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Invariants of three types of generalized Bessel beams

Barnett and Allen (1994 Opt. Commun. 110 670–8) used a superposition of Bessel beams to theoretically construct a monochromatic light beam with finite energy, momentum and angular momentum contents per unit length. The same superposition of Bessel functions gives solutions of the Helmholtz equation with exp(i m) azimuthal dependence, from which exact solutions of Maxwell's equations are obtained for three types of beam: TM (or TE), TE+iTM and 'CP' ('circularly polarized'). The invariants of these three types of beam are calculated and compared. One remarkable fact is that the energy and angular momentum contents per unit length are invariants for all the beams considered, whereas these quantities are in general dependent on the longitudinal beam coordinate.