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

TL;DR

This paper investigates how non-Hermitian mode topology influences the sensing capabilities of plasmonic waveguides, highlighting the importance of eigenmode excitation, spectral features, and the exceptional point for optimizing sensor performance.

Contribution

It introduces a model that accounts for eigenmode excitation and propagation, clarifies the limitations of modal dispersion alone, and links spectral features to sensing sensitivity in plasmonic waveguides.

Findings

Resonant wavelength and spectral width depend on sensing region length.

Optimal detection occurs at directional coupling points with narrow spectra.

Eigenmode splitting shows a square root dependence on permittivity perturbation.

Abstract

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.