Polar-azimuthal angle dependent efficiency of different infrared superconducting nanowire single-photon detector designs

The illumination-angle-dependent absorptance was determined for three types of superconducting-nanowire singlephoton detector (SNSPD) designs: 1. periodic bare niobium-nitride (NbN) stripes with dimensions of conventional SNSPDs, 2. the same NbN patterns integrated with ~quarter-wavelength hydrogensilsesquioxane-filled nanocavity, 3. similar cavity-integrated structures covered by a thin gold reflector. A three-dimensional finite-element method was applied to determine the optical response and near-field distribution as a function of p-polarized light illumination orientations specified by polar-angle, φ, and azimuthal-angle, γ. The numerical results proved that the NbN absorptance might be maximized via simultaneous optimization of the polar and azimuthal illumination angles. Complementary transfer-matrix-method calculations were performed on analogous film-stacks to uncover the phenomena contributing to the appearance of extrema on the optical response of NbN-patterns in P-structure-configuration. This comparative study showed that the absorptance of bare NbN patterns is zero at the angle corresponding to total internal reflection (TIR). In cavity-integrated structures the NbN absorptance curve indicates a maximum at the same orientation due to the phase shift introduced by the quarter-wavelength HSQ layer. The reflector promotes the NbN absorptance at small polar angles, but the available absorptance is limited by attenuated TIR in polar angle-intervals, where surface modes are excited on the gold film.