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The photonic crystal is investigated as a substrate material for planar antennas in the microwave and millimeter-wave bands. Experimental results are presented for a bow-tie antenna on a (111)-oriented face-centered-cubic photonic-crystal substrate with a band gap between approximately 13 and 16 GHz. When driven at 13.2 GHz, the antenna radiates predominantly into the air rather than into the substrate. This suggests that highly efficient planar antennas can be made on photonic-crystal regions fabricated in semiconductor substrates such as GaAs.