Vector electromagnetic pulsed beam fields are constructed by using current dipoles located at complex coordinate points. As in the scalar case, the direction, collimation, and directivity of the field are determined essentially by the imaginary displacement of the source coordinate. The vector fields also depend on the polarization of the dipole with respect to the beam axis. The properties of the field for two special cases in which the dipole is directed either along or transverse to the beam axis are examined analytically and numerically. The general polarization case is thereby considered as a superposition of these two special cases. As expected, the strongest radiation is achieved when the dipole is directed transverse to the beam axis.
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