Optical trapping techniques hold great interest for their advantages that enable direct handling of nanoparticles. In this work, we study the optical trapping effects of a diffraction-limited focal field possessing an...Optical trapping techniques hold great interest for their advantages that enable direct handling of nanoparticles. In this work, we study the optical trapping effects of a diffraction-limited focal field possessing an arbitrary photonic spin and propose a convenient method to manipulate the movement behavior of the trapped nanoparticles. In order to achieve controllable spin axis orientation and ellipticity of the tightly focused beam in three dimensions, an efficient method to analytically calculate and experimentally generate complex optical fields at the pupil plane of a high numerical aperture lens is developed. By numerically calculating the optical forces and torques of Rayleigh particles with spherical/ellipsoidal shape, we demonstrate that the interactions between the tunable photonic spin and nanoparticles lead to not only 3D trapping but also precise control of the nanoparticles' movements in terms of stable orientation, rotational orientation, and rotation frequency. This versatile trapping method may open up new avenues for optical trapping and their applications in various scientific fields.展开更多
Isovaleroyl oxokadsurane,a novel dibenzocyclooctadiene lignan pos- sessing a spirobenzofuranoid skeleton was isolated from the stems of Kadsura coccinea.Its structure and relative configuration were determined by X-ra...Isovaleroyl oxokadsurane,a novel dibenzocyclooctadiene lignan pos- sessing a spirobenzofuranoid skeleton was isolated from the stems of Kadsura coccinea.Its structure and relative configuration were determined by X-ray diffraction analysis.展开更多
Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（...Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986展开更多
基金National Natural Science Foundation of China(NSFC)(11504049,11474052,11774055)Natural Science Foundation of Jiangsu Province,China(BK20150593)National Key Basic Research Program of China(2015CB352002)
文摘Optical trapping techniques hold great interest for their advantages that enable direct handling of nanoparticles. In this work, we study the optical trapping effects of a diffraction-limited focal field possessing an arbitrary photonic spin and propose a convenient method to manipulate the movement behavior of the trapped nanoparticles. In order to achieve controllable spin axis orientation and ellipticity of the tightly focused beam in three dimensions, an efficient method to analytically calculate and experimentally generate complex optical fields at the pupil plane of a high numerical aperture lens is developed. By numerically calculating the optical forces and torques of Rayleigh particles with spherical/ellipsoidal shape, we demonstrate that the interactions between the tunable photonic spin and nanoparticles lead to not only 3D trapping but also precise control of the nanoparticles' movements in terms of stable orientation, rotational orientation, and rotation frequency. This versatile trapping method may open up new avenues for optical trapping and their applications in various scientific fields.
文摘Isovaleroyl oxokadsurane,a novel dibenzocyclooctadiene lignan pos- sessing a spirobenzofuranoid skeleton was isolated from the stems of Kadsura coccinea.Its structure and relative configuration were determined by X-ray diffraction analysis.
文摘Let m be a positive integer, g（m） be the number of integers t for which 1 ≤ t ≤ m and there does not exist a positive integer n satisfying （ t = t（n） ） t^n＋1≡t（modm）.For a number x≥3, let G（x）=∑m≤tg（m） In this paper, we obtain the asymptotic formula： .G（x）=αx^2＋O（xlogx）,ax x→∞ Our result improves the corresponding result with an error term O（xlog^2 x） of Yang Zhaohua obtained in 1986
