Properties of periodic metasurfaces versus amorphous arrangements at oblique incidence

Electromagnetic properties of resonant metasurfaces are studied in transition from a periodic to an amorphous arrangement of their constituents. Emphasis is put to investigate the response at oblique incidence and for TM polarized light. Our metasurfaces possess both electric and magnetic resonances which makes them to be canonical samples that reflect properties of many metasurfaces. The suggested analytical model explains many if not to say all far-field optical properties that can be observed in resonant metasurfaces. For example, the resonance broadening and damping for the electric mode which contrasts with the persistence of these properties for the magnetic mode in transition from crystalline to the amorphous state can be fully explained. All theoretical predictions are verified with complementary numerical calculations and experimental measurements.