Abstract
An analytical expression of an elliptical Bessel beam (EBB) is deduced on the basis of the angular spectrum decomposition (ASD) method, starting from an elliptical Bessel-like profile in the initial transverse plane. The angular spectrum representation is also obtained for another approximate EBB that is produced by the refraction of a circular Bessel beam at an interface in oblique incidence. The expressions are further expanded into a series of vector spherical harmonic functions for describing the scattering of the beams by a spherical particle. Numerical calculations are implemented with different parameters and the results are discussed. A length parameter is obtained for evaluating the variation of the EBB along the propagation. It is confirmed that the refracted CBB at small incident angle behaves in a similar way to the EBB. When the incident angle increases, the asymmetry of the transverse beam profile becomes serious and the propagation of the beam deviates gradually from the predicted direction.
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