Effective electric and magnetic properties of metasurfaces in transition from crystalline to amorphous state

In this paper we theoretically study electromagnetic reflection, transmission, and scattering properties of periodic and random arrays of particles which exhibit both electric-mode and magnetic-mode resonances. We compare the properties of regular and random grids and explain recently observed dramatic differences in resonance broadening in the electric and magnetic modes of random arrays. We show that randomness in the particle positioning influences equally on the scattering loss from both electric and magnetic dipoles, however, the observed resonance broadening can be very different depending on the absorption level in different modes as well as on the average electrical distance between the particles. The theory is illustrated by an example of a planar metasurface composed of cut-wire pairs. We show that in this particular case at the magnetic resonance the array response is almost not affected by positioning randomness due to lower frequency and higher absorption losses in that mode. The developed model allows predictions of behavior of random grids based on the knowledge of polarizabilities of single inclusions.