Optical and Electronic Fourier Surfaces

According to Fourier optics, the surface profile of an ideal diffraction grating should contain a precise sum of sinusoidal waves. However, because fabrication techniques typically yield profiles with only two depth levels, complex “wavy” surfaces cannot be obtained, limiting the straightforward design and implementation of sophisticated diffractive surfaces. Here, we eliminate this design–fabrication mismatch and produce optical surfaces with an arbitrary number of specified sinusoids, yielding previously unattainable diffractive surfaces including intricate two-dimensional moiré patterns, quasicrystals, and holograms. We then show that such patterns can be reduced to nanometer length scales, creating wavy Fourier surfaces for 2D electronics.