Binary surface reliefs with sub-wavelength features making up a pseudorandom pattern based on mathematical Galois fields GF(p m) [1, 2] can scatter incoming waves into a large number of diffraction maxima within a huge solid angle. A one-dimensional (1D) Galois number sequence can be folded into a two-dimensional (2D) array by the sino-representation [2]. This concept was been verified for acoustic waves a long time ago [3, 4] and is investigated here for visible light and THz waves. Our Galois diffusers are designed as reflection reliefs and realised by electron beam lithography for the optical regime and UV photolithography for the THz regime. Our results show that optical and THz Galois surfaces are excellent diffusers for electromagnetic waves; they distribute the reflected intensity evenly over a large number of maxima nearly within the entire half solid angle in the backward direction.

Glass surface roughness can be considered positive for certain applications in optics. Results of maskless (i.e., lithography-free) reactive-ion-etch runs are given, where (depending on etch parameters) self-masking leads to very different surface morphologies. The latter's variety allows for virtually any desired scattered visible light power portion, a result that we term dosed scattering. The surfaces are characterized, for example, by the root-mean-square roughness delta(rms), while their optical scattering is described by the diffuse transmission as well as the Harvey parameters. Since the wavelengths lambda in glass are around delta(rms), the shapes of the individual scatterers account for local refraction adding up to the usual scattering.

Scattering and scattering plates have a large diversity of applications. Scattering of optical and THz electromagnetic waves can be performed with Galois scattering plates, which had found applications in acoustics first (i.e., with sound waves in concert hall acoustics). For binary Galois scattering plates, the single scattering entities, i.e., mesas (for a binary 1) or voids (for a binary 0), have characteristic lateral dimensions of half the wavelength of the electromagnetic waves to be scattered. Their optimal height is a quarter of the wavelength for plates used in reflection. Meanwhile, not too elaborate lithographic techniques allow for the implementation of Galois plates for the THz range and even for the visible spectral range. We had reported on such scattering plates before. However, in this paper, also the mathematical concept is described and the fabrication technologies are emphasized. In contrast to the case of scattering plates with irregular surface morphologies, Galois plate scattering is not diffuse, but there are many scattering/diffraction orders.