Longitudinal iso-phase condition and needle pulses

We study the properties of pulsed solutions to the scalar and vector wave equations composed of plane-waves with equal longitudinal spatial frequency. This condition guarantees that, at all times, the field profile is invariant in the longitudinal direction. Particular emphasis is placed on solutions with rotational symmetry. For these solutions, the wave concentrates strongly near the axis at a given time. We provide closed-form expressions for some of these fields, and show that their wavefronts are approximately spherical. Solutions carrying orbital and spin angular momenta are also considered.