Miniature astronomical spectrographs using arrayed-waveguide gratings: capabilities and limitations

The size of the optical elements (gratings, mirrors, lenses) in traditional astronomical spectrographs scales with telescope diameter (unless the instrument is operating at the diffraction limit). For large telescopes, this leads to spectrographs of enormous size and implied cost. The integrated photonic spectrograph offers the potential to break this scaling law and allow massively multiplexed instruments. One proposed format for such a spectrograph recently demonstrated on-sky employs the arrayed-waveguide grating, which creates dispersion using interference between a series of waveguides with precisely defined length increments. Arrayed-waveguide gratings fabricated via planar techniques are used extensively in the telecommunications industry as optical (de)multiplexers. Current commercial devices are not directly applicable for astronomical use, and several design modifications are thus required. Here we investigate the potential capabilities and limitations of arrayed-waveguide grating technology to provide massively multiplexed spectroscopy for astronomy. In particular, we examine the dependence of the arrayed-waveguide grating design parameters (such as focal length, device order, array spacing, array length increment, refractive index contrast, chip size, number and structure of input modes, and configuration of output imaging or cross-dispersive optics) on the characteristics of the device output (operating wavelength, free spectral range, spectral resolution, multiplexing capacity, and number of required detector pixels).