We propose a novel design of an all-dielectric optical antenna based on photonic-band-gap confinement. Specifically, we have engineered the photonic-crystal dipole mode to have broad spectral response (Q~70) and well-directed vertical-radiation by introducing a plane mirror below the cavity. Considerably large local electric-field intensity enhancement~4,500 is expected from the proposed design for a normally incident planewave. Furthermore, an analytic model developed based on coupled-mode theory predicts that the electric-field intensity enhancement can easily be over 100,000 by employing reasonably high-Q (~10,000) resonators.