We investigate the terahertz conductivity of conventional superconductors in Voigt and Faraday magneto-optical configurations. First, we review theoretical approaches describing vortex formation and the suppression of superconductivity by magnetic fields, including the filling of in-gap states. We demonstrate that the optical conductivity is comprehensively described by the Herman–Hlubina model [Phys. Rev. B 96, 014509 (2017)], which accounts for both pair-conserving and magnetic-field-dependent pair-breaking disorder scattering.

In the Voigt geometry, we distinguish two cases: (i) Ultrathin films (vortex-free case) – The magnetic field fully penetrates ultrathin films and interacts with spins, modifying the optical gap and condensate density. For this case, we provide an alternative description of recent gapless conductivity measurements on a Nb film [Lee et al., Nat. Commun. 14, 2737 (2023)], which better fits their data for magnetic fields above 1 T.
(ii) Thin samples – The magnetic field is screened, and vortices are arrange in columns. We observe an induced anisotropy between linear polarization parallel and perpendicular to the vortex core axis.

Our results establish a unified framework for terahertz magneto-optical response in conventional superconductors, bridging vortex dynamics and pair-breaking scattering.