Family of oscillatory electromagnetic pulses

We discuss the properties of electromagnetic transverse electric and transverse magnetic (TE and TM) pulses based on a family of oscillatory solutions of the wave equation. The energy and momentum densities of the TE and TM pulses are annular. These pulses are sufficiently localized to have finite norm, total energy, momentum, and angular momentum, which are evaluated analytically. All the solutions given are proved to be strictly forward propagating (unidirectional). The wave function is characterized by a length a and a wave number K. The longitudinal extent of the pulses and the number of oscillations are of order 2a and Ka, respectively. Far from the focal region, the annular TE and TM pulses diverge from the axis of propagation on a cone, the angle of which is determined.