Determination of Mid-Infrared Refractive Indices of Superconducting Thin Films Using Fourier Transform Infrared Spectroscopy

Abstract: In this work, we present a technique to determine the mid-infrared refractive indices of thin superconducting films using Fourier transform infrared spectroscopy (FTIR). In particular, we performed FTIR transmission and reflection measurements on 10-nm-thick NbN and 15-nm-thick MoSi films in the wavelength range of 2.5 to 25 $\mu$m, corresponding to frequencies of 12-120 THz or photon energies of 50-500 meV. To extract the mid-infrared refractive indices of these thin films, we used the Drude-Lorentz oscillator model to represent their dielectric functions and implemented an optimization algorithm to fit the oscillator parameters by minimizing the error between the measured and simulated FTIR spectra. We performed Monte Carlo simulations in the optimization routine to estimate error ranges in the extracted refractive indices resulting from multiple sources of measurement uncertainty. To evaluate the consistency of the extracted dielectric functions, we compared the refractive indices extrapolated from these dielectric functions in the UV to near-infrared wavelengths with the values separately measured using spectroscopic ellipsometry. We validated the applicability of the extracted mid-infrared refractive indices of NbN and MoSi at temperatures below their critical temperatures by comparing them with the Mattis-Bardeen model. This FTIR-based refractive index measurement approach can be extended to measure the refractive indices of thin films at wavelengths beyond 25 $\mu$m, which will be useful for designing highly efficient photon detectors and photonic devices with enhanced optical absorption in the mid- and far-infrared wavelengths.