A thorough theoretical study of the optical properties of periodic Si nanosphere arrays is undertaken, placing a particular emphasis on the synergy between multipolar, electric and magnetic, Mie resonances, which occur in high-refractive-index nanoparticles and can lead to a rich variety of phenomena ranging from perfect reflection to controlled diffraction. Systematic calculations using the layer-multiple-scattering method, which we properly extended to describe periodic arrays with many different scatterers per unit cell, in conjunction with finite-element simulations are presented. It is shown that rectangular arrays of pairs of Si nanospheres can efficiently diffract light in reflection or transmission mode at large angles as well as split light with minimum backreflection by properly adjusting the geometry of the structure. Our rigorous full-electrodynamic calculations highlight the importance of higher-order multipoles, which are not taken into account in the commonly employed dipole approximation, in the description of these effects.

A generalized rigorous Floquet scattering-matrix method for stratified anisotropic optical media, subject to a periodic spatiotemporal modulation, is formulated and implemented. The method is applied for studying an optomagnonic cavity formed by an in-plane magnetized ferrite film, in which a magnetostatic surface spin wave propagates, sandwiched between two nonmagnetic dielectric Bragg mirrors. Our results provide unambiguous evidence that externally incident light, when trapped in a cavity mode, experiences a strongly enhanced interaction with the spin wave due to the increased coupling time, which can give rise to pronounced effects if the appropriate selection rules are fulfilled. By means of systematic calculations we reveal and explain some remarkable features of this interaction, such as formation of spectral gaps, controllable transmission, and the emergence of inelastic diffracted beams, and show that efficient conversion of the optical wave can be achieved by triply resonant inelastic scattering through (multi)magnon absorption and emission processes.

We report a thorough theoretical investigation of magnon-assisted photon transitions in magnetic garnet micron-sized spheres, which operate as optomagnonic resonators. In this case, matching the intraband splitting of optical Mie modes, induced by particle magnetization, to the eigenfrequency of the uniform-precession spin wave, high-efficiency triply resonant optical transitions between these modes, through respective emission or absorption of a cavity magnon, are enabled. By means of rigorous full electrodynamic computations, supported by corresponding approximate analytical calculations, we provide compelling evidence of greatly increased optomagnonic interaction, compared to that in similar processes between whispering gallery modes of corresponding submillimeter spheres, due to the reduced magnon mode volume. We explain the underlying mechanisms to a degree that goes beyond existing interpretation, invoking group theory to derive general selection rules and highlighting the role of the photon spin as the key property for maximizing the respective coupling strength.