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We analytically and numerically investigate the dynamic propagation of the quadratically chirped Airy beams in right-handed material (RHM) and left-handed material (LHM) slabs. Based on the analytical expressions and numerical calculations, we find that through choosing the appropriate value of the quadratic chirp, one can modify the diffraction, the intensity distribution, the propagation path, and acceleration and deceleration of the quadratically chirped Airy beams to meet the actual usage accordingly. In addition, we also demonstrate the effect of the quadratic chirp on the Poynting vector and the angular momentum of the quadratically chirped Airy beams, respectively. Furthermore, we explore the gradient and scattering forces on a Rayleigh dielectric particles induced by the quadratically chirped Airy beams.

Through analytical derivation and numerical analysis, the propagation properties of the chirped Airy(CAi) beams in the gradient-index medium are investigated. The intensity and the phase distributions, the propagation trajectory and the Poynting vector of the CAi beams are demonstrated to investigate the propagation properties. Owing to the special and symmetrical refractive index profile of the gradient-index medium, the CAi beams propagate periodically. The effects of the distribution factor and the chirped parameter on the propagation of the CAi beams are analyzed. As the increasing of the distribution factor, the intensity distribution of the CAi beams is more scattering. However, with the chirped parameter increasing, the focusing property of the CAi beams strengthens. The variation of the chirped parameter can change the position of the peak intensity maximum, but it cannot alter the period of the peak intensity. The variations of the initial phase and the energy of the beams in the transverse plane expedite accordingly.

We present an investigation on the propagation properties of the chirped Airy vortex (CAiV) beams through slabs of left-handed materials (LHMs) and right-handed materials (RHMs). We discuss the influence of chirped parameter C on the propagation of the CAiV beams through LHM and RHM slabs. Our simulation results show that a maximum accelerated velocity appears during the propagation process. The intensity concentration of the CAiV beams increases with the absolute value of the chirped parameter. The peak intensity of the CAiV beams changes abruptly, and the chirped parameter plays an active role on the difference of the maximum and the minimum. In the energy flow, we find that the effects of the chirped parameter on the strength of the vortex are different at different propagation distances.

The retrieval of the extinction coefficients of aerosols and clouds without assumptions is the most important advantage of the high-spectral-resolution lidar (HSRL). The standard method to retrieve the extinction coefficient from HSRL signals depends heavily on the signal-to-noise ratio (SNR). In this work, an iterative image reconstruction (IIR) method is proposed for the retrieval of the aerosol extinction coefficient based on HSRL data, this proposed method manages to minimize the difference between the reconstructed and raw signals based on reasonable estimates of the lidar ratio. To avoid the ill-posed solution, a regularization method is adopted to reconstruct the lidar signals in the IIR method. The results from Monte-Carlo (MC) simulations applying both standard and IIR methods are compared and these comparisons demonstrate that the extinction coefficient and the lidar ratio retrieved by the IIR method have smaller root mean square error (RMSE) and relative bias values than the standard method. A case study of measurements made by Zhejiang University (ZJU) HSRL is presented, and their results show that the IIR method not only obtains a finer structure of the aerosol layer under the condition of low SNR, but it is also able to retrieve more reasonable values of the lidar ratio.

The planetary boundary layer height (PBLH) is a vital parameter to characterize the surface convection, which determines the diffusion of air pollutants. The accurate inversion of PBLH is extremely important for the study of aerosol concentrations, in order to predict air quality and provide weather forecast. Aerosol lidar, a powerful remote sensing instrument for detecting the characteristics of atmospheric temporal and spatial evolution, can continuously retrieve the planetary boundary layer (PBL) and obtain high resolution measurements. However, multi-layer conditions, including one or more layers of aerosol, or cloud above the PBL, can seriously interfere the accuracy of PBLH determined by lidar. A new technique of maximum limited height initialization and range restriction (MLHI-RR) is proposed to eliminate the impact of multi-layer conditions on PBLH determination. Four widely used methods for deriving PBLH are utilized, in addition to the MLHI-RR constraint. Comparisons demonstrate that the proposed technique can determine the PBLH in multi-layer conditions with higher accuracy. The proposed technique requires no affiliate information besides lidar signals, which provide a convenient method for PBLH determination under complicated conditions.

With the transfer matrix method, analytical expressions of radially and azimuthally polarized chirped-Airy vortex beams (RPCAiVBs and APCAiVBs, respectively) through right-handed materials and left-handed materials are derived. We mainly discuss the effects of the radial and azimuthal polarizations as well as the effects of the chirped parameter on the propagation properties, including the propagation trajectory, the transverse intensity and the phase distributions, the peak intensity, the radiation forces, and the transverse orbital and spin currents of the RPCAiVBs and APCAiVBs in the x direction, the y direction, and their synthesizing direction. It is shown that the x, y, and synthesizing directions of the RPCAiVBs and APCAiVBs satisfy the vector synthesis rule, owing to the axial symmetry, and intensity modulation of the RPCAiVBs and APCAiVBs can be achieved by varying the chirped parameter.