Initial Chirp Research Articles

Generation and control of optical rogue waves by super-Gaussian pulses with varying steepness

We investigate the dynamics of optical rogue waves induced by super-Gaussian (SG) pulses in fiber optics. SG pulses with controlled steep leading and trailing edges can produce high-intensity self-focusing when propagating in nonlinear fibers with weak dispersion and strong nonlinearity. We observe the emergence of various rogue waves, including Peregrine breathers, Akhmediev breathers (ABs), and second-order ABs. By adjusting the steepness of the SG pulses, the generation of these rogue waves can be controlled. As the steepness of the SG pulse increases, we find the fundamental-order AB can stably coexist. Simultaneously, we reveal that the period of these ABs can be effectively controlled by adjusting the steepness of the SG pulse. At a certain steepness, the second-order AB with high power can also be observed. We also investigated the propagation of SG pulses with an initial chirp in fiber optics and found that they can also control AB and second-order Peregrine breathers. To our knowledge, our findings present a new approach to generating controllable rogue waves.

Coherence evolution of multi-pulse pumped supercontinuum generation in all-normal dispersion fibers.

We numerically calculate the coherence of supercontinuum (SC) spectrum generated in all-normal dispersion (ANDi) fibers by multiple picosecond pulses. We show that multi-pulse pumping significantly mitigates the phenomenon of coherence degradation and maintains high spectral coherence over a broader wavelength range compared to the single pumping. It is found that inter-pulse four-wave-mixing (FWM) and stimulated Raman scattering (SRS) significantly contribute to the superior coherence characteristics of the SC. We further discuss the impact of key parameters on the multi-pulse pumped SC. Results indicate that a large temporal interval between pulses reduces spectral broadening efficiency, while closely spaced pulses generate a significant number of incoherent photons, severely degrading spectral coherence. Introducing initial chirp effectively mitigates this coherence degradation. A slight increase in the dispersion parameter notably suppresses the spectral broadening efficiency of the multi-pulse generation. Pulse shape primarily affects the SC shape without significantly impacting the spectral broadening efficiency.

Abrupt focus and bright spot formation in fractional system with PT-symmetric nonlocal nonlinearity

Abstract We study the dynamics of Gaussian beams in fractional system with PT-symmetric nonlocal nonlinearity. It is found that the Gaussian beam with transverse displacement can abruptly focus to form bright spot in one sub-branch after experiencing a symmetric split, depending on the nonlinear intensity, initial launched amplitude, angle and chirp of the beam, and the initial chirp can shift the time of abrupt focus and bright spot formation. Furthermore, the Talbot-like effect and breather train are explored by setting the initial amplitude parameter of every component of an initial Gaussian beam train. Moreover, for longitudinally periodically modulated nonlinearity, the bright spots can be formed periodically and asymmetrically in two sub-branches for a single Gaussian beam, and Moiré-like lattices can be generated for a Gaussian beam train. Finally, the conical diffraction and crescent-like evolution in the two-dimensional system are investigated in detail. It is found that the direction of crescent-like evolution is determined by the initial launched angles, which may be an inspiration to design channel path through choosing suitable initial launched angles at will.

Reflection and refraction of a super-Gaussian optical pulse at a moving temporal boundary

We investigate the transmission properties of super-Gaussian pulses at a moving temporal boundary. The incident spectrum of super-Gaussian pulses, determined by different shape parameters, affects the reflected and transmitted pulse energy and the sidelobes distribution after crossing the temporal boundary. When the incident pulse is an initial unchirped super-Gaussian pulse or a super-Gaussian pulse with a small chirp parameter, the reflected pulse energy increases and the transmitted pulse energy decreases as the incident pulse shape parameter increases. When the incident pulse with a initial chirp and |C|≥2, the incident pulse spectrum mainlobe energy increases as the shape parameter increases, resulting in reflected pulse energy decreases and transmitted pulse energy increases. This study also discusses the pulse splitting occurs in the anomalous dispersion region. The super-Gaussian pulse sidelobes can theoretically be removed by creating two temporal boundaries.

Estimation of LFM signal parameters using RD compressed sampling and the DFRFT dictionary

In this paper, a method combining random demodulator (RD) and discrete fractional Fourier transform (DFRFT) dictionary is suggested to directly estimate the parameters of linear frequency modulation (LFM) signals from compressed sampling data. First, the RD system parameters are modified in accordance with the characteristics of the LFM signal to produce effective compressed sampling data. Next, a DFRFT dictionary is built using the fractional Fourier transform theory, and sparse representation coefficients are obtained by reconstructing the compressed sampling data using the recovery algorithm and DFRFT dictionary. The signal exhibits characteristics that make it pulse under the best fractional transform order, so the problem of signal parameter estimation can be reduced to searching for the location of the maximum value of sparse representation coefficients. The location is determined by a parameter optimization algorithm, and from there, the initial frequency and Chirp rate of the LFM signal can be estimated. Lastly, simulation and real data tests are performed to confirm that the suggested method can directly be utilized to estimate the parameter of LFM signals using compressed sampling data in addition to having high sparse representation ability for LFM signals.

Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Crystal Fiber with Three Zero-Dispersion Points

The supercontinuum generation and manipulation of Airy-Gaussian pulses in a photonic crystal fiber with three zero-dispersion points are studied using the split-step Fourier method. Firstly, the spectral evolution of Airy-Gaussian pulses in four photonic crystal fibers with different barrier widths was discussed, and the optimal fiber was determined after considering the factors of width and flatness. By analyzing the mechanism of supercontinuum generation in photonic crystal fibers with single, double and three zero-dispersion points, it is found that the photonic crystal fiber with three zero-dispersion points have a larger spectral width due to the component of tunneling solitons. Then, the effects of four characteristic parameters (truncation factor a, distribution factor χ0, initial chirp C and central wavelength λ) on forming the supercontinuum spectrum of Airy-Gaussian pulses are analyzed in detail. The results show that the spectral width and energy intensity of the dispersive wave and tunneling soliton generation can be well controlled by adjusting the barrier width and initial parameters of the pulse. These research results provide a theoretical basis for generating and manipulating high-power mid-infrared supercontinuum sources.

Flying focus laser Wakefield scheme for efficient acceleration

The acceleration of charged particles with a short laser pulse is a revolutionary acceleration technology, but many restrictions limit their advantages. Wave breaking and dephasing are most important of these restrictions which weaken acceleration efficiency in the laser Wakefield acceleration scheme. The purpose of this paper is to demonstrate that flying focus laser Wakefield acceleration (FF-LWFA) can confirm this effectiveness. Flying focus creates in the focal region of a hyper-chromatic lens when the chirped laser pulse passing through them. Therefore, by controlling the lens chromaticity and initial chirp characteristics, the focal point velocity can be controlled and adjusted near the speed of light. For a realistic working parameter, two-dimensional simulation results show the flying focus pulse can retain its shape and energy within a few centimeters (one order of magnitude greater than Rayleigh's length). We introduce a velocity interval around velocity of light in which dephasing and wave breaking are restricted and high acceleration gradients (about a hundred of GeV/m) are achieved in the flying focus region. Moreover, in the optimized condition for negative chirp, wakefield amplitude is increased 50 %. Under this ideal situation, 0.5 % of background electrons accelerate to 2GeV in the 5 cm, where the acceleration gradient reaches to, 40GeV/m, and about 0.2 % of them accelerate up to 10GeV.

Impact of higher-order effects on the stationary and pulsating localized soliton in a nonlinear and dissipative medium

In this paper, we have investigated by numerical solution of the basic equation as well as by the dynamical model the influence of higher-order effects on the dissipative soliton mapping in the complex cubic-quintic Ginzburg–Landau equation (CCQGLE). We generated stationary and pulsating solutions, localized and delocalized from the equilibrium point. This was done using a mathematical formula developed on the basis of our finite degree of freedom dynamical model. This formula linking all the parameters of disturbance, allowed us to explain certain phenomena. It presented several aspects under the influence of the fourth-order dispersion. It was shown that long-lived pulsed solutions with relatively small fluctuations can be considered as nonlinear solutions. We found that the limit cycle that appeared was faster in the case where the initial frequency was zero and the initial chirp was non-zero. The higher-order effect that moved the trajectory away from the limit cycle was compensated by another effect (the nonlinearity compensated the dispersion). The oscillations were maintained (oscillation of the energy around a fixed value) thanks to the stable limit cycles and we obtained preserved structures over long distances. In the presence of noise, we found that the structure was more robust in the self-frequency shift case compared to the fourth-order dispersion case. The resulting pulsating solutions are distorted and frequency shifted. The self-frequency shift allowed us to modify the initial pulse by changing its amplitude, frequency and bandwidth. Intrapulse Raman scattering allowed us to have a large stability domain. All higher-order effects can influence the dynamics of the initial pulse. A comparison between the results obtained by the basic equation and the dynamical model was presented to verify its applicability. These results allow us to transmit information over long distances.

Parameters estimation of hybrid modulated signal combining BPSK and LFM Based on Born-Jordan Distribution

Aiming at the problem of the estimation of hybrid modulated signal combining Binary Phase Shift Keying and Linear Frequency Modulation (LFM-BPSK), the existing methods have low estimation accuracy in low SNR. To solve this problem, the algorithm based on Born-Jordan time-frequency distribution (BJD) is proposed, which uses the Hough transform (HT) to estimate the initial frequency and chirp rate of LFM-BPSK signal, and then estimates the code element width by dimensionality reduction time-domain signal. Finally, simulation experiments show that the parameter estimation accuracy of the proposed algorithm under low SNR is significantly better than that of existing algorithms, and the performance is close to MCRLB.

Chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating upwards in the atmosphere

The chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating from the ground through the atmosphere to the space orbit are studied. The analytical expressions of the additional chirp caused by group-velocity dispersion (GVD) and self-focusing effects in the atmosphere are derived, respectively. It is shown that the behavior of the additional chirp caused by GVD effect is quite different from that caused by self-focusing effect. On the other hand, it is found that there exists a minimum of pulse width on the target when a certain negative initial chirp arrives. In particular, it is demonstrated that the beam quality on the target can be optimized (i.e., the target intensity can be improved and the temporal pulse splitting on the target can be avoided) by the preliminary chirp method.

A method for LFM signal parameter estimation based on MWC system and STFT-DPT

A method of estimating linear frequency modulation (LFM) signal parameters using compressed sampling (CS) data of a Modulated Wideband Converter (MWC) system is proposed. The short-time Fourier transform algorithm is used to analyze the CS signal of the MWC system, and the obtained CS signal frequency will present a form of multi-segment distribution. By intercepting the CS signal corresponding to the first segment frequency and analyzing the intercepted segment signal with discrete polynomial transform and Rife algorithm, the chirp rate and initial frequency estimation of the segment CS signal can be preliminarily estimated. According to the random sequence with cyclic displacement, the spectrum shift relationship between the input signal and the output signal can be calculated. Therefore, the parameter of the original signal can be estimated by using single channel CS data. Then, all channels are analyzed with the same method, and a more stable parameter estimation result can be obtained than the single channel output. Finally, combined with the simulation experiment, the proposed method can be used to estimate the initial frequency and chirp rate of the LFM signal using CS data effectively.

Generation and Manipulation of Airy Breathing Solitons in an Inhomogeneous Medium with Periodic Potential

The propagation characteristics of Airy beams in an inhomogeneous medium with periodic potential are studied theoretically and numerically. The Gross–Pitaevskii equation was solved with periodic potential using the separating variables method, and a breathing soliton solution and the breathing period were obtained. Further, the propagation properties of an Airy beam, and the interaction between two Airy beams while considering the medium parameters and beam parameters were numerically simulated in detail. First, we discuss the influence of the initial medium parameters (modulation intensity P and modulation frequency ω) on the propagation characteristics. Then, we investigate the effect of the initial beam parameters (initial chirp C and position x0) on the propagation characteristics. Lastly, the interaction of two Airy beams with opposite spatial positions for different phase φ, amplitude A, and initial interval x0 is analyzed. The breathing period and central position of the breathing solitons could be controlled by changing the initial medium parameters. By varying the initial beam parameters, the deflection direction and size, and the maximal intensity of the breathing solitons were manipulated. The breathing solitons of different bound states were formed by changing the phase φ, amplitude A, and initial interval x0 of two Airy beams. The results provide a theoretical basis for the propagation and manipulation of Airy beams.

Soliton self-frequency shifts control via Pearcey Gaussian pulses in GRIN fiber

We numerically investigate the nonlinear propagation dynamics of the Pearcey-Gaussian (PG) pulse in the presence of spatial self-imaging and Raman scattering effects in a Graded-index (GRIN) multimode optical fiber. We demonstrate that the Raman-induced frequency shift (RIFS) can be effectively controlled when PG pulse is incident. We find that the decrease of parameter can lead to the increase of full width at half maximum (FWHM) of the red-shifted solitons and RIFS of PG pulses. In addition, the effects of the FWHM of the incident pulse and the initial chirps of the PG pulse on the RIFS are also considered. These results can broaden the application range of PG pulses in RIFS-based tunable light sources, optical communication and spectroscopy, and provide some inspiration for the PG and its derivative pulses in other nonlinear optical systems.

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

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.

A Method Based on Random Demodulator and Waveform Matching Dictionary to Estimate LFM Signal Parameter

The compressed sampling theory provides a good idea for sampling broadband linear frequency‐modulated (LFM) signal, but the signal reconstruction after sampling should be considered when using the compressed sampling system to sample the signal. For the problem of estimating the parameters of the LFM signal under the condition of nonreconstruction, a method combining random demodulation (RD) and waveform matching (WM) dictionary is proposed in this paper. Firstly, the RD system is used to collect the compressed sampling data of LFM signal. In order to ensure the validity of the compressed sampling data, the value of the compressed sampling rate R in the RD system is discussed. Then, the feasibility of using compressed sampling data to estimate LFM signal parameters is theoretically demonstrated. According to the construction principle of waveform matching dictionary, the corresponding relationship between sparse representation coefficients, dictionary atoms, and signal parameters can be determined. Using this theory, the LFM signal parameters can be estimated. Finally, simulation and real signal experiments verify that the proposed method can realize the estimation of initial frequency and chirp rate of LFM signal when some prior information is known.

Chirped soliton fission and fusion in dispersion oscillating fibers

We found that pre-chirp of initial pulses allows to control both the fission and fusion of solitons in dispersion oscillating fiber characterized by a sinusoidally varying group velocity dispersion. The fission of second order solitons and collision of two co-propagated solitons are considered. It is shown that initial chirp can prevent the resonant fission of second order soliton into two pulses propagating with different group velocities. Inelastic collision of two in-phase solitons is found can be quite different, when the chirp imposed on initial pulses. The soliton transformation reflects in the set of output eigenvalues of the Zakharov–Shabat spectral problem. Manipulation of the input pulse chirp allows to control both real and imaginary parts of the eigenvalues at the output of the fiber.

Theoretical Analysis of Spectral Broadening Through Saturable Photoexcited-Carrier Refraction in Graphene-Covered Nanowires

We perform a thorough study of the spectral broadening of short and intense pulses propagating in graphene- covered nanowires departing from a saturable photoexcited-carrier refraction (SPCR) model. In particular, we put forth an analytical expression for the instantaneous frequency of the traversing pulse, in a relevant limiting case, which allows to calculate the spectral broadening and frequency shift experienced by the pulse and elucidate the role of its initial chirp. Most interestingly, both the spectral broadening and frequency shift are found to be maximized for an optimal input power. In all cases, results from analytical expressions are found to be in excellent agreement with numerical solutions of the propagation equations.

Mutual manipulation between a dark soliton and an Airy pulse at the optical event horizon

A fiber-optical analog of the event horizon is proposed via the collision dynamics between a dark soliton and an Airy pulse for the first time, under the effect of soliton-induced Kerr nonlinear effect. An Airy wave packet is more effective in manipulating the properties of a dark soliton than a Gaussian-like pulse in the regime of the optical event horizon since the Airy-soliton horizon can be regarded as the successively isolated horizon processes. Besides, the initial chirp and attenuation factor are two key regulators of the Airy pulse, which can not only adjust the flatness and width of the output spectrum during the collision process but also modify the properties of the output dark soliton. The interesting dynamic investigated in this work as a process of mutual manipulation can be considered as a promising candidate for frequency conversion and broadband supercontinuum generation, which proves the theory basis for further understanding of the light-by-light controlling in a more controllable manner.

Manipulation of Long-Distance femtosecond laser Filamentation: From physical model to acoustic diagnosis

The promising application of femtosecond laser filamentation in atmospheric remote sensing brings imperative demand for diagnosing and controlling the spatiotemporal dynamics of long-distance filamentation. Here, the acoustic method was adopted to quantitatively diagnose the long-distance filamentation of femtosecond pulses manipulated by energy and temporal domain. The onset and length of filament can be conveniently obtained from a simple analytic formula based on reasonable approximation and further demonstrated by the experimental results. The influence of pulse energy and initial pulse chirp under three different focal lengths (∼10 m, 20 m, and 30 m) on the filamentation in the air were studied experimentally. These findings provide a guiding significance for the optimal control of the long-distance propagation of filament, thereby laying a firm foundation for femtosecond laser-based atmospheric remote sensing.

Controllable focusing behavior of chirped Pearcey-Gaussian pulses under time-dependent potentials.

We investigate the propagation dynamics of the Pearcey-Gaussian (PG) pulses in the presence of time-dependent potentials in a linear medium both theoretically and numerically. We demonstrate that the combination of the linear potential and the initial chirp of PG pulses can flexibly control the propagation trajectory and inherent focusing properties of the PG pulses. When the parabolic potential is taken into account, the chirped PG pulses are periodically focused and reversed. By adjusting the parabolic potential and the pulse chirp, the characteristics of the focal points, such as position, intensity, and spacing between focal points, can be manipulated effectively. The interaction of two temporally separated PG pulses still shows a periodic evolution with controllable focusing characteristics. These results can broaden the application range of PG pulses and provide some inspiration for the control of PG pulses under nonlinear conditions.