This paper presents the first security study of THz networks employing antennas with the angle-frequency coupling property. Using Leaky Wave Antennas (LWAs) as a representative, we explore the unique security properties due to the frequency-dependent radiation. We show via both analytical models and over-the-air experiments that LWA links exhibit non-uniform secrecy capacity across sub-channels, yielding advantages to an eavesdropper at edge frequencies. Yet, because different frequencies emit towards different angles, the eavesdropper is thwarted from easily intercepting an entire wideband transmission. The experiments diverge from the analytical model in that the model underpredicts the eavesdropper’s advantage at angles smaller than the target user and subsequent asymmetric performance across angles. Nonetheless, both the model and measurements show that increasingly wide bandwidth and correspondingly wide beams have only a modest marginal security penalty. Further, we find the LWA link secrecy not only depends on the target user angle (due to nonlinearity of LWA’s frequency-angle coupling), but also the beamwidth of the frequency components that constitute the collective LWA transmission.