Propagation And Focusing Properties Of The Laser Beam Of Hypergeometric Modes

Light have a great impact on the current development of science and technology, medicine, information transmission, as a defense information carrier. The basic properties of amplitude, frequency and phase of light, the study has been further obtained the widespread application. Especially hollow beam has the unique light intensity distribution and focusing properties make it in optical communication, polarization remote sensing, high resolution imaging technique, is widely used in particle capture etc. In view of this, this paper studies the propagation and focusing properties of the Hypergeometric beams, the main contents are as follows:(1) In this paper just consider a special case, which is an axially symmetric beam vector solution with the electric field aligned in the azimuthally direction. Solving the nonparaxial wave equation of parabolic coordinate transformation using the method of separation of variables, through numerical simulation the intensity distribution profile for such a beam, The results showed: A new analytical solution of the nonparaxial vector wave equation is discussed to describe the propagation of a laser light beam. The electric field of such a beam is found to be based on the solutions of Confluent Hypergeometric function and the Meijer function, and the intensity distribution similar to the Bessel model, being a set of alternating bright and dark concentric rings. But the light intensity performance infinitely large in near-optical axis and the amplitude drops faster toward the periphery. At the same time, the simulated intensity was shown to decrease along the optical axis behind the focal point.(2) Based on Collins integral formula and Lohmann I, Lohmann II system, theoretical derivation of the Hypergeometric-Gaussian beam passing through fractional Fourier transform optical system of light field analytic expression. Through the introduction of a hard edge aperture function. Detailed derivation of the Hypergeometric-Gaussian beam through a field containing fractional Fourier transform the hard edge aperture approximation analytic formula. And calculation is carried out and the corresponding numerical analysis shows that the fractional Fourier transform is a kind of very good beam shaping method.(3) The focusing properties of the radially polarized Hypergeometric-Gaussian beam are studied. Based on Richards and Wolf’s vectorial diffraction method, high beam quality and subwavelength focusing are achieved for the radially polarized incident Hypergeometric-Gaussian beam. Meanwhile, due to the influence of the imaginary parameter variables of the electric field at the pupil, we obtain the offset phenomenon of the focal spot on the focal plane. Therefore, Hypergeometric-Gaussian beam can be applied in the focusing system with a high numerical aperture(NA) objective to achieve focusing with superresolution and widely used in application such as data storage, laser drilling and optical trapping.(4) The optical trapping characteristics of high numerical-aperture(NA) focused higher-order radially polarized Hypergeometric-Gaussian type-II(HyGG-II) beam acting on gold nanoparticles are studied theoretically. The intensity and radiation forces are calculated by using the vector diffraction theory and the Rayleigh scattering theory. Numerical results show that for the radially polarized HyGG-II beams input field of an unified truncation parameter the higher-order radially polarized HyGG-II beams like the fundamental lowest-order radially polarized beam, can stably 3-D trap a particle to the focus plane; And with increasing the beam order, transverse trapping gradient stress value increases, the longitudinal capture gradient force in the beam order is equal to 2 of the maximum; At the same time, the optical trapping capture stability of the higher-order radially polarized HyGG-II beam has also made the corresponding theoretical analysis.