Mie Resonators Made of Time-Varying Materials for Dynamic Control of Electromagnetic Radiation

Dielectric nanostructures are known to support optical resonances with high quality factors, making them ideal candidates for various advanced light-matter interaction applications. The interaction of light with dielectric particles is often described using generalized Lorenz-Mie theory, where electromagnetic fields are expanded in terms of the eigenfunctions of the vector Helmholtz equation, also known as electromagnetic multipoles. Depending on the shape, size, and refractive index of the particles, they can support different Mie resonances, including dipolar, quadrupolar, and higher-order modes. The interplay of these resonances can be engineered to enable applications such as unidirectional light scattering, nonradiating optical modes, levitating optical forces, and asymmetric imaging. Despite these remarkable achievements, traditional approaches mainly rely on tuning the geometric properties of the particles to achieve desired functionalities, which limits the design of more intricate devices requiring strong spatial dispersion effects. Recently, the emergence of materials with time-varying permittivity has introduced an additional degree of freedom in the design paradigm, which can be exploited to achieve novel functionalities. In our study, we utilize time modulation to dynamically tune the scattering characteristics of optical resonators without relying on their inherent geometrical or dispersion properties. We demonstrate that resonators with time-varying characteristics can dynamically control both spatially coherent light, like plane waves, and incoherent light sources, such as quantum dots. Specifically, we control the interaction of the excited magnetic and electric dipolar modes within a single scatterer using time modulation and demonstrate that forward or backward unidirectional scattering can be obtained by satisfying the Kerker conditions on demand. Moreover, we propose a viable pathway for controlling incoherent quantum light sources using time-modulated dielectric resonators. Our results indicate that a precisely designed set of dielectric resonators can remarkably enhance the spontaneous emission rate of a quantum emitter, while the time-variation in the permittivity can be judiciously optimized to act as a closed feedback loop and compensate for the frequency detuning in the quantum emitter radiation. Finally, we illustrate that the interplay between the excited magnetic and electric multipole moments can be controlled through time modulation to direct the far-field radiation of the quantum emitter to the desired angles. This work not only paves the way for the development of more sophisticated nanophotonic devices but also holds potential for significant advancements in fields such as quantum computing, telecommunications, and advanced imaging technologies.