Localized electromagnetic pulses with azimuthal dependence

We present a family of solutions of the wave equation which are localized in space–time and have azimuthal dependence, thus enlarging the previously known set of solutions. These wavefunctions are used to construct two types of solutions of Maxwell's equations which represent localized electromagnetic pulses. The energy, momentum and angular momentum of these pulses are calculated analytically for simple special cases of the family of wavefunctions. Solutions of the wave equation with exp(i m) azimuthal dependence, but otherwise unrestricted, are shown to result in separation of angular momentum into spin and orbital parts for two classes of pulse. However, reversal of the sign of m can produce major changes in the pulse structure.