A Non-diffracting Resonant Angular Filter

We conceptualise and numerically simulate a resonant metamaterial interface incorporating non-local, or beyond nearest neighbour, 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 wavenumber windows. The theory is developed in the setting of discrete, infinitely periodic quantum graphs and we realise it numerically as an acoustic meta-grating. 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.