We obtain an eigenmode expansion of the electromagnetic Green’s tensor <i>G</i>(<i>r,r'</i>) for lossy resonators in open
systems, which is simple yet complete. This enables rapid simulations by providing the spatial variation of <i>G</i><sub>0</sub>(<i>r,r'</i>) over both <i>r</i> and <i>r'</i> in one simulation. Few eigenmodes are often necessary for nanostructures, facilitating
both analytic calculations and unified insight into computationally intensive phenomena such as Purcell
enhancement, radiative heat transfer, van der Waals forces, and Förster resonance energy transfer. We bypass
all implementation and completeness issues associated with the alternative quasinormal eigenmode methods, by
defining modes with permittivity rather than frequency as the eigenvalue. Thus, modes decay rather than diverge
at infinity, and are defined by a linear eigenvalue problem, readily implemented using any numerical method.
We demonstrate its general implementation in COMSOL Multiphysics, using the default in-built tools.
Metamaterials consisting of long, circular, cylinders are very popular. It is a fundamental challenge to characterize the effective electromagnetic response of such composites. In this framework, the radius of cylinder is assumed to be considerably smaller than the external wave length, thus the dominant scattered EM fields can be approximately replaced by dipole fields. Previous works dealt mainly with two dimensional (2D) scenarios, i.e., characterizing the effective electromagnetic response for light propagation perpendicular to the cylinder axis. In this work, we generalize this treatment to three dimensions (3D), i.e., we characterize the effective electromagnetic response for light propagation at any angle, and find that the resulting electromagnetic response is non-local, i.e., it depends on the wavevector component parallel to the cylinder axis. We retrieve analytically, the full polarizability tensor and show that it has different contributions for different polarized incoming EM waves (transverse electric and transverse magnetic with respect to the cylindrical axis). It is also diagonal, i.e., it contains no magneto-electric coupling, showing that claims in previous studies were incorrect. Having closed form expressions for polarizability allows us to use effective medium approximation methods, and tailor the spectral response for both electric and magnetic dipolar contributions. It is important to emphasize that for the first time, this gives a fully systematic way to characterize the magnetism. Our analysis holds for additional structures based on cylindrical geometry, such as hole arrays, all-dielectric metamaterials, and multi-layer cylinders. It can be used to explain the electromagnetic response of wire media attributed with a negative refractive index, effective magnetism and hyperbolic dispersion relations. In addition, this approach can be applied to more complex unit cells e.g., consisting of clusters of parallel cylinders.
We show that metal nanoparticles can be used to improve the performance of super-resolution fluorescence nanoscopes based on stimulated-emission-depletion (STED). Compared with a standard STED nanoscope, we show theoretically a resolution improvement by more than an order of magnitude, or equivalently, depletion intensity reductions by more than 2 orders of magnitude and an even stronger photostabilization. Moreover, we present experimental evidence that an optimum resolution, limited by the sizes of the particles used, can be reached for the hybrid NPs for a power of the STED beam one order of magnitude smaller than for the bare cores.