  Optical spectrometers are the central instruments for exploring the
interaction between light and matter. The current pursuit of the field is to
design a spectrometer without the need for wavelength multiplexing optics to
effectively reduce the complexity and physical size of the hardware. Based on
computational spectroscopic results and combining a broadband-responsive
dynamic detector, we successfully demonstrate an optics-free single-detector
spectrometer that maps the tunable quantum efficiency of a superconducting
nanowire into an ill-conditioned matrix to build a solvable inverse
mathematical equation. Such a spectrometer can realize a broadband spectral
responsivity ranging from 660 to 1900 nm. The spectral resolution at the
telecom is 6 nm, exceeding the energy resolving capacity of existing infrared
single-photon detectors. Meanwhile, benefiting from the optics-free setup,
precise time-of-flight measurements can be simultaneously achieved. We have
demonstrated a spectral LiDAR with 8 spectral channels. This work provides a
concise method for building multifunctional spectrometers and paves the way for
applying superconducting nanowire detectors in spectroscopy.
