High-precision two-dimensional displacement metrology based on matrix metasurface.

A long-range, high-precision, and compact transverse displacement metrology is of crucial importance in both industries and scientific researches. However, it is a great challenge to measure arbitrary two-dimensional (2D) displacement with angstrom-level precision and hundred-micrometer range. Here, we demonstrated a prototype of high-precision 2D-displacement metrology with matrix metasurface. Light passing through the metasurface is diffracted into three beams in horizontal (H), vertical (V), and diagonal (D) linear polarization. 2D transverse displacement of the metasurface relative to the incident light beam is retrieved from the interferential optical powers arisen from coherent superposition between H-polarized and D-polarized beams or V-polarized and D-polarized beams. We experimentally demonstrate that arbitrary displacement in 2D plane can be determined with high precision down to 0.3 nm in a large range of 200 micrometers. Our work broadens the application scope of metasurface and paves the way for development of ultrasensitive optical 2D displacement metrology.