At-will chromatic dispersion by prescribing light trajectories with cascaded metasurfaces

Abstract

Chromatic dispersion spatially separates white light into colours, producing rainbows and similar effects. Detrimental to imaging but essential to spectroscopy, chromatic dispersion is the result of material properties in refractive optics and is considered an inherent characteristic of diffractive devices such as gratings and flat lenses. Here, we present a fundamental relation connecting an optical system's dispersion to the trajectories light takes through it and show that arbitrary control over dispersion may be achieved by prescribing specific trajectories, even in diffractive systems. Using cascaded metasurfaces (2D arrays of sub-micron scatterers) to direct light along predetermined trajectories, we present an achromatic twisted metalens and experimentally demonstrate beam deflectors with arbitrary dispersion. This new insight and design approach usher in a new class of optical systems with wide-ranging applications.

Keywords: Metamaterials; Nanophotonics and plasmonics; Sub-wavelength optics.

Fig. 1. Illustration of focusing by a cascaded metasurface system.

Rays of angular frequency ω (blue lines) travel from object point O through a system of M surfaces to image point I. The system is achromatic if rays of a different angular frequency (red lines) leaving O also converge at I. Purple interfaces represent metasurfaces, and black interfaces represent boundaries between materials of different refractive indices.

Fig. 2. Achromatic beam deflector.

a Schematic of an achromatic bilayer metasurface beam deflector. b Phase profiles of the metasurfaces composing the beam deflector shown in a. c Full-wave simulation results for the deflection of a Gaussian beam by the beam deflector. d Wavelength dependence of the deflection angle for the achromatic bilayer beam deflector and a single-layer metasurface beam deflector.

Fig. 3. Achromatic and apochromatic bilayer metalenses.

a Illustration of a twisted achromatic bilayer metalens. b Radial portions of the phase profiles of the two metasurfaces of the metalens shown in a. c Wavelength dependence of the focal lengths of the twisted bilayer metalens shown in a and a single-layer metalens. d Ray schematic, intensity, and field distribution on a plane between the metasurfaces of the twisted metalens (left) and the axial-plane (centre) and focal-plane (right) intensity distributions at three different wavelengths. e Ray schematic (left) and axial-plane (centre) and focal-plane (right) intensity distributions for an annular single-layer metalens. f Illustration of an apochromatic bilayer metalens and an annular single-layer metalens with the same aperture and NA, which serves as a control. g Wavelength dependence of the focal lengths of the metalenses shown in f. The apochromatic bilayer metalens satisfies the achromaticity criterion at two wavelengths, λ = 494.1 nm and λ = 604.5 nm.

Fig. 4. Beam deflector schematics and images.

a Comparison of a single-layer metasurface grating beam deflector with bilayer superchromatic (s.c.) and positive-dispersion designs. b Schematics showing (left) the cascaded metasystem, which uses a gold mirror on the back of the fused silica substrate to ‘fold’ the cascaded systems depicted in a; a portion of one of the metasurfaces (centre); and a unit cell (right) showing a single meta-atom. c A photograph (left) showing the beam deflector patterns and their reflections, an optical microscope image (centre) of the folded achromatic beam deflector and an SEM image (right) of the nano-posts.

Fig. 5. Beam deflector characterization.

a Schematic of the measurement setup. The sample is illuminated by a tuneable light source, and the deflected beam is imaged on a camera. b Deflection angles for the control, achromatic, positive-dispersion, and superchromatic beam deflectors as functions of wavelength. The solid curves represent the simulated responses. c Deflection efficiencies of the beam deflectors as functions of wavelength. The solid lines serve as guides for the eye. The power measurements were obtained at the locations indicated in a.