We propose a design of a dielectric (silicon nitride) optical leaky wave antenna (OLWA) with periodic semiconductor (silicon) corrugations, capable of producing narrow beam radiation. The optical antenna radiates a narrow beam because a leaky wave (LW) with low attenuation constant is excited at one end of the corrugated dielectric waveguide. We show that pointing angle, beam-width, and operational frequency are all related to the LW complex wavenumber, whose value depends on the amount of silicon perturbations in the waveguide. In this paper, the propagation constant and the attenuation coefficient of the LW in the periodic structure are extracted from full-wave simulations. The far-field radiation patterns in both glass and air environments predicted by LW theory agree well with the ones obtained by full-wave simulations. We achieve a directive radiation pattern in glass environment with about 17.5 dB directivity and 1.05 degree beam-width at the operative free space wavelength of 1.55 μm, pointing at a direction orthogonal to the waveguide (broadside direction). We also show that the use of semiconductor corrugations facilitate electronic tuning of the radiation pattern via carrier injection.