Electromagnetic trapped modes in ensembles of dielectric particles: Concept and perspectives

Electromagnetic trapped modes are finite-energy, non-radiating solutions of Maxwell’s equations whose eigenfrequencies lie within the continuous spectrum of propagating waves. Such modes arise when the induced polarization fields cancel all open radiation channels, either due to symmetry-protection or destructive multipole interference, leading to bound states in the continuum. Using the Lippmann–Schwinger integral formulation, trapped modes in dielectric particles, clusters, and metasurfaces can be rigorously described as eigenfunctions of an integral operator with real eigenfrequencies. For spherical resonators, the conditions reduce to characteristic equations involving spherical Bessel functions, while for periodic metasurfaces, radiation suppression is equivalent to the vanishing of Fourier components of the polarization at open Floquet channels. Extensions to parity-time symmetric systems link trapped modes to lasing and coherent perfect absorption, while spatiotemporal analysis reveals their undamped oscillatory dynamics and flat-band localization. This unified theoretical framework highlights the fundamental mechanisms underlying electromagnetic trapping and their practical realization in high-Q resonators, photonic devices, and metasurfaces.