Identification of Analytical Singularity in a Non-Plasmonic Nanosensing System

Optical sensing works most efficiently around the singularity of resonances. In the pursuit of high quality-factor and sensitivity, non-plasmonic nanosensors are desired as metallic materials are intrinsically lossy. However, standalone resonant systems of dielectric nanoparticles (NPs) generally do not possess a pole or its identification has proven to be hard across the complex frequency domain. To solve this problem, an active external cavity is designed and the dielectric NP is put inside it to formulate a cavity-NP (C-NP) system. The dielectric NP has dimensions comparable with the effective wavelength in the particle material and the coupled resonance is shown to exhibit a pole when a singular optimum gain is applied, overcoming the no-pole-limitation of dielectric NPs. The underlying physics of the coupled system is studied with the pseudo-orthonormal eigenmode method (POEM), which can treat such non-Hermitian systems and quickly pinpoint the singularity from the real frequencies. The POEM study generates a set of guidelines that facilitate device design and experimental optimization. Through dynamic finite-difference time-domain simulations, the all-dielectric gain-assisted cavity-NP structure thus identified is shown to reach a pole at small optical gain. When used as a sensor, the system accommodates nanoscale sensing volume and giant sensitivity when operated around its pole.