Cascades of quasi-bound states in the continuum.

Future technologies aim to radically increase photonic integration, which can be achieved either by structuring the materials or by cleverly manipulating photonic resonances. The latter method involves several tunable resonant modes in a single simple structure. Here we demonstrate experimentally and theoretically the existence of multiple cascades of quasi-bound states in the continuum in single dielectric resonators with rectangular cross sections - in rings, split rings, and cuboids, which form the basis of modern photonics. The effect is determined by the photonic structure of such resonators: it consists of individual galleries, each starting with a transverse Fabry-Pérot-like resonance in height or width and continuing with an equidistant sequence of longitudinal modes. When only one of the transverse dimensions in the spectrum changes, only one gallery type is predominantly shifted, leading to the avoiding crossings with the other gallery and the formation of multiple cascades of quasi-bound states in the continuum via the Friedrich-Wintgen mechanism. This "Fabry-Pérot-tronic" has an obvious advantage over the "Mie-tronic", whose only variable geometric parameter is the radius of the sphere. Such single dielectric resonators with cascades of quasi-bound states in the continuum can become building blocks for multichannel sensors, antennas, amplifiers, and lasers with a wide range of equidistant generation frequencies; in addition, such a simple resonator creates a new platform for multifrequency sensing using machine learning.