Using terahertz (THz) time-domain spectroscopy, we investigated the temperature (T)- and magnetic-field (H)-dependent optical conductivity of a moderately disordered superconducting NbN film with the field applied along the sample plane. The thickness of the film, ~5 nm, was comparable with the coherence length, thus precluding the formation of vortices. This was confirmed by the observation of almost identical spectra for THz electric field directed along the sample plane or perpendicularly to it. Such thin films behave effectively as two-dimensional superconductors; applying a sufficiently strong in-plane magnetic field can induce a superconductor-insulator transition. 

Experimentally obtained complex transmittance spectra were used to calculate the complex optical conductivity as a function of frequency, temperature and applied magnetic field. In order to reproduce the data, we employed the Maxwell-Garnett effective medium theory assuming a mixture of two components: one in a normal conductivity state, described by the Drude formula, and one in the superconducting state, described by the model by Herman and Hlubina. Reaching an excellent match between the theory and experimental data, we deduced that the Cooper-pair-breaking scattering rate is linearly growing with H, while the volume fraction of superconducting inclusions f_s is decreasing; it reached the value of f_s ≈ 0.93 for the highest magnetic field value of μ₀H = 7 T. The observed onset of a superconductor-insulator transition hints at a scenario where nanoscale superconducting domains are enclosed in a normal-state matrix.