Optical resonators are widely used in modern photonics. Their spectral response and temporal dynamics are fundamentally driven by their natural resonances, the so-called quasinormal modes (QNMs), with complex frequencies.For optical resonators made of dispersive materials, the QNM computation requires solving a nonlinear eigenvalue problem. This rises a difficulty that is only scarcely documented in the literature. We review our recent efforts for implementing efficient and accurate QNM-solvers for computing and normalizing the QNMs of micro-and nanoresonators made of highly-dispersive materials. We benchmark several methods for three geometries, a twodimensional plasmonic crystal, a two-dimensional metal grating, and a three-dimensional nanopatch antenna on a metal substrate, in the perspective to elaborate standards for the computation of resonance modes.

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We present a Krylov model-order reduction approach to efficiently compute the spontaneous decay (SD) rate of arbitrarily shaped 3D nanosized resonators. We exploit the symmetry of Maxwell's equations to efficiently construct so-called reduced-order models that approximate the SD rate of a quantum emitter embedded in a resonating nanostructure. The models allow for frequency sweeps, meaning that a single model provides SD rate approximations over an entire spectral interval of interest. Field approximations and dominant quasinormal modes can be determined at low cost as well.

We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature.

An experiment to study an exotic atom with infrared spectroscopy will measure a fundamental parameter related to the spatial dimensions of a proton.