Chirp Factor Research Articles

Propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam in the fractional nonlinear Schrödinger equation

We present the propagation dynamics of the second-order chirped circular Pearcey Gaussian vortex beam (CCPGVB) in the Fractional nonlinear Schrödinger equation (FNSE) numerically and find some interesting behaviors. The CCPGVB can propagate like quasi solitons along the propagation direction. The autofocusing effect of the CCPGVB gets stronger while the autofocusing length monotonously decreases and the number of focus become lessen as the Lévy index approaches 2. By adjusting the Lévy index, the chirp factor β, the input power Pin, as well as the order of the off-axis vortex pair (m,l), the results show that these factors can effectively control the propagation dynamics of the CCPGVB, including intensity distribution, focal length, focal intensity, the light spot and the number of focus. Finally, the Poynting vector and the angular momentum of the CCPGVB prove the autofocusing and diffraction behaviors.

Propagation of spatiotemporal Airy-Laguerre complex-variable-function Gaussian wave packets in a chiral medium

We analyze the propagation of spatiotemporal Airy-Laguerre complex-variable-function Gaussian (ALCG) wave packets using phase modulation. These wave packets can split into left circularly polarized ALCG (LCP-ALCG) and right circularly polarized ALCG (RCP-ALCG) components due to circular birefringence in a chiral medium. Our discussion primarily focuses on the effects of polynomial order, angle parameters, distribution factor, cross-phase factor, first-order chirp factor, and chiral parameter on the ALCG wave packets. The distinct LCP-ALCG and RCP-ALCG wave packet characteristics are obtained, and the radiation forces on Rayleigh dielectric particles are investigated. Our results emphasize the influence of various parameters in the propagation properties of ALCG wave packets, unveiling their potential for advancements in optical communication and optical trapping domains.

Evolution of the Masked Pearcey beams array with the second-order chirp factor in Kerr medium

We introduce the evolution characteristics of the Masked Pearcey beams array (MPBA) with the second-order chirp factor in Kerr medium, and discuss the evolution characteristics of the MPBA with different absolute values of the second-order chirp factor and the initial plane energy structure in detail. The results show that the MPBA with the second-order chirp factor can form a stable breath-like structure under appropriate input power, and eventually form a filament with the increase of input power. Meanwhile, increasing the absolute value of the second-order chirp factor can help us to obtain a shorter distance filament. In addition, with the increase of the number of superposition, the critical power of the formation of the breath-like structure gradually decreases. It is worth noting that by adding a circular aperture and choosing a suitable input power, the MPBA with the second-order chirp factor will form multiple breath-like structures in Kerr medium.

Multifocal tornado beams carrying chirality

The significance of abruptly autofocusing vortex beams with a unique helical phase structure lies in particle trapping and optical spanner applications. This paper presents a novel modulation of a circular Pearcey beam utilizing a multicyclic helical phase and a chirp factor. Both theoretical analyses and experimental results demonstrate that we have successfully designed a beam with tornado properties and optically chiral structure. This beam has multidimensionally tunable parameters, allowing not only different focusing intensities, focal lengths and focal spot shape distributions, but also controllable rotational propagation directions. Furthermore, it has the ability to produce two dual focusing modes with dissimilar focal spot distributions. We believe that such a beam holds potential applications in the realisation of optical spanners, multi-region trapping of particles and the fabrication of chiral metamaterials.

Spatiotemporal Airyprime complex-variable-function wave packets in a strongly nonlocal nonlinear medium.

A type of circular Airyprime function of complex-variable Gaussian vortex (AFCGV) wave packets in a strongly nonlocal nonlinear medium is introduced numerically, combining the properties of helicity states and abrupt autofocusing. We investigate the effects of the chirp factor, distribution parameter, and decay factor on the AFCGV wave packets in the strongly nonlocal nonlinear medium. Interestingly, by adjusting the distribution parameter, the AFCGV wave packets can exhibit stable rotational motions in various shapes, such as symmetric lobes and doughnuts. In addition, the Poynting vector and the gradient force of the AFCGV wave packets are also discussed. Our research not only explains the theoretical model for controlling AFCGV wave packets but also advances fundamental research on self-bending and autofocusing structured light fields.

Multioptical bottles from the chirped circular Bessel Gaussian beams carrying annular spiral-zone power-exponent-phase

In this paper, we introduce a new structure of multioptical bottles formed by the chirped circular Bessel Gaussian beams carrying annular spiral-zone power-exponent-phase (ASP). The ASP is a general term for complex phases composed of the radial phase, equiphase, and power spiral phase. By combining the influence of autofocusing properties, chirp factor, and ASP mode, the propagation dynamics of the proposed multioptical bottles beam such as the sizes, lengths, number and locations can be flexibly manipulated. Intriguingly, the effect of the power order of ASP mode on the beam propagation dynamics is firstly introduced and examined. The proposed beams can enable diversification the optical tweezers system in multiparticle manipulation, which is verified by the radiation force analysis on a Rayleigh particle.

Role of chirped factor on the focusing and imaging properties of the autofocusing beam

The focusing and imaging properties of the beam have attracted considerable attention recently. In this work, we generated an autofocusing beam termed a chirped autofocusing beam (CAFB) by using the phase of multiple chirped two-dimensional Airy beams, which has autofocusing and imaging properties. Through simulation analysis and experimental verification, it was found that the CAFB is endowed with multiple degrees of freedom to control the focusing properties of the CAFB. Specially, in the range of negative and weak chirp, the focal length of the CAFB increases with decreasing chirped factor. Moreover, the imaging property of the CAFB can be controlled by a chirp factor, the transverse displacement of the CAFB, and the transverse scale factor of the CAFB. The larger the transverse displacement and transverse scale factor of the beam, the better the image quality. Due to these properties, the CAFB may broaden the potential applications in optical microscopy imaging.

Propagation dynamics of the controllable circular Airyprime beam in the Kerr medium.

In this paper, we study the propagation dynamics of the circular Airyprime beam (CAPB) in the Kerr medium for the first time. We investigate the effects of the astigmatism factor, the chirp factor, and vortices on the CAPB propagating in the Kerr medium. At the same time, we are also introducing a special-shaped Airyprime beam (SAPB) during its propagation. The transmission characteristics of the CAPB and the SAPB in the Kerr medium are compared under identical conditions. Our theoretical results provide additional possibilities for CAPB modulation in the Kerr medium, thereby promising wider applicability of CAPB in various research areas.

Key to an extension or shortening of focal length in the enhancement of autofocusing ability of a circular Airyprime beam caused by a linear chirp factor.

Researchers are puzzled whether the enhancement of the abruptly autofocusing ability caused by a linear chirp factor is accompanied by the shortening or the extension of the focal length. In this Letter, a circular Airyprime beam is chosen as the research object to reveal this mystery. Extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability depends on the exponential decay factor a and the dimensionless radius of the primary ring. When a is small enough, there exists a critical value for the dimensionless radius. If the dimensionless radius is greater than the critical value, the focal length is shortened in the enhancement of the abruptly autofocusing ability. If the dimensionless radius is less than the critical value, the focal length is extended in the enhancement of the abruptly autofocusing ability. As a increases, the critical value for the dimensionless radius decreases until it reaches zero. The physical mechanism of extension or shortening of the focal length in the enhancement of the abruptly autofocusing ability is elucidated.

Nonparaxial propagation and the radiation forces of the chirped circular Airy derivative beams.

In this paper, we investigate the nonparaxial propagation dynamics of the chirped circular Airy derivative beams (CCADBs) based on vector angular spectrum method. In the case of nonparaxial propagation, the CCADBs still maintains excellent autofocusing performances. Derivative order and chirp factor are two important physical quantities of the CCADBs to regulate the nonparaxial propagation characteristics, such as focal length, focal depth and K-value. In the nonparaxial propagation model, the radiation force on a Rayleigh microsphere induced the CCADBs are also analyzed and discussed in detail. The results demonstrate that not all derivative order CCADBs can achieve stable microsphere trapping effect. The derivative order and chirp factor of the beam can be used to coarse and fine tune the capture effect of Rayleigh microsphere, respectively. This work will contribute to the more precise and flexible use of circular Airy derivative beams in optical manipulation, biomedical treatment and so on.

Periodic oscillation behavior of chirped cosh-Gaussian beam in parabolic potential

In this paper, based on the normalized linear Schrödinger equation, we analytically and numerically investigate the propagation dynamics of cosh-Gaussian beams in a medium with parabolic potential. The obtained results show that cosh-Gaussian beams perform a periodic oscillation behavior and the parabolic potential determines the focusing ability, including the focal distance as well as peak intensity at the focus. Especially, the intensity distributions of cosh-Gaussian beam are related to the initial parameter. We also demonstrate the effect of chirp factors on the beam and find the periodic oscillating behavior caused by linear chirp can be used to manipulate the propagation trajectory. The influence of quadratic chirp on the evolution of beam is also discussed and we find that it plays a significant role in the modulation of the energy localization.

Distributed optical fiber sensing in coherent Φ-OTDR with a broadband chirped-pulse conversion algorithm.

We propose a broadband chirped-pulse conversion algorithm (BCPCA) to convert a finite-step scanning probe pulse into an equivalent broadband chirped probe pulse by convolving a chirp factor on the received signal in coherent phase-sensitive optical time domain reflectometry (Φ-OTDR). Combined with Rayleigh interference pattern (RIP) demodulation in chirped-pulse Φ-OTDR (CP-ΦOTDR), environmental perturbations, such as strain and temperature along the sensing fiber, can be quantitatively measured. The equivalent broadband chirped pulse is generated by digital processing, and its bandwidth can be increased by changing the composition of the scanning pulse. Thus, the measurable perturbation range of the system can be expanded. As a proof-of-concept experiment, a high-performance distributed strain measurement was realized on a 10 km fiber, the frequency response was 5 kHz, which is only limited by the fiber length, and the strain resolution was 8.04 p ε/H z. The proposed method of generating equivalent broadband chirped pulse through the digital domain can be used as a supplement to CP-ΦOTDR.

Generation and control of multiple optical bottles from chirped Airy–Gaussian vortex beams: theory and experiment

New structures in the form of multiple optical bottles (OBs), produced by the chirped Airy–Gaussian vortex beams (CAGVBs) in free space, are derived numerically and experimentally. By selecting appropriate parameters, multiple OB structures with different sizes, different locations, and amounts of individual ‘bottles’ in them are produced. These characteristics of the output can be adjusted by selecting the chirp factor, width, and topological charge of the input beams, as well as by offset of the embedded vortices from the central position. In this work, we address the structured built of one, two, three and four OBs. The produced beams demonstrate the self-healing effect, restoring their complex shape after hitting an obstacle. Experimental results are consistent with the numerical ones, directly demonstrating the creation of OBs and their ability to trap and keep microparticles, offering the potential for the use in optical tweezers.

Autofocusing field constructed by ring-arrayed Pearcey Gaussian chirp beams.

In this work, we propose and demonstrate the ring-arrayed Pearcey Gaussian chirp beams (RAPGCBs) synthesized by multiple two-dimensional Pearcey beams. The general analytical formula for the propagation of RAPGCBs is presented. We find that, depending on synthesized number n, the profiles of the beams present different polygonal shapes, and the autofocusing properties can be controlled by chirp factor β. Furthermore, we study the properties of the RAPGCBs carrying optical vortices (OVs). It shows that a single OV or two positive OVs form an autofocusing hollow field, and opposite OVs will annihilate, which results in greatly increased autofocusing ability. Our experimental results agree with the simulations. Such beams have potential applications in particle trapping and biology medical fields.

Broadband optical frequency comb generation based on single electro-absorption modulation driven by radio frequency coupled signals

Broadband optical frequency comb (OFC) generation based on a single electro-absorption modulator (EAM) is proposed. The EAM is driven by a radio frequency (RF) multi-frequency signal generated by a multiplication coupler composed of an electrical power splitter and an arithmetic circuit. Thus the number of comb-lines of the generated OFC can be increased. A complete theoretical model of OFC generation by an EAM driven by nth power of the RF source is established, and the performance of the OFC is analyzed by using OptiSystem software. The results show that, the number of comb-lines of the OFC is positively correlated with the number of multiplication of the RF source signal. The frequency spacing of the comb-lines is twice the frequency of the RF source signal and is tunable by adjusting the frequency of the RF source signal. Increasing chirp factor and modulation index of EAM could increase the number of comb-lines of the generated OFC. The amplitude of the RF source signal had little impact on the flatness of the OFC and the average OFC power. The scheme developed is not only simple and low-cost, but also can produce a large number of comb-lines.Graphical

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.

Paraxial Propagation Properties of Symmetric Dual Pearcey Gaussian Beams in Free Space

AbstractIn this article, a new kind of symmetric dual Pearcey Gaussian beam (SDPGB) is introduced and their properties of auto‐focusing, self‐similarity, inversion, and self‐healing are discussed. The self‐similarity, the auto‐focusing, and the inversion properties of the propagating SDPGBs are turned out by analytical derivation and experimental observation. Additonally, a second‐order chirp factor for SDPGBs is introduced to investigate their secondary auto‐focusing and abrupt auto‐focusing properties in further detail. Finally, the effects of the obstacle diameter and the obstacle placement plane on the self‐healing of the SDPGBs are discussed.

The effect of chirp parameter on laser propagation in collisional quantum plasma

This manuscript investigates the effect of the chirp factor on the relativistic self-focusing of a Gaussian chirped pulse laser in collisional quantum plasmas. Nonlinear equations are derived to describe the propagation of a linear chirped laser frequency; afterward, by considering dielectric function obtained by quantum kinetic equation and BGK collision integral in coordinate space, evolution differential equations of laser beam width are found; and numerically solved by the fourth-order Runge-Kutta method. It studies oscillations of the beam width along the propagation direction for different values of collision frequency, chirp parameter, plasma density, and laser intensity. Numerical analyses show that a laser beam is defocused after focusing on a definite value; nonetheless, the positive chirp parameter could reduce the defocusing and strengthen the self-focusing in collisional quantum plasma. Also, the higher chirp value leads to a smaller oscillation amplitude and a greater oscillation rate. Furthermore, the self-focusing effect becomes stronger by increasing plasma density and laser intensity. These consequences could be beneficial in the improvement of fast ignition experiments.

The multi-consecutive optical bottles generated from the chirped elliptical Pearcey Gaussian vortex beams

The evolution of the chirped elliptical Pearcey Gaussian vortex (CEPGV) beams in free space is numerically investigated. The optical bottle and multi-consecutive optical bottles can be directly generated from an elliptical Pearcey Gaussian beam with central vortices and the second-order chirp. In particular, the focusing intensity of CEPGV beams will increase when the elliptical structure deflects larger or the ratio of the long axis to the short axis of the ellipse is larger. Furthermore, we can obtain multi-consecutive optical bottles by manipulating elliptical structure parameters and second-order chirp factors. In the meantime, the transverse intensity distributions at foci of CEPGV beams appear like a slit in a fixed direction. Our results show that the focusing intensity, the focal length and the transverse intensity distribution of CEPGV beams during the propagation can be controlled.

Single polarization, narrow linewidth hybrid laser based on selective polarization mode feedback

We demonstrate a single polarization, narrow linewidth hybrid laser by using a semiconductor gain chip and a birefringence silica-on-silicon waveguide Bragg grating. The hybrid laser shows good linewidth and single polarization characteristics with the selective polarization mode feedback of high birefringence grating. The temperature phase modulation on the characteristics of the potentially lasing modes is displayed. In addition, the performances of different mode power, side mode suppress ratio, spectrum and linewidth during temperature tuning are characterized. We based on the rate equation method and the chirp factor reduction theory analysis the variation of laser linewidth with power and lasing wavelength. The best linewidth achieves 4.36 kHz and the best polarization extinction ratio is 38.6 dB. The output power in fiber is 6.58 mW.