Micro-Spec: An Ultra-Compact, High-Sensitivity Spectrometer for Far-Infrared and Sub-Millimeter Astronomy

High-performance, integrated spectrometers operating in the far-infrared and sub-millimeter promise to be powerful tools for the exploration of the epochs of reionization and initial galaxy formation. These devices, using high-efficiency superconducting transmission lines, can achieve the performance of a meter-scale grating spectrometer in an instrument implemented on a four-inch silicon wafer. Such a device, when combined with a cryogenic telescope in space, provides an enabling capability for studies of the early universe. Here, the optical design process for Micro-Spec (mu-Spec) is presented, with particular attention given to its two-dimensional diffractive region, where the light of different wavelengths is focused on the different detectors. The method is based on the stigmatization and minimization of the light path function in this bounded region, which results in an optimized geometrical configuration. A point design with an efficiency of approx. 90% has been developed for initial demonstration, and can serve as the basis for future instruments. Design variations on this implementation are also discussed, which can lead to lower efficiencies due to diffractive losses in the multimode region.