Nondiffracting resonant angular filter

We conceptualize and numerically simulate a resonant metamaterial interface incorporating nonlocal, or beyond-nearest-neighbor, coupling that acts as a discrete angular filter. It can be designed to yield perfect transmission at customizable angles of incidence, without diffraction, allowing for tailored transmission in arbitrarily narrow wave-number windows. The theory is developed in the setting of discrete, infinitely periodic quantum graphs and we realize it numerically as an acoustic metagrating. The theory is then applied to continuous acoustic waveguides, first for the medium surrounding the interface and then for the interface itself, showing the efficacy of quantum graph theory in interface design.