Showing papers on "Chirp published in 2022"

Perturbation of chirped localized waves in a dual-power law nonlinear medium

Abstract: We investigate the transmission of localized waves through a dual-power law medium exhibiting the perturbations including the inter-modal dispersion, self-steepening, and self-frequency shift effects. A novel class of nonlinear waves that are periodic wave, kink soliton, algebraic soliton and bright soliton, along with the corresponding chirping, are reported. We found the nonlinear contribution chirp is proportional to n power of the light intensity, which is arising from the perturbations. Finally, the influence of degree of nonlinearity on the dynamical properties of the obtained chirped structures is presented.

Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system

Abstract: The propagation of ultrashort light pulses in a birefringent optical fiber exhibiting spatiotemporal dispersion, cross- and self-phase modulation, self-steepening, and group-velocity dispersion effects is addressed. The evolution of light pulses in such system is described by the coupled Fokas-Lenells equations which offer an accurate description of pulse dynamics in the femtosecond range when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrödinger equation are sustained. We report the first analytical demonstration of the propagation of chirped solitons in a birefringent fiber medium governed by the coupled Fokas-Lenells equations. The formation of those nonlinearly chirped solitons in the optical material may be attributed to the presence of self-steepening process. The results show that the frequency chirp associated with each of the two field components is directly proportional to the total intensity of the pulse. The chirped solitons for the system including the dark-dark and bright-bright soliton pairs in the presence of all fiber parameters are retrieved. The chirps accompanying the soliton pairs are also determined. The existence constraints of these chirped solitons are presented. In addition, the stability of the chirped solutions with respect to the finite perturbations is studied numerically.

First order surface grating fiber coupler under the period chirp and apodization functions variations effects

Abstract: The paper has demonstrated the first order surface grating fiber coupler under the period chirp and apodization functions variations effects. The Fiber coupler transmittivity/reflectivity, the fiber coupler grating index change and the fiber coupler mesh transmission cross-section are clarified against the grating length with the quadratic/cubic root period chirp and Gaussian/uniform apodization functions. The fiber coupler delay and dispersion are simulated and demonstrated with grating wavelength with quadratic/cubic root period chirp and Gaussian/uniform apodization function. As well as the fiber coupler output pulse intensity is simulated against the time period with the quadratic/cubic root period chirp and Gaussian/uniform apodization function. The fiber coupler peak intensity variations against the transmission range variations is also demonstrated by OptiGrating simulation software.

Phase-matching-induced near-chirp-free solitons in normal-dispersion fiber lasers

Abstract: Abstract Direct generation of chirp-free solitons without external compression in normal-dispersion fiber lasers is a long-term challenge in ultrafast optics. We demonstrate near-chirp-free solitons with distinct spectral sidebands in normal-dispersion hybrid-structure fiber lasers containing a few meters of polarization-maintaining fiber. The bandwidth and duration of the typical mode-locked pulse are 0.74 nm and 1.95 ps, respectively, giving the time-bandwidth product of 0.41 and confirming the near-chirp-free property. Numerical results and theoretical analyses fully reproduce and interpret the experimental observations, and show that the fiber birefringence, normal-dispersion, and nonlinear effect follow a phase-matching principle, enabling the formation of the near-chirp-free soliton. Specifically, the phase-matching effect confines the spectrum broadened by self-phase modulation and the saturable absorption effect slims the pulse stretched by normal dispersion. Such pulse is termed as birefringence-managed soliton because its two orthogonal-polarized components propagate in an unsymmetrical “X” manner inside the polarization-maintaining fiber, partially compensating the group delay difference induced by the chromatic dispersion and resulting in the self-consistent evolution. The property and formation mechanism of birefringence-managed soliton fundamentally differ from other types of pulses in mode-locked fiber lasers, which will open new research branches in laser physics, soliton mathematics, and their related applications.

Joint Radar-Communication Systems: Modulation Schemes and System Design

Abstract: The joint radar-communication (RadCom) concept has been continuously gaining interest due to the possibility of integrating radar sensing and communication functionalities in the same radio frequency hardware platform. Besides a number of challenges in terms of hardware design and signal processing, the choice of suitable modulation schemes plays a significant role in driving the performance of RadCom systems. In this sense, this article presents an overview of state-of-the-art modulation schemes for RadCom systems, namely, chirp sequence, phase-modulated continuous wave, orthogonal frequency-division multiplexing, and orthogonal chirp-division multiplexing. For each of them, a detailed system model is outlined, and parameters for quantifying both radar and communication performances are presented. Finally, a comparative analysis of the aforementioned RadCom modulation schemes is carried out to illustrate the presented discussion.

Phase-matching-induced near-chirp-free solitons in normal-dispersion fiber lasers

Abstract: Abstract Direct generation of chirp-free solitons without external compression in normal-dispersion fiber lasers is a long-term challenge in ultrafast optics. We demonstrate near-chirp-free solitons with distinct spectral sidebands in normal-dispersion hybrid-structure fiber lasers containing a few meters of polarization-maintaining fiber. The bandwidth and duration of the typical mode-locked pulse are 0.74 nm and 1.95 ps, respectively, giving the time-bandwidth product of 0.41 and confirming the near-chirp-free property. Numerical results and theoretical analyses fully reproduce and interpret the experimental observations, and show that the fiber birefringence, normal-dispersion, and nonlinear effect follow a phase-matching principle, enabling the formation of the near-chirp-free soliton. Specifically, the phase-matching effect confines the spectrum broadened by self-phase modulation and the saturable absorption effect slims the pulse stretched by normal dispersion. Such pulse is termed as birefringence-managed soliton because its two orthogonal-polarized components propagate in an unsymmetrical “X” manner inside the polarization-maintaining fiber, partially compensating the group delay difference induced by the chromatic dispersion and resulting in the self-consistent evolution. The property and formation mechanism of birefringence-managed soliton fundamentally differ from other types of pulses in mode-locked fiber lasers, which will open new research branches in laser physics, soliton mathematics, and their related applications.

Chirped periodic waves for an cubic-quintic nonlinear Schrödinger equation with self steepening and higher order nonlinearities

Abstract: In this paper, we study the cubic-quintic nonlinear Schrödinger equation (CQ-NLSE) to describe the propagation properties of nonlinear periodic waves (PW) in an optical fiber . We find chirped periodic waves (CPW) with some Jacobi elliptic functions (JEF). We also obtain some solitary waves (SW) like dark, bright, hyperbolic and singular solitons. The chirp that corresponds to each of these optical solitons is also determined. The pair intensity is shown to be related to the nonlinear chirp, which is determined by self-frequency shift and pause self-steepening (SS). The shape of profile for these waves will also be display.

Space-time wave packets localized in all dimensions

Abstract: Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to nonlinear and quantum optics. However, synthesizing such wave packets requires introducing non-differentiable angular dispersion with high spectral precision in two transverse dimensions, a capability that has eluded optics to date. Here, we describe an experimental strategy capable of sculpting the spatio-temporal spectrum of a generic pulsed beam by introducing arbitrary radial chirp via two-dimensional conformal coordinate transformations of the spectrally resolved field. This procedure yields propagation-invariant `space-time' wave packets localized in all dimensions, with tunable group velocity in the range from $0.7c$ to $1.8c$ in free space, and endowed with prescribed orbital angular momentum. By providing unprecedented flexibility in sculpting the three-dimensional structure of pulsed optical fields, our experimental strategy promises to be a versatile platform for the emerging enterprise of space-time optics.

Exploring Features in the Binary Black Hole Population

Abstract: Vamana is a mixture model framework that infers the astrophysical distribution of chirp mass, mass ratio, and spin component aligned with the orbital angular momentum for the binary black hole population. We extend the mixing components in this framework to also model the redshift evolution of merger rate and report all the major one and two-dimensional features in the Binary Black Hole population using the 69 gravitational wave signals detected with a false alarm rate $<1\mathrm{yr}^{-1}$ in the third Gravitational-Wave Transient Catalog (GWTC)-3. Endorsing our previous report and a corroborating recent report from LIGO Scientific, Virgo, and KAGRA Collaborations, we observe the chirp mass distribution has multiple peaks and a lack of mergers with chirp masses $10 \textrm{--} 12M_\odot$. In addition, we observe aligned spins show mass dependence with heavier binaries exhibiting larger spins, mass ratio shows a dependence on the chirp mass but not on the aligned spin, and the redshift evolution of the merger rate for the peaks in the mass distribution is disparate. These features possibly reflect the astrophysics associated with the binary black hole formation channels. However, additional observations are needed to improve our limited confidence in them.

Quantitative detection of locomotive wheel polygonization under non-stationary conditions by adaptive chirp mode decomposition

Abstract: Abstract Wheel polygonal wear is a common and severe defect, which seriously threatens the running safety and reliability of a railway vehicle especially a locomotive. Due to non-stationary running conditions (e.g., traction and braking) of the locomotive, the passing frequencies of a polygonal wheel will exhibit time-varying behaviors, which makes it too difficult to effectively detect the wheel defect. Moreover, most existing methods only achieve qualitative fault diagnosis and they cannot accurately identify defect levels. To address these issues, this paper reports a novel quantitative method for fault detection of wheel polygonization under non-stationary conditions based on a recently proposed adaptive chirp mode decomposition (ACMD) approach. Firstly, a coarse-to-fine method based on the time–frequency ridge detection and ACMD is developed to accurately estimate a time-varying gear meshing frequency and thus obtain a wheel rotating frequency from a vibration acceleration signal of a motor. After the rotating frequency is obtained, signal resampling and order analysis techniques are applied to an acceleration signal of an axle box to identify harmonic orders related to polygonal wear. Finally, the ACMD is combined with an inertial algorithm to estimate polygonal wear amplitudes. Not only a dynamics simulation but a field test was carried out to show that the proposed method can effectively detect both harmonic orders and their amplitudes of the wheel polygonization under non-stationary conditions.

Analytical and numerical study of chirped optical solitons in a spatially inhomogeneous polynomial law fiber with parity-time symmetry potential

Abstract: This work studies the dynamical transmission of chirped optical solitons in a spatially inhomogeneous nonlinear fiber with cubic-quintic-septic nonlinearity, weak nonlocal nonlinearity, self-frequency shift and parity-time (  ) symmetry potential. A generalized variable-coefficient nonlinear Schrödinger equation that models the dynamical evolution of solitons has been investigated by the analytical method of similarity transformation and the numerical mixed method of split-step Fourier method and Runge–Kutta method. The analytical self-similar bright and kink solitons, as well as their associated frequency chirps, are derived for the first time. We found that the amplitude of the bright and kink solitons can be controlled by adjusting the imaginary part of the  -symmetric potential. Moreover, the influence of the initial chirp parameter on the soliton pulse widths is quantitatively analyzed. It is worth emphasizing that we could control the chirp whether it is linear or nonlinear by adjusting optical fiber parameters. The simulation results of bright and kink solitons fit perfectly with the analytical ones, and the stabilities of these soliton solutions against noises are checked by numerical simulation.

On the existence of chirped algebraic solitary waves in optical fibers governed by Kundu–Eckhaus equation

Abstract: This paper reports the first analytical demonstration of propagation of algebraic solitary waves accompanied with a nonlinear chirp in optical fibers governed by the Kundu–Eckhaus equation. Both chirped dark and bright algebraic solitary waves can exist in the system with higher-order effects such as Raman effect and quintic nonlinearity. The chirp associated with each of these algebraic solitary waves is shown to be dependent on the intensity of the wave. It is found that the Raman process has a profound impact in the chirp of these localized pulses.

A chirplet transform-based mode retrieval method for multicomponent signals with crossover instantaneous frequencies

Abstract: In nature and engineering world, the acquired signals are usually affected by multiple complicated factors and appear as multicomponent nonstationary modes. In such and many other situations, it is necessary to separate these signals into a finite number of monocomponents to represent the intrinsic modes and underlying dynamics implicated in the source signals. In this paper, we consider the mode retrieval of a multicomponent signal which has crossing instantaneous frequencies (IFs), meaning that some of the components of the signal overlap in the time-frequency domain. We use the chirplet transform (CT) to represent a multicomponent signal in the three-dimensional space of time, frequency and chirp rate and introduce a CT-based signal separation scheme (CT3S) to retrieve modes. In addition, we analyze the error bounds for IF estimation and component recovery with this scheme. We also propose a matched-filter along certain specific time-frequency lines with respect to the chirp rate to make nonstationary signals be further separated and more concentrated in the three-dimensional space of CT. Furthermore, based on the approximation of source signals with linear chirps at any local time, we propose an innovative signal reconstruction algorithm, called the group filter-matched CT3S (GFCT3S), which also takes a group of components into consideration simultaneously. GFCT3S is suitable for signals with crossing IFs. It also decreases component recovery errors when the IFs curves of different components are not crossover, but fast-varying and close to each other. Numerical experiments on synthetic and real signals show our method is more accurate and consistent in signal separation than the empirical mode decomposition, synchrosqueezing transform, and other approaches.

Smoothed Lv Distribution based Three-dimensional Imaging for Spinning Space Debris

Abstract: Three-dimensional (3-D) imaging plays a vital role in the recognition of spinning space debris. However, the image may be blurred due to the range migration caused by fast rotation of space debris. Moreover, the image quality, which depends on the estimation accuracy of Doppler frequency and chirp rate of scattering centers, is influenced by cross-terms and sidelobes. In this paper, we propose a novel 3-D imaging method based on smoothed Lv distribution (SLVD). Firstly, the selection criterion for best imaging time based on the time-frequency moment is proposed to guarantee that the echo is approximated as a linear frequency modulation signal. Then, we operate the Khatri-Rao product on the centroid frequency and chirp rate (CFCR) representation and the range-Doppler (RD) image to obtain the 3-D image. To decrease the influence of range migration, we process a short time window during the RD imaging procedure. For cross-term and sidelobe suppression, the SLVD is proposed to obtain the CFCR representation by expressing the Lv distribution (LVD) in a convolution form and introducing a centroid frequency window. Experimental results verify the effectiveness of the proposed imaging method and the good performance of the proposed SLVD for cross-term and sidelobe suppression.

Frequency-modulated continuous waves controlled by space-time-coding metasurface with nonlinearly periodic phases

Abstract: The rapid development of space-time-coding metasurfaces (STCMs) offers a new avenue to manipulate spatial electromagnetic beams, waveforms, and frequency spectra simultaneously with high efficiency. To date, most studies are primarily focused on harmonic generations and independent controls of finite-order harmonics and their spatial waves, but the manipulations of continuously temporal waveforms that include much rich frequency spectral components are still limited in both theory and experiment based on STCM. Here, we propose a theoretical framework and method to generate frequency-modulated continuous waves (FMCWs) and control their spatial propagation behaviors simultaneously via a novel STCM with nonlinearly periodic phases. Since the carrier frequency of FMCW changes with time rapidly, we can produce customized time-varying reflection phases at will by the required FMCW under the illumination of a monochromatic wave. More importantly, the propagation directions of the time-varying beams can be controlled by encoding the metasurface with different initial phase gradients. A programmable STCM prototype with a full-phase range is designed and fabricated to realize reprogrammable FMCW functions, and experimental results show good agreement with the theoretical analyses.

Optical Pulse Compression Assisted by High‐Q Time‐Modulated Transmissive Metasurfaces

Abstract: In this paper, based on the recently introduced concept of time‐varying media, an alternative approach is presented for controlling the compression ratio of an optical pulse in the near‐infrared regime via two all‐dielectric transmissive metasurfaces consisting of a zigzag array of silicon‐based elliptical nanodisks. Upon introducing in‐plane asymmetries and under normal incidence, the supported symmetry‐protected bound‐state in the continuum resonant mode collapses into two Fano resonances, which can be spectrally overlapped to satisfy the first Kerker's condition. To acquire an amplified signal, the desired chirp is applied to the incident pulse via a purely temporal waveform that modulates the optical response of the first layer, while the required group delay dispersion is imparted to the phase‐modulated pulse by the second metasurface in order to compress its temporal distribution. Following such a configuration, the temporal duration of the output pulse decreases from 25 to 15 ps, leading to a peak intensity enhancement of 50%. On account of time‐varying features of the first metasurface, the instantaneous frequency of the chirped light can be controlled dynamically, giving rise to the active tuning of the peak intensity from 0% up to 200%.

A Theoretical Framework of Chorus Wave Excitation

Abstract: We propose a self-consistent theoretical framework of chorus wave excitation, which describes the evolution of the whistler fluctuation spectrum as well as the supra-thermal electron distribution function. The renormalized hot electron response is cast in the form of a Dyson-like equation, which then leads to evolution equations for nonlinear fluctuation growth and frequency shift. This approach allows us to analytically derive for the first time exactly the same expression for the chorus chirping rate originally proposed by Vomvoridis et al.,1982. Chorus chirping is shown to correspond to maximization of wave particle power exchange, where each individual wave belonging to the whistler wave packet is characterized by small nonlinear frequency shift. We also show that different interpretations of chorus chirping proposed in published literature have a consistent reconciliation within the present theoretical framework, which further illuminates the analogy with similar phenomena in fusion plasmas and free electron laser physics.

Attosecond field emission

Abstract: Field-emission of electrons underlies major advances in science and technology, ranging from imaging the atomic-scale structure of matter to signal processing at ever-higher frequencies. The advancement of these applications to their ultimate limits of temporal resolution and frequency calls for techniques that can confine and probe the field emission on the sub-femtosecond time scale. We used intense, sub-cycle transients to induce optical field emission of electron pulses from tungsten nanotips and a weak replica of the same transient to directly probe the emission dynamics in real-time. Access into the temporal profile of the emerging electron pulses, including the duration $\tau$ = (53 as $\pm$ 5 as) and chirp, and the direct probing of nanoscale near-fields, open new prospects for research and applications at the interface of attosecond physics and nanooptics.

Measuring the Joint Spectral Mode of Photon Pairs Using Intensity Interferometry

Abstract: The ability to manipulate and measure the time-frequency structure of quantum light is useful for information processing and metrology. Measuring this structure is also important when developing quantum light sources with high modal purity that can interfere with other independent sources. Here, we present and experimentally demonstrate a scheme based on intensity interferometry to measure the joint spectral mode of photon pairs produced by spontaneous parametric down-conversion. We observe correlations in the spectral phase of the photons due to chirp in the pump. We show that our scheme can be combined with stimulated emission tomography to quickly measure their mode using bright classical light. Our scheme does not require phase stability, nonlinearities, or spectral shaping and thus is an experimentally simple way of measuring the modal structure of quantum light.

Frequency-modulated continuous waves controlled by space-time-coding metasurface with nonlinearly periodic phases

Abstract: The rapid development of space-time-coding metasurfaces (STCMs) offers a new avenue to manipulate spatial electromagnetic beams, waveforms, and frequency spectra simultaneously with high efficiency. To date, most studies are primarily focused on harmonic generations and independent controls of finite-order harmonics and their spatial waves, but the manipulations of continuously temporal waveforms that include much rich frequency spectral components are still limited in both theory and experiment based on STCM. Here, we propose a theoretical framework and method to generate frequency-modulated continuous waves (FMCWs) and control their spatial propagation behaviors simultaneously via a novel STCM with nonlinearly periodic phases. Since the carrier frequency of FMCW changes with time rapidly, we can produce customized time-varying reflection phases at will by the required FMCW under the illumination of a monochromatic wave. More importantly, the propagation directions of the time-varying beams can be controlled by encoding the metasurface with different initial phase gradients. A programmable STCM prototype with a full-phase range is designed and fabricated to realize reprogrammable FMCW functions, and experimental results show good agreement with the theoretical analyses.

ISAR Imaging of a Maneuvering Target Based on Parameter Estimation of Multicomponent Cubic Phase Signals

Abstract: In inverse synthetic aperture radar (ISAR) imaging for a uniformly moving rigid-body target, a finely focused ISAR image can be obtained by using the conventional range-Doppler algorithm. However, the ISAR image quality may significantly deteriorate when the time-vary Doppler phases in virtue of target maneuvering motions are present, such as an airplane with nonuniformly rotation and a ship with fluctuation. This has become a challenging task, especially under nonhigh signal-to-noise ratio (SNR) environment. In this article, a novel ISAR imaging algorithm for a maneuvering target with moderate reflection intensity is proposed. After motion compensation, the radar echo signal in a range cell is modeled as a multicomponent cubic phase signal (CPS), in which the chirp rate and the quadratic chirp rate are two important physical quantities that may determine the target ISAR focusing quality. Based on a symmetrical instantaneous autocorrelation function, the received CPSs are transformed into the time and lag-time plane, and then a 2-D coherent integration can be realized after the generalized time-scaled transform and 1-D maximization. This forms a high-quality ISAR image. The effectiveness and superiority of the proposed algorithm are validated by the ISAR imaging results of simulated and real measured data.

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

Abstract: 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.