity, and gain or loss. The equation arises in modeling femtosecond light propagation in an optical fiber with spatial parameter variations. The newly found self-similar structures take the shape of gray and kink pulses. It is observed that the frequency chirp accompanying these self-similar pulses depends crucially on the intensity of the wave and its amplitude can be effectively governed by adjusting the self-steepening parameter. The dynamical behaviors of the chirped self-similar gray and kink waves are analyzed in a periodic distributed amplification system. The acquired self-similar structures display rich dynamical evolutions that are important in practical applications.

Hybrid simulations of beta-induced Alfvén eigenmode with reversed safety factor profile

Based on the experimental parameters in the HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of the beta-induced Alfvén eigenmode (BAE). It is found that the (m/n = 3/2) BAE is excited by co-passing energetic ions with q min = 1.5 in linear simulation, and the mode frequency is consistent with the experimental measurement. The simulation results show that the energetic ions β h, the injection velocity v 0, and orbit width parameter ρ h of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of q min (with the fixed shape of the q profile) is studied, and it is found that when q min ⩽ 1.5, the excited modes are BAEs, which are located near q = 1.5 rational surfaces; when q min > 1.5, the excited modes are similar to the reversed-shear Alfvén eigenmodes, which are mainly localized around q = q min surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE are sensitive to the EP drive. For the strongly driven case, firstly, redistribution and transport of energetic ions are trigged by 3/2 BAE, which raised the radial gradient of the distibution function of energetic ions near the q = 2 rational surface, and then an energetic particle mode (EPM) (m/n = 4/2) is driven in the nonlinear phase. Finally, these two instabilities triggered a significant redistribution of energetic ions, which results in the twice-repeated and mostlydownward frequency chirping of 3/2 BAE. For the weakly driven case, there are no 4/2 EPM being driven nor twice-repeated chirping in the nonlinear phase, since the radial gradient near q = 2 rational surface is small and almost unchanged.

Analysis of the nonlinear dynamics of a chirping-frequency Alfvén mode in a tokamak equilibrium

Chirping Alfvén modes are considered as potentially harmful for the confinement of energetic particles in burning tokamak plasmas. In fact, by changing their frequency, they are able to extract as much power as possible from these particles, possibly increasing their transport. In this paper, the nonlinear evolution of a single-toroidal-number chirping mode is analyzed by numerical particle simulation. The relevant resonant structures are identified by numerical techniques based on the use of a coordinate system including two constants of motion: the magnetic moment and a suitable function of the initial particle coordinates. The analysis is focused on the dynamics of two different resonant structures in the particle phase space: those yielding the largest drive during the linear and the nonlinear phase, respectively. It is shown that, for each resonant structure, a density-flattening region is formed around the respective resonance radius, with a radial width that increases as the mode amplitude grows. It is delimited by two steepened negative density gradients, drifting inwards and outward. If the mode frequency were constant, phase-space density flattening would quench the resonant-structure drive as the steepened gradients leave the original resonance region. The frequency chirping, however, causes the resonance radius and the resonance region to drift inwards. This drift, along with a relevant increase in the resonance width, delays the moment in which the inner density gradient reaches the inner boundary of the resonance region, leaving it. On the other hand, the island evolves consistently with the resonance radius; as a consequence, the steepened density gradient further moves inward. This process continues as long as it allows to keep the steepened gradient within the resonance region. When this is no longer possible, the resonant structure ceases to be effective in driving the mode. To further extract energy from the particles, the mode has to tap a different resonant structure, possibly making use of additional frequency variations.

Post-compression of femtosecond laser pulses using self-phase modulation: from kilowatts to petawatts in 40 years

The pulse duration at the output of femtosecond lasers is usually close to the Fourier limit, and can be shortened by increasing the spectral width. To this end, use is made of self-phase modulation when a pulse propagates in a medium with cubic nonlinearity. Then, the pulse with a chirp (frequency dependence of the spectrum phase) is compressed due to a linear dispersion element, which introduces a chirp of the same modulus, but opposite in sign. This pulse post-compression, known since the 1960s, has been widely used and is being developed up to the present for pulses with energies from fractions of a nJ to tens of J. The review is devoted to the theoretical foundations of this method, problems of energy scaling, and a discussion of the results of more than 150 experimental studies.

One‐Dimensional gcPIC‐δf Simulation of Hooked Chorus Waves in the Earth’s Inner Magnetosphere

AbstractChorus waves are coherent electromagnetic emissions in the inner magnetosphere, generally composed of a series of discrete and repetitive elements. These elements usually have rising frequency chirpings, which are occasionally mingled with one or several elements with a hooked spectrogram. In this letter, we perform a one‐dimensional general curvilinear particle‐in‐cell (gcPIC)‐δf simulation of chorus waves excited by temperature anisotropic electrons in a dipole magnetic field, and identify one chorus element with a hooked spectrogram, which is embedded in several chorus elements with a rising frequency chirping. In the hooked chorus element, the frequency increases first, and then decreases. Interestingly, we find that there are clear electron holes in the electron velocity space, no matter whether the chorus element has a rising‐tone or hooked‐tone spectrogram. Our study presents an important clue for the theoretical analysis of the frequency chirping in the chorus waves.