Abstract
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing ap-plications. Computationally, it presents, however, a fundamental challenge owing to the nature of the eigenstates of an open system lacking completeness outside it. We solve this challenge by making a linear transformation of Maxwell's equations which maps perturbations of the surrounding medium onto effective perturbations within the system where the resonant states are complete. By treating such perturbations with a rigorous resonant-state expansion, we find the modified modes of the system for arbitrary homogeneous perturbations of the medium with any required accuracy. A numerically efficient single-mode approximation is shown to be highly accurate, as illustrated for various plasmonic nanoparticles, including gold nanospheres and silver bowtie antennas.