The characteristics of surface waves from a Hertzian (elementary) dipole on a multilayer structure with planar periodic material elements are investigated. An integral-equation moment method in conjunction with an analytical array scanning scheme is applied to the boundary-value problem associated with source interaction with infinite periodic structures. A pole-extraction technique and the saddle-point method are applied to find the far-zone periodic surface waves due to a current source. The investigation provides a fundamental study of surface wave properties of printed circuit antennas on planar artificial periodic (photonic bandgap) structures. It is found from the power patterns that surface waves are suppressed in the directions with wave bandgap and greatly enhanced in the directions just outside the bandgap zones. The surface wave pattern may be highly directive and the beam angle varies with frequencies. The finding suggests possible frequency-space selection devices. Experiments are carried out to validate the surface wave bandgap phenomenon and the beam angle frequency-selection property.