  We propose an all-silicon multi-layer interference filter composed solely of
silicon with sub-wavelength structure (SWS) in order to realize high
performance optical filters operating in the THz frequency region with
robustness against cryogenic thermal cycling and mechanical damage. We
demonstrate fabrication of a three-layer prototype using well-established
common micro-electro-mechanical systems (MEMS) technologies as a first step
toward developing practical filters. The measured transmittance of the
three-layer filter agrees well with the theoretical transmittances calculated
by a simple thin-film calculation with effective refractive indices as well as
a rigorous coupled-wave analysis simulation. We experimentally show that SWS
layers can work as homogeneous thin-film interference layers with effective
refractive indices even if there are multiple SWS layers in a filter.
