Polarization of electromagnetic pulses

We show the impossibility, for localized and exact solutions of the Maxwell equations, of perfect circular polarization in a fixed plane, or perfect linear polarization along a fixed direction. A measure of polarization of electromagnetic pulses is obtained by analogy with that useful in monochromatic radiation, and its limitations discussed. Using oscillatory solutions of the free-space Maxwell equations, for which all components of the electric and magnetic fields satisfy the wave equation, we construct explicit examples of TE pulses which are linearly polarized with an azimuthal electric field, TE+iTM pulses approximately linearly polarized along the propagation direction, and also approximately circularly polarized pulses. The latter have perfect circular polarization on the propagation axis.