| Light can be regarded as a form of electromagnetic wave,and the classical electromagnetic field theory based on Maxwell's equation can be used to solve the diffraction and propagation of an optical field.The scalar diffraction theory of an optical field is still valid for most practical problems of the light beam propagation.However,with the further development of the theory of the near field optics,the contradiction of non-self-consistent of the optical scalar approximation theory is more and more obvious.In particular,in recent years,with the rapid development of semiconductor laser diode,micro cavity laser,micro optics,near-field optics and photonic crystals,a rigorous vector theory is essential to deal with the near-field optical properties of some applications in practice.The major topic of this paper is focused on the vector electromagnetic field(i.e.,the states of polarization(So P)in the cross-section of the optical field are inhomogeneous)which is different from the conventional scalar field.The vector diffraction theory of an electromagnetic wave is used in this paper.Firstly,based on the approximation method and the angular spectrum method of vector diffraction theory,the vector structure of an Airy beam and the propagation characteristics of a cylindrical vector beam with variant So P along the radial direction in the field cross-section in the free space are analyzed in detail.The rigorous vector solution of the diffraction is presented through the analytical calculation and numerical calculation.The propagation characteristics of these beams in free space are analyzed.The main content of this paper can be divided into the three parts as following:1.By using the vector angular spectrum method and the approximate method,the analytical expressions for different components of the electromagnetic field have been deduced.The vector structure of an Airy beam is studied.The ratio of the transverse energy flow density and the longitudinal energy flow density is increased with the increasing propagation distance.The energy flux density of the TM(Transverse Magnetic mode)component increases faster than that of the TE(Transverse Electric mode)component in the Fresnel diffraction region,and this ratio is determined by the transverse size x0 and the wavelength ?.The characteristics of the vector structure are analyzed further by the physical picture of propagation dynamics of the Airy beam,which provides the theoretical basis for the potential applications of Airy beam in relevant fields,such as nano photonics,tightly focused light field.2.The near field properties of a cylindrical vector optical field with the variant So P along with the radial direction are analyzed by the method of the angular spectrum.The vector structures of evanescent waves and propagating waves provide an intuitive image to describe the vector optical field in the near field.In particular,the effect of longitudinal component on the distributions of the total optical field and the density of the optical spin angular momentum(SAM)are described in detail.The numerical calculations indicate that the distributions of evanescent waves and propagating waves with different polarization topological charges are different,and are closely related to the initial So P distribution in the cross section of the optical field.The influence of longitudinal component on the optical spin angular momentum density leads to a vector distribution structure of the spin angular momentum density.The results of this work can provide very useful information for the manipulation of a cylindrical vector optical field in the near-field and angular momentum density by purposely choosing the proper distribution of So P in the cross section of the optical field.3.A unit for the image acquisition device is designed to develop a data acquisition and image facility of optical field and realize data acquisition and imaging by using vector beam and the further study of the potential applications of a vector optical field by using USB3.0 outer controller. |
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