  We present the novel design of microfabricated, silicon-substrate based
mirrors for use in cryogenic Fabry-Perot Interferometers (FPIs) for the mid-IR
to sub-mm/mm wavelength regime. One side of the silicon substrate will have a
double-layer metamaterial anti-reflection coating (ARC) anisotropically etched
into it and the other side will be metalized with a reflective mesh pattern.
The double-layer ARC ensures a reflectance of less than 1% at the surface
substrate over the FPI bandwidth. This low reflectance is required to achieve
broadband capability and to mitigate contaminating resonances from the silicon
surface. Two silicon substrates with their metalized surfaces facing each other
and held parallel with an adjustable separation will compose the FPI. To create
an FPI with nearly uniform finesse over the FPI bandwidth, we use a combination
of inductive and capacitive gold meshes evaporated onto the silicon substrate.
We also consider the use of niobium as a superconducting reflective mesh for
long wavelengths to eliminate ohmic losses at each reflection in the resonating
cavity of the FPI and thereby increase overall transmission. We develop these
silicon-substrate based FPIs for use in ground (e.g. CCAT-prime), air (e.g.
HIRMES), and future space-based telescopes (e.g. the Origins Space Telescope
concept). Such FPIs are well suited for spectroscopic imaging with the upcoming
large IR/sub-mm/mm TES bolometer detector arrays. Here we present the
fabrication and performance of multi-layer, plasma-etched, silicon metamaterial
ARC, as well as models of the mirrors and FPIs.
