The scattering theory of a Hermite-Gaussian mode laser beam by a homogeneous sphere is reviewed and the transformation of laser beam parameters is discussed. Radiation force of the average of $10^{-5}$ dyne exerted on a sphere with refractive index 1.47 by 1 watt laser beam is numerically calculated as a function of size parameters and position in the laser beam. The stable levitation of an $Al_2O_3$ particle of 0.3㎛ in average size, vacuum oil droplet and a [glycerol (10%)+$H_2O(90%)$] droplet of 1-20 ㎛ in diameter at 1 atmospheric pressure is achieved by using a vertically directed $Ar^+$ laser beam pressure. An $Ar^+$ laser beam of $TEM_{∞}$ mode is controlled to 5145 Å in wavelength and 11 ㎛ in focal spot size. An optical feedback technique is used for the stable levitation of vaporizing liquid droplets. Two or three droplets levitated simultaneously in a single beam have been found. The intensity of light scattered by a [glycerol (10%) + H_2O(90%)$] droplet levitated in the passage of the focused $TEM_{∞}$ mode $Ar^+$ laser beam is measured as a function of size parameters and the sharp optical resonances of 90℃ scattered intensity are observed in time domain with a period of 2.44 minutes. The scattered power per unit solid angle is alos numerically calculated with the focal spot size 11㎛ of the laser beam and the refractive index 1.47 of the droplet. The distance between two adjacent resonances is found 1.51 in size parameter and its comparison with experiment gives evaporation of about 50nm/min. in radius. This technique can be used to measure the size and refractive index of a particle or the evaporation rate and vapor pressure. An expression of the circularly polarized laser beam is obtained from the electromagnetic vector potential, of which the scalar part becomes the complex-source-point spherical wave.
Based on the laser beam scattering theory the analytical formulas of the optical force components exerted on the sphere levitated stationarily in the circularly polarized focused laser beam are derived. The optical torque is numerically calculated and the interpretations of the results are presented. For the sphere with the size parameter, $\rho=(ka)=10π$ and the complex refractive index, $N=1.47+i 0.000001$, levitated at the center of 1 watt Ar$^+$ laser beam, the z-component of angular velocity in air wrot,z is found to be about 4.0 radians/sec.
