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where [g.sup.m.sub.n,TM] and [g.sup.m.sub.n,TE] are the generalized functions of GLMT, an and bn are the scattering coefficient of Mie theory, and E and H are the magnetic and electric energy.
According to the GLMT, the particle is randomly located in the Gaussian beam, and the scattering properties are also determined by the location information in the beam.
After making the average of the position information, we can obtain the general location for the random particles, and then the average scattering cross section of particles is also calculated with the GLMT framework.
In this paper, the scattering cross sections of nonspherical mineral particles are investigated with in the Gaussian beam based on the GLMT. In the framework of GLMT, the general location information is statistic by the Monte Carlo statistical estimate method, and the scattering cross sections of spheroid particles including the feldspar, quartz, and red clay are calculated.
In this paper, we present a detailed discussion of the expansion of Gaussian beam in spheroidal coordinates within the GLMT framework, and of the scattering of Gaussian beam by a dielectric spheroid and coated spheroid.
Within the framework of the GLMT, the incident Gaussian beam can be expanded in terms of the spherical vector wave functions with respect to the system [O.sub.xyz] as follows 
In the framework of the GLMT for a spheroid, once the Gaussian beam expansion is obtained, the scattered fields as well as the fields within the spheroidal particle can be expanded in terms of appropriate spheroidal vector wave functions as follows :
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