  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.
