An analytical discontinuity is reported in what was thought to be the
discontinuity-free exact nonparaxial vortex beam phasor obtained within the
complex source/sink model. This discontinuity appears for all odd values of the
orbital angular momentum mode. Such discontinuities in the phasor lead to
nonphysical discontinuities in the real electromagnetic field components. We
identify the source of the discontinuities, and provide graphical evidence of
the discontinuous real electric fields for the first and third orbital angular
momentum modes. A simple means of avoiding these discontinuities is presented.Comment: 10 pages, 4 figure
