Exceptional point enhanced small particle detection in systems of subwavelength resonators

TL;DR

The paper addresses sensing tiny particles with systems of subwavelength resonators that operate at an exceptional point. It develops a forward-model based on boundary-integral operators and a capacitance-matrix $\mathcal{C}$, using a two-reflection Neumann-series expansion to capture perturbations caused by a small particle. At simple eigenvalues, resonance shifts scale as $\omegã^2 \approx \omega^2 + (y^* D_\delta E x)/(y^* x)$, while at exceptional points of order $r$ the shifts follow $\widetilde{\omega}=\sqrt{\omega^2+\xi^{1/r}}$, yielding amplified sensitivity $|\xi|=O(|\partial\Omega|^{1/(2r)} d^{-1/r})$. Numerical experiments on a chain of resonators show that exceptional points enhance the signal-to-noise ratio in locating the perturbation, supporting the potential of EP-based sensors for detecting viruses or nanoparticles in the presence of noise.

Abstract

This paper considers the effects of small highly contrasted particles on the subwavelength resonances of a system of high-contrast resonators, with an application to sensing. The key technique is a multiple scattering expansion of the capacitance matrix associated with the perturbed system. At leading order, the perturbation of the scattering resonances is characterized by the associated term of the truncated multiple scattering expansion. When an exceptional point is present in the resonance structure, the perturbation critically affects the subwavelength resonances, which improves the sensitivity of a sensing task in the presence of noise. Numerical experiments demonstrate the use of the proposed reconstruction techniques.

Figures (3)

• Figure 5.1: Perturbation of the simple subwavelength resonance ($\omega_1$) and the degenerate resonance at $\omega_2$ and $\omega_3$, when an additional highly contrasted resonator with a decreasing radius is present.
• Figure 5.2: Visualization of the loss $\ell$, visualized on the $x_3=0$-plane, for a fixed radius $R_\Omega=10^{-4}$. The exact center is set at $z = (3,0,0)^T$.
• Figure 5.3: Applying the steepest descent method \ref{['eq:descent-method']} to a set of nodes near the exact perturbation (sitting at $z=(3,0,0)$). On the right plots, the physical parameters have been tuned, such that the capacitance matrix has an exceptional point. From the top down an increasing level of noise is simulated in the measurements.

Theorems & Definitions (16)

• Lemma 2.1
• Remark 2.2: Assumptions on the contrast of the perturbation
• Lemma 3.1
• proof
• Lemma 3.2
• Proposition 3.3
• proof
• Theorem 3.4
• proof
• Corollary 3.5