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.
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