Channeled spectropolarimeter (CSP) measures the spectrally resolved Stokes vector of light from only one single spectral acquisition, which makes it possible to accurately measure dynamic events. The accurate reconstruction of Stokes vector plays a key role in this snapshot technique shifting the main burden of measurement to computational work. The state-ofthe-art algorithm runs the Fourier transform of the channeled spectrum or linear operator model of the system and its pseudo-inverse to reconstruct Stokes vector. However, they may suffer from the lack of signal-to-noise ratio (SNR) then reduce the accuracy of reconstruction. To accurately reconstruct Stokes vector from noise-contaminated data, we propose an effective method called fast compressed channeled spectropolarimeter (FCCSP). In our FCCSP method, the spectrum from spectrometer is seen as the compressive representation of Stokes vector, thus the FCCSP algorithm is to solve an underdetermined problem, where we reconstruct the 4N×1 Stokes vector from only N×1 spectral data acquisition points. Simulation results show that our FCCSP method is more accurate to reconstruct Stokes vector changing gradually with wavelength from noise-contaminated spectrum than Fourier and linear operator methods. Besides, it is faster and more memory and computation-friendly than other compressed CSP method.
Vortex beams have drawn much attention for their distinct properties. When vortex beams propagate along optical axis, they exhibit complicated physical phenomena. Under tight focusing condition, we investigate the defocusing behavior of two superposed vortex beams with opposite but arbitrary topological charge. The results reveal that the intensity distribution of the focus will be petal-shaped if the two topological charges have opposite sign, where the number of intensity lobes in the focal plane is |<i>m</i>− <i>n</i> + 2| . Meanwhile, we find that the focusing intensity of topological charge <i>m</i> = −<i>n</i> would not appear the helical structure when a defocusing occurs. Otherwise, the defocusing would result in the helical structure of intensity when <i>m</i> ≠ −<i>n</i> , and the rotation of helical structure depends on the sign of <i>m</i> + <i>n</i> . Of which clockwise rotation of defocus intensity is related to the negative <i>m</i> + <i>n</i> , and anti-clockwise direction corresponds to the positive <i>m</i> + <i>n</i> . Furthermore, the helical degree of the helical intensity also depends on the magnitude of <i>m</i> + <i>n</i> . The interesting results obtained in this paper will lead to further advances in the field of optical vortices.
Optical vortices have been applied in many fields for their distinct properties. In this paper, we explore the focusing intensity distribution of the radially and azimuthally polarized vortex beam (VB) with varying beam waist parameter. The results reveal that low beam waist parameter is beneficial to form a super-resolution spot. In the condition of the high beam waist parameter, the focusing intensity of radially and azimuthally polarized VB along the longitudinal direction would split to multi-spots. Meanwhile, the focal plane intensity distribution become non-symmetrical as well as expansion when the beam waist parameter increase. Therefore, appropriate beam waist must be chosen for the two kind beam in actually application. Furthermore, we also investigate the focal properties affected with helical phase TC. The results reveal that the focal spot size of radially polarized VB along the longitudinal gradually increases with the order of helical phase. The peak intensity ratio of the longitudinal and transverse field of radially polarized VB holds a maximum value when helical phase order l = 0 and becomes to minimum when l =1 , then gradually increases with the order of helical phase. For the azimuthally polarized VB, when l =1 , the focal intensity would exhibit an excellent small solid spot. The results obtained in this paper are useful for application of radially and azimuthally polarized VB.