By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived. In this formula VPWS is composed of TM- and TE-mode plane wave spectrum, where the amplitude and unit polarized direction of every plane wave are separable, which has more obviously physical meaning and is more convenient to apply in some cases compared to previous formula of VPWS. As an example, the formula of VPWS is applied to the well-known radially and azimuthally polarized beam. In addition, vector Fourier-Bessel transform pairs of an arbitrary polarized electromagnetic wave with circular symmetry are also derived.
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