Asymmetrical Bessel modes of the first and second type and their superpositions

We considered nonparaxial asymmetric Bessel modes of the first and second type, which differ from a conventional symmetric Bessel mode by a real-valued shift along one Cartesian coordinate and imaginary shift along the other (both shifts are equal in modulus). Bessel modes of the first and second type differ only in the shift sign and, therefore, have different orbital angular momentum (OAM) (integer or fractional). Addition and subtraction of two identical asymmetric Bessel modes of the first and second type leads to light beams with the same integer OAM equal to the topological charge of the generating mode, but with different transverse intensity distributions, which depend on the shift magnitude.