High-Q Localized States in Finite Arrays of Subwavelength Resonators

Abstract

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.

Fast Simulation of Light Scattering and Harmonic Generation in Axially Symmetric Structures in COMSOL

“…123 The band- edge states have already been successfully utilized for enhancing light matter interaction enhancing PL emission of quantum dots 124,125 and achieving lasing regime. 126 The Q-factor of these states rapidly grows ∼N 3 with the number of particles in the array or even faster ∼N 5 for degenerate band-edge or even as ∼N 7 under further engineering of the band structure and radiative-loss channels, consistently with works by Blaustein et al, 127 Figotin and Vitebskiy, 123 and Kornovan et al, 128 respectively. The high Q-factor of band-edge-like modes in the finite arrays of resonant dielectric cylinders provides sufficient field enhancement for observing intense SHG.…”

“…The additional side peaks in the SHG spectrum are also associated with the resonances in the array close to the wavelength of the second harmonic. The further engineering of Q-factor in onedimensional arrays may increase the SHG efficiency even further 128 making them perspective components of nonlinear planar nanophotonics.…”

Engineering of High-Q States via Collective Mode Coupling in Chains of Mie Resonators

“…Note that the other dispersion branches are well separated in frequency from the considered one, thus simplifying the experimental observation of the resonances in the finite chain; see Supporting Information, Section C. The resonant frequencies of the eigenmodes of the finite chain of N = 8 cylinders are shown in Figure a with the square markers colored to indicate the Q -factor of the corresponding resonances. A particular wavenumber for each mode of a finite chain was determined based on the field distribution of the dominant field component: ( qa /π) s = s /( N + 1), where s – 1 is the number of sign changes in the distribution of the dipole moments in the chain. For instance, according to the field distribution in Figure c, s = 8 for mode M 1 , making it the closest one to the edge of the Brillouin zone.…”

“…Although experimental results reported in the literature show relatively moderate Q -factors typically growing as Q ∝ N 3 with the number of periods in the chain N , generally they can have a compact footprint and provide more flexibility owing to the bottom-up approach in their design. Moreover, it was recently predicted that the Q -factor of such collective states can be substantially increased in a chain of nanoresonators with a purely dipole response due to coupling between two modes via a radiation continuum. , However, this requires periods of the chain a ≈ 0.2λ (where λ is the operational wavelength), which is practically impossible to achieve in realistic optical chains in a resonant regime due to the upper limit of the available refractive index n ≲ 4.…”

“…Moreover, it was recently predicted that the Qfactor of such collective states can be substantially increased in a chain of nanoresonators with a purely dipole response due to coupling between two modes via a radiation continuum. 25,26 However, this requires periods of the chain a ≈ 0.2λ (where λ is the operational wavelength), which is practically impossible to achieve in realistic optical chains in a resonant regime due to the upper limit of the available refractive index n ≲ 4.…”