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Finding reliably and efficiently the spectrum of the resonant states of anoptical system under varying parameters of the medium surrounding it is atechnologically important task, primarily due to various sensing applications.Computationally, it presents, however, a fundamental challenge owing to thenature of the eigenstates of an open system lacking completeness outside it. Wesolve this challenge by making a linear transformation of Maxwell's equationswhich maps perturbations of the surrounding medium onto effective perturbationswithin the system where the resonant states are complete. By treating suchperturbations with the rigorous resonant state expansion, we find the modifiedmodes of the system for arbitrary perturbations of the medium with any requiredaccuracy. Numerically efficient single and few mode approximations are shown tobe precise in practically important cases of, respectively, plasmonicnanoparticles and dielectric micro resonators.

Varying the medium surrounding an optical resonator: An efficient and rigorous way to calculate its spectral changes