High- Q Localized States in Finite Arrays of Subwavelength Resonators

We uncover how to achieve giant Q -factors in finite-length periodic arrays of subwavelength optical resonators. The underlying physics is based on interference between the band-edge mode and a standing mode in the array, and it leads to the formation of spatially localized states with dramatically suppressed radiative losses. We demonstrate this concept for an array of N dipoles with simultaneous cancellation of multipoles up to N -th order and the Q -factor growing as Q ∝ N α, where α ≳ 6.88. We study a realistic array of nanoparticles ( N ≲ 37) supporting the magnetic dipole Mie resonances with the enhanced Purcell factor (∼7600) achieved by tuning the array parameters.