Influence of non-Hermitian mode topology on refractive index sensing with plasmonic waveguides

We evaluate the sensing properties of plasmonic waveguide sensors by calculating their resonant transmission spectra in different regions of the non-Hermitian eigenmode space. We elucidate the pitfalls of using modal dispersion calculations in isolation to predict plasmonic sensor performance, which we address by using a simple model accounting for eigenmode excitation and propagation. Our transmission calculations show that resonant wavelength and spectral width crucially depend on the length of the sensing region, so that no single criterion obtained from modal dispersion calculations alone can be used as a proxy for sensitivity. Furthermore, we find that the optimal detection limits occur where directional coupling is supported, where the narrowest spectra occur. Such narrow spectral features can only be measured by filtering out all higher-order modes at the output, e.g., via a single-mode waveguide. Our calculations also confirm a characteristic square root dependence of the eigenmode splitting with respect to the permittivity perturbation at the exceptional point, which we show can be identified through the sensor beat length at resonance. This work provides a convenient framework for designing and characterizing plasmonic waveguide sensors when comparing with experimental measurements.