Controlling multiple diffraction with quasiperiodic gratings

Complex diffraction patterns are formed by sophisticated diffraction gratings. However, the methods of synthesizing of such gratings are complicated and resource intensive. We propose a simple analytical approach to forming one- and two-dimensional quasiperiodic gratings supporting multiple diffraction consisting of a set of diffraction maxima with the specified spatial frequency of certain diffraction order. The structure of a quasiperiodic grating is a superposition of harmonic functions, which provide a discrete spatial spectrum. The number of diffraction maxima, their angular positions, and intensity distribution between them can be controlled by choosing appropriate reciprocal lattice vectors and their amplitudes. This effect confirmed by the experiment opens new possibilities for light shaping, imaging, and radiation coupling.