Compact Aberration‐Corrected Spectrometers in the Visible Using Dispersion‐Tailored Metasurfaces

DOI: 10.1002/adom.201801144 The key components of a spectrometer are a dispersive element, such as a grating, followed by a focusing lens. These are usually arranged in a Czerny–Turner configuration.[7] However, different wavelengths of incident light are focused along a curved surface as opposed to a planar one; as a result the focal spot broadens and becomes aberrated due to astigmatism and field curvature.[7] These factors result in a tradeoff between the spectral resolution, which is related to the size and quality of the focal spot, and the spectral range of the spectrometer. Conventional methods to overcome this challenge involve additional optical components (e.g., multiple lenses) or precisely machined parts to correct for these aberrations, such as wedge-shaped cylindrical lenses,[8] toroidal gratings,[9] and freeform elements.[10] These are typically fabricated from aspheric blanks and introduce a significant overhead in terms of overall device cost and complexity. This also poses a significant challenge for truly compact, low-cost, handheld aberration-corrected spectrometers. Recently, metasurfaces comprising of subwavelength scale nanostructures have received much attention from the research community.[11] They allow for exquisite control over the output wavefront of light,[12–15] and have been used to demonstrate ultracompact analogs of numerous optical components, such as lenses,[16–18] holograms,[19–21] and polarimeters.[22–24] An important advantage of metasurfaces is their ability to integrate multiple functionalities within a single planar device, thereby greatly reducing bulk and system complexity. For example, in an earlier work,[25] we demonstrated off-axis focusing metalenses capable of simultaneously focusing and dispersing light: they thus integrate the functionality of both the grating and the focusing lens in a single optical component. Additionally, by engineering the off-axis focusing angle very large dispersions can be obtained;[26] this allows one to achieve a miniature spectrometer with subnanometer resolution with a working distance of only a few centimeters from the lens to the detector. This distance is not fundamentally limited in any way; it is dependent on the desired specifications of the metalens, and in principle could even be much smaller, enabling monolithic integration with detectors. However, these off-axis focusing metalenses face the same challenges as their refractive and diffractive counterparts[27–30] The spectral resolution and range of conventional spectrometers are typically limited by optical aberrations of their focusing elements, mainly due to chromatically induced astigmatism and an intrinsically curved focal plane. Traditional approaches to overcome this challenge require additional optical components which introduce significant bulk and design complexity to the system and prevent easy integration with portable devices. Here a single planar off-axis focusing metalens consisting of subwavelength TiO2 nanofins whose focal spots lie along a plane and undergo minimal focal spot broadening for almost 200 nm across the visible spectrum is demonstrated. This allows us to achieve a miniature aberration-corrected spectrometer with nanometer spectral resolution, while having a beam propagation distance of only 4 cm to the camera plane. This is achieved by dispersion engineering: tailoring the phase, group delay (GD) and GD dispersion of the metalens. This approach is general and can also be used to introduce customized functionalities to the metalens such as a linear dispersion in the frequency domain with minimal additional overhead.