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We demonstrate a high-resolution, crossed-dispersion integrated photonic spectrometer capable of high-etendue, multimode operation. The first experimental single-mode design achieves record performance per volume with 1.5 GHz resolution and 13 THz band-width in a 0.5 mm2 footprint. 

Integrated astrophotonic spectrometers are integrated variants of conventional free-space spectrometers that offer significantly reduced size, weight, and cost and immunity to alignment errors, and can be readily integrated with other astrophotonic instruments such as nulling interferometers. Current integrated dispersive astrophotonic spectrometers are one-dimensional devices such as arrayed waveguide gratings or planar echelle gratings. These devices have been limited to ${10}^4$resolving powers and $<<\#comment/>1000$spectral bins due to having limited total optical delay paths and 1D detector array pixel densities. In this paper, we propose and demonstrate a high-resolution and compact astrophotonic serpentine integrated grating (SIG) spectrometer design based on a 2D dispersive serpentine optical phased array. The SIG device combines a 5.2 cm long folded delay line with grating couplers to create a large optical delay path along two dimensions in a compact integrated device footprint. Analogous to free-space crossed-dispersion high-resolution spectrometers, the SIG spectrometer maps spectral content to a 2D wavelength-beam-steered folded-raster emission pattern focused onto a 2D detector array. We demonstrate a SIG spectrometer with $\sim <\#comment/>100\mathrm{k}$resolving power and $\sim <\#comment/>6750$spectral bins, which are approximately an order of magnitude higher than previous integrated photonic designs that operate over a wide bandwidth, in a $0.4{\mathrm{m}\mathrm{m}}^2$footprint. We measure a Rayleigh resolution of $1.93\pm <\#comment/>0.07\mathrm{G}\mathrm{H}\mathrm{z}$and an operational bandwidth from 1540 nm to 1650 nm. Finally, we discuss refinements of the SIG spectrometer that improve its resolution, bandwidth, and throughput. These results show that SIG spectrometer technology provides a path towards miniaturized, high-resolution spectrometers for applications in astronomy and beyond.