The scalar wave theory of nondiffracting electromagnetic (EM) high-order Bessel vortex beams of fractional type α has been recently explored, and their novel features and promising applications have been revealed. However, complete characterization of the properties for this new type of beam requires a vector analysis to determine the fields’ components in space because scalar wave theory is inadequate to describe such beams, especially when the central spot is comparable to the wavelength (, where is the radial component of the wavenumber k). Stemming from Maxwell’s vector equations and the Lorenz gauge condition, a full vector wave analysis for the electric and magnetic fields is presented. The results are of particular importance in the study of EM wave scattering of a high-order Bessel vortex beam of fractional type α by particles.
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