An ultra-compact spectrometer-on-a-chip, when fully developed, will simultaneously image and extract full spectral information (including redshifts) from galaxies in the instrument field-of-view, a powerful new capability for studies of galaxy evolution and large-scale structure. It can be incorporated in Japanese-led SPICA space telescope's BLISS spectrometer instrument. It would enhance and extend the long wavelength capability of BLISS or a similar instrument. The horn antenna array, integrated on direct-detector instruments as well as heterodyne arrays will also pave the way for optimal science return with future NASA-led cryogenic far-IR space missions: CALISTO/SAFIR, SPIRIT, and future SOFIA instruments. It will have applications in NASA's future astrophysics, Earth science, and planetary missions with multi-pixel spectrometers and imager instruments. The horn antenna array we are developing will have a direct impact on the terahertz radar imagers and cameras under development by the Department of Homeland Security and other defense organizations.