The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized Lorenz-Mie theory (GLMT). The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients (G(m)(n),(TM),G(m)(n),(TE)). Analytical expressions of the far-field scattering and extinction cross sections are derived. As two special cases, plane wave scattering by a spheroid and shaped beam scattered by a sphere can be recovered from the present theory, which is verified both theoretically and numerically. Calculations of the far-field scattering and cross sections are performed to study the shaped beam scattered by a spheroid, which can be prolate or oblate, transparent or absorbing.
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