  The far-infrared and submillimeter portions of the electromagnetic spectrum
provide a unique view of the astrophysical processes present in the early
universe. Micro-Spec ($\mu$-Spec), a high-efficiency direct-detection
spectrometer concept working in the 450-1000-$\mu$m wavelength range, will
enable a wide range of spaceflight missions that would otherwise be challenging
due to the large size of current instruments and the required spectral
resolution and sensitivity. This paper focuses on the $\mu$-Spec
two-dimensional multimode region, where the light of different wavelengths
diffracts and converges onto a set of detectors. A two-step optimization
process is used to generate geometrical configurations given specific
requirements on spectrometer size, operating spectral range, and performance.
The canonically employed focal-plane constraints for the power combiner were
removed to probe the design space in its entirety. A new four-stigmatic-point
optical design solution is identified and explored for use in far-infrared and
submillimeter spectroscopy.
