Detecting nanometric displacements with optical ruler metrology.

We introduce the optical ruler, an electromagnetic analog of a physical ruler, for nanoscale displacement metrology. The optical ruler is a complex electromagnetic field in which singularities serve as the marks on the scale. It is created by the diffraction of light on a metasurface, with singularity marks then revealed by high-magnification interferometric observation. Using a Pancharatnam-Berry phase metasurface, we demonstrate a displacement resolving power of better than 1 nm (λ/800) at a wavelength of 800 nm. We argue that resolving power of ~λ/4000, the typical size of an atom, may be achievable. An optical ruler with dimensions of only a few tens of microns offers applications in nano-metrology, nano-monitoring and nano-fabrication, in particular in the demanding and confined environment of future smart manufacturing tools.