Because of a growing bandwidth problem within wireless communications, the terahertz (THz) spectrum is being investigated as a possible technology for short-range, high-bandwidth communications. For this reason, it is worth implementing known communications technologies within the radio frequency (RF) and microwave bands, such as antennas, in the terahertz band. One such technology is the leaky-wave antenna. Leaky-wave antennas have been in use within the RF and microwave bands since the 1940’s. The leaky-wave antenna is a travelling wave antenna in which a fast wave with a phase velocity greater than the speed of light, c, propagates through a waveguide. This fast wave is allowed to leak out of the waveguide via an opening along the length of the waveguide. A THz leaky-wave antenna is implemented using the TE1 mode of a parallel-plate waveguide (PPWG). Various plate separations are used during this project in order to show the leaky-wave effect for different dispersion relations. Using a commercial THz time domain spectroscopy (THz-TDS) system, the input of the waveguide is a broadband THz signal. The expected output from such an input would be dispersed in the frequency domain. This is particularly interesting because it would allow the leaky-wave antenna to act as a THz demultiplexer by separating a broadband signal into individual frequency components that vary with angle. Our measured experimental results show that the waveguide indeed produces a dispersed output matching the analytical result. The propagation angle of lower frequencies is closer to perpendicular to the waveguide, with the cutoff frequency of the PPWG at the normal. Higher frequencies are transmitted closer to the axis of the waveguide. Since the phase-matching condition for a leaky-wave antenna can work in either direction, this THz leaky-wave antenna can also receive radiation. Our results show that when operating in this orientation, the receiving angle matches the angle of transmission from the transmitter setup for each frequency. This again shows agreement with the analytical result froe leaky-wave antennas. Using the leaky-wave antenna in this manner, we see the potential for THz frequency domain multiplexing. Varying the plate separation of a PPWG changes the dispersion relation. Since the angle of leaky-wave propagation depends on the dispersion, by varying the plate separation, one can vary the angle of the leaky-wave along the length of the waveguide. We implement such a waveguide in order to focus a chosen frequency to a point. Simulations of the field intensity show that this is possible. By mapping out the field intensity for each design frequency, our results validate this concept by showing that the field focuses within the plane of propagation. To the best of our knowledge, this work shows for the first time that these types of antennas can be implemented within the THz spectrum in order to transmit and receive THz signals.