Scattered and internal intensity of a sphere illuminated with a Gaussian beam

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Abstract
A method of calculating the internal and scattered electric fields of a spherical dielectric object illuminated with a Gaussian beam is presented. The vector nature of the beam is considered. The fields satisfy Maxwell's equations, and the beam can be located arbitrarily with respect to the object. A polarized Gaussian beam is first represented as an angular spectrum of plane waves. These waves are then expanded in vector spherical harmonics. Although the details of the expansion are presented for a lowest-order Gaussian beam, the method can be applied to any wave which can be expressed as a sum of homogeneous plane waves. The interaction of an arbitrarily located Gaussian beam with a spherical object is analyzed using the T-matrix method. Calculated results for beams having waists much smaller than the radius of the sphere help in visualizing how a narrow beam reflects and refracts at the spherical dielectric interfaces. The combination of the plane-wave spectrum technique and the T-matrix method can be applied to the problem of an arbitrary beam interacting with an axisymmetric, nonspherical, homogeneous or layered object.