A leaky wave antenna is a structure into which you feed a radio wave, which then, as the name implies, leaks this wave into the surrounding space along the length of the guiding structure. Because of how these leaks interfere with eachother, the emitted signal can be made very directional. An interesting property of these structures is that when the phase velocity of the wave inside the guiding structure is lower than the speed of light, it will not radiate any radio waves, but at or above the speed of light, it will happily radiate. Now, I will not pretend to understand even half of the underlying principles here: Waveguides (the guiding structures) are scary, apparently they are not just tubes for radio, but rather transfer waves through different "transverse modes" or something, the phase velocities of which apparently go from c to infinity depending on frequency and whatnot. Empty space appears equally scary and intellectually impenetrable, where maxwell's godforsaken equations apply: to numerically model maxwell's equations in three dimensions seems both hard and slow, and any analytical approach is wayyy above my skill level. Luckily, the 2D wave equation, a very poor proxy, is trivial to model numerically. Similarly, leaks off of a waveguide can be modeled just as a scrolling sinusoidal perturbation. By some miracle, this poor model of the system exhibits many of the same phenomena as a real leaky wave antenna. Above are two setups: one where the phase velocity in the waveguide is exactly c, and one where it is just 10% slower than c. This tiny difference in speed almost entirely kills radiated waves, a surprisingly hard cutoff! According to wikipedia, these slow waves only radiate at discontinuities, clearly shown in the slow antenna, where radiation occurs mainly from the very tip, where the waveguide goes from being there to not being there, a clear discontinuity. You'll have to excuse the windows snipping tool annotations, which I tried to use to digestibly share my sim results with my friends, who remain unwaveringly uncurious in spite of my attempts to share my enthusiasm, and now I feel I want to share my enthusiasm elsewhere, i.e. here. RF is cool, go do RF.