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Radiation from printed antennas is investigated with emphasis placed on producing - and -plane radiation patterns that are as nearly omnidirectional as possible. This is achieved using criteria which are derived for a nonzero radiation field extending down to the layer surface (radiation into the horizon). It is determined that this phenomenon arises when a surface wave pole coincides with a branch point in the complex plane. A simple ray optics interpretation is given for the phenomenon, and graphs are presented to easily enable design of printed antenna geometry to achieve nearly omnidirectional - or -plane patterns.