Fundamental limits to slow-light arrayed-waveguide-grating spectrometers.

We present an analytical model that describes the limiting spectral performance of arrayed-waveguide-grating (AWG) spectrometers that incorporate slow-light methods. We show that the loss-limited spectral resolution of a slow-light grating-based spectrometer scales as the loss-group-index ratio of the waveguide array. We further show that one can achieve a spectral resolution of a few GHz using currently available slow-light photonic crystal waveguides while greatly shrinking the on-chip footprint of the spectrometer.