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

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 applications. 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 the rigorous resonant state expansion, we find the modified modes of the system for arbitrary perturbations of the medium with any required accuracy. Numerically efficient single and few mode approximations are shown to be precise in practically important cases of, respectively, plasmonic nanoparticles and dielectric micro resonators.

References in corpus (16)

• Rigorous modal analysis of plasmonic nanoresonators
• Optimizing the Drude-Lorentz model for material permittivity - method, program, and examples for gold, silver, and copper
• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Exact mode volume and Purcell factor of open optical systems
• Resonant state expansion applied to three-dimensional open optical systems
• Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing
• Resonant-state expansion of dispersive open optical systems
• Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials
• Shape deformation of nanoresonator: a quasinormal-mode perturbation theory
• How to calculate the pole expansion of the optical scattering matrix from the resonant states
• Quasinormal-mode analysis of grating spectra at fixed incidence angles
• Resonant-state expansion of three-dimensional open optical systems: Light scattering
• Resonant-state expansion of light propagation in non-uniform waveguides
• Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion
• First-order perturbation theory for material changes in the surrounding of open optical resonators
• Applying the resonant-state expansion to realistic materials with frequency dispersion

Cited by in corpus (4)

• Substrate-induced maximum optical chirality of planar dielectric structures
• First-order perturbation theory of eigenmodes for systems with interfaces
• Extending completeness of the eigenmodes of an open system beyond its boundary, for Green's function and scattering-matrix calculations
• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study