Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α

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 (k(r)/k≈1, where k(r) 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.