Robustness of subwavelength devices: a case study of cochlea-inspired rainbow sensors

TL;DR

This paper derives formulas to analyze how errors affect subwavelength devices, demonstrating that cochlea-inspired rainbow sensors maintain stability in their filtering properties despite imperfections and resonator removal.

Contribution

It provides a mathematical framework for assessing the robustness of subwavelength devices, specifically applying it to cochlea-inspired rainbow sensors.

Findings

Device properties are stable under small positional and size errors.

Stability persists even when a resonator is removed, given a sufficiently large array.

Formulas accurately predict the impact of imperfections on device performance.

Abstract

The aim of this work is to derive precise formulas which describe how the properties of subwavelength devices are changed by the introduction of errors and imperfections. As a demonstrative example, we study a class of cochlea-inspired rainbow sensors. These are devices based on a graded array of subwavelength resonators which have been designed to mimic the frequency separation performed by the cochlea. We show that the device's properties (including its role as a signal filtering device) are stable with respect to small imperfections in the positions and sizes of the resonators. Additionally, if the number of resonators is sufficiently large, then the device's properties are stable under the removal of a resonator.