  Current wireless systems are experiencing unprecedented pressure that could
be relieved by shifting carrier frequencies towards the terahertz spectrum.
Yet, components are required to enable spectrally efficient communications at
such high frequencies. Recently, the photonic crystal platform has been shown
to enable signal processing at the chip-scale. Similarly, leaky-wave antennas
were used to generate highly directional THz beams. Here, we combine photonic
crystals with leaky-wave antennas. Practically, we propose to use an array of
cylinders sandwiched between two plates, and we demonstrate a bandgap in the
250-350 GHz range by judicious geometric design. We introduce a linear defect
in the crystal by removing a row of cylinders, allowing to guide the THz beam.
Then, a careful study of the relation dispersion of the guided mode shows that
its propagation constant is larger to that of free space. This allows the mode
to efficiently outcouple when a thin aperture slot is introduced above the
defect. We numerically demonstrate that the far-field diffracted beam can cover
a wide angular range from 30 to 90 degrees. Finally, we show how the photonic
crystals can be further engineered to enable coverage in two opposite angular
directions.
