Study On The Interaction Of Arbitrarily Incident Gaussian Beam With Eccentric Sphere And Bi-sphere

The interaction between the particles and the shaped beams is one of the rather active research topics in many theoretical investigations and engineering applications. It provides a very important guidance and has practical meanings for the development of so many fields such as biomedicine, physics, chemistry, etc. The electric-magnetic scattering of the beam, the optical trapping and manipulating of the particles by the beam are the unquestionable focus of the research. The studies on the interaction between the homogeneous, layered particles and the shaped beams have been reported for many times. However, still there is a number of work should be done about the eccentric particles and multi-particles which more commonly exist in nature.This article refers to the study on the interaction of arbitrarily incident Gaussian beam with eccentric sphere and bi-sphere. It includes the discussion on the beam scattering of the particles and the optical trapping and optical binding of the particles by the beam. The main achievements are summarized as follows:Firstly, according to the expansion of the off-axis incidence beam in terms of the spherical vector wave functions (SVWFs) and considering the influence of the polarization direction of the beam, the expansion of the off-axis incidence polarized beam is given by using the superposition of vector field. Based on the expansion of the oblique incidence beam and combining the coordinates rotation matrix in the Cartesian coordinates, the expansion and the beam-shape coefficients (BSCs) of the beam in the particle coordinate system are given when the beam is polarized in any angle, off-axis and obliquely incoming, so the universal description of the incident beam is provided. Then the arbitrarily incident BSCs with respect to the normalized SVWFs are calculated. The relations between the off-axis BSCs with respect to positive-time factor and that with respect to negative-time factor has been re-derived and numerically verified, meanwhile the existed expressions are amended.Secondly, according to the generalized Lorenz-Mie theory (GLMT), utilizing the boundary conditions at each boundary of the eccentric sphere and bi-sphere, the scattering equations of the two systems have been deduced by using the additional theorems of the spherical vector wave functions when r≥|d| and when r≤|d| respectively. The effects on the scattering characteristics of eccentric sphere and bi-sphere of the parameters, such as the particle size, the distance between the centers of sphere, the incidence angle, polarization angle, etc., have been calculated and analyzed. Additionally, the scattering equations and the scattering characteristics for the cases of a sphere with an eccentric conductor inclusion, two conductor spheres and a bi-sphere composed by a conductor sphere and a dielectric sphere, have been compared and discussed respectively.Thirdly, the radiation forces and radiation torques exerted on the eccentric sphere by the arbitrarily incident Gaussian beam are investigated. Based on the study on the scattering theoies of the arbitrarily incident Gaussian beam by eccentric sphere, the series expressions of the radiation forces and torques are deduced by combining Maxwell Stress Tensor (MST) and the generalized Lorenz-Mie theory. After the comparison with the results presented in the literature, the radiation forces and torques are numerically calculated when the locations of the beam waist center, the incident directions, the polarized directions, the particle's sizes, the inner core's relative sizes and positions are different respectively, and the influence of the changes of these parameters to the forces and torques is analyzed.Fourthly, on the basis of the expansion of the arbitrarily incident Gaussian beam, the expression of BSCs for double beams is given by using the superposition of the vector field. Combining with the scattering theory of the eccentric sphere illuminated by a single Gaussian beam, the scattered field of dual-beam is evaluated and analyzed for different parameters, such as the incidence direction, polarization direction and phase difference, etc.. The radiation forces and radiation torques of the eccentric sphere acted by the dual-beam are investigated, and the influence to the forces and torques of the particle's parameters, incidence angle and the phase difference of the two beams is discussed.Fifthly, based on the generalized Lorenz-Mie theory, the expressions of the dual-beam is applied to the study of the scattering characteristics of bi-sphere, and combining the scattering equations of bi-sphere for single beam incidence, the scattered field of the bi-sphere system is computed when the dual-beam arbitrarily incidents. Then, the optical binding force of the bi-sphere system is analyzed theoretically, the force in the single beam potential well and that in the dual-beam potential well are numerically calculated respectively. And the influence to the optical binding force of such parameters as the particle size, the refractive index, the distance between the centers of the spheres, the incident direction, the polarized direction, etc., is analyzed.