  We deposit thin titanium-nitride (TiN) and TiN/Ti/TiN multilayer films on
sapphire substrates and measure the reflectance and transmittance in the
wavelength range from 400 nm to 2000 nm using a spectrophotometer. The optical
constants (complex refractive indices), including the refractive index n and
the extinction coefficient k, have been derived. With the extracted refractive
indices, we propose an optical stack structure using low-loss amorphous Si
(a-Si) anti-reflective coating and a backside aluminum (Al) reflecting mirror,
which can in theory achieve 100% photon absorption at 1550 nm. The proposed
optical design shows great promise in enhancing the optical efficiency of
TiN-based microwave kinetic inductance photon-number-resolving detectors.
