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Resonances, also known as quasinormal modes (QNM) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The non-Hermiticity arises from the system losses, whether they are material (Joule losses in electromagnetism) or linked to the openness of the problem (radiation losses). In this paper, we focus on the latter delicate matter when considering bounded computational domains mandatory when using e.g. Finite Elements. Dispersive perfectly matched layers and absorbing boundary conditions are studied.

Light emission of europium (Eu3+) ions placed in the vicinity of optically resonant nanoantennas is usually controlled by tailoring the local density of photon states (LDOS). We show that the polarization and shape of the excitation beam can also be used to manipulate light emission, as azimuthally or radially polarized cylindrical vector beam offers to spatially shape the electric and magnetic fields, in addition to the effect of silicon nanorings (Si-NRs) used as nanoantennas. The photoluminescence mappings of the Eu3+ transitions and the Si phonon mappings are strongly dependent of both the excitation beam and the Si-NR dimensions. The experimental results of Raman scattering and photoluminescence are confirmed by numerical simulations of the near-field intensity in the Si nanoantenna and in the Eu3+-doped film, respectively. The branching ratios obtained from the experimental PL maps also reveal a redistribution of the electric and magnetic emission channels. Our results show that it is possible to spatially control both electric and magnetic dipolar emission of Eu3+ ions by switching the laser beam polarization, hence the near-field at the excitation wavelength, and the electric and magnetic LDOS at the emission wavelength. This paves the way for optimized geometries taking advantage of both excitation and emission processes., Comment: 8 pages, 4 figures

We design planar silicon antennas for controlling the emission rate of magnetic or electric dipolar emitters. Evolutionary algorithms coupled to the Green Dyadic Method lead to different optimized geometries which depend on the nature and orientation of the dipoles. We discuss the physical origin of the obtained configurations thanks to modal analysis but also emphasize the role of nanoscale design of the LDOS. We complete our study using finite element method and demonstrate an enhancement up to 2000 of the magnetic Purcell factor in europium ions. Our work brings together random optimizations to explore geometric parameters without constraint, a first order deterministic approach to understand the optimized designs and a modal analysis which clarifies the physical origin of the exaltation of the magnetic Purcell effect., Comment: 18 pages, 11 figures, research article

pyGDM is a python toolkit for electro-dynamical simulations of individual nano-structures, based on the Green Dyadic Method (GDM). pyGDM uses the concept of a generalized propagator, which allows to solve cost-efficiently monochromatic problems with a large number of varying illumination conditions such as incident angle scans or focused beam raster-scan simulations. We provide an overview of new features added since the initial publication [Wiecha, Computer Physics Communications 233, pp.167-192 (2018)]. The updated version of pyGDM is implemented in pure python, removing the former dependency on fortran-based binaries. In the course of this re-write, the toolkit's internal architecture has been completely redesigned to offer a much wider range of possibilities to the user such as the choice of the dyadic Green's functions describing the environment. A new class of dyads allows to perform 2D simulations of infinitely long nanostructures. While the Green's dyads in pyGDM are based on a quasistatic description for interfaces, we also provide as new external python package pyGDM2_retard a module with retarded Green's tensors for an environment with two interfaces. We have furthermore added functionalities for simulations using fast-electron excitation, namely electron energy loss spectroscopy and cathodoluminescence. Along with several further new tools and improvements, the update includes also the possibility to calculate the magnetic field and the magnetic LDOS inside nanostructures, field-gradients in- and outside a nanoparticle, optical forces or the chirality of nearfields. All new functionalities remain compatible with the evolutionary optimization module of pyGDM for nano-photonics inverse design., Comment: 29 pages, 20 figures

In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil geometry, filtering mask, tip/tilt modulation. In a second part we focus the study on the special case of convolutional Kernels. The assumptions required to be in such a regime are described. We then show that these convolutional kernels allow to drastically simplify the WFS's model by summarizing its behavior in a concise and comprehensive quantity called the WFS's Impulse Response. We explain in particular how it allows to compute the sensor's sensitivity with respect to the spatial frequencies. Such an approach therefore provides a fast diagnostic tool to compare and optimize Fourier-based WFSs. In a third part, we develop the impact of the residual phases on the sensor's impulse response, and show that the convolutional model remains valid. Finally, a section dedicated to the Pyramid WFS concludes this work, and illustrates how the slopes maps are easily handled by the convolutional model., Comment: 21 pages, 7 figures

Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the electromagnetic field. This method is applied to multi-domain cavities and photonic crystals including Drude and Drude-Lorentz metals. Numerical results are compared to analytical solutions for simple cavities and to previous results of the literature for photonic crystals, showing excellent agreement. The advantages of the developed method lie on the versatility of the finite element method regarding geometries, and in sparing the use of tedious complex poles research algorithm. Hence the complex spectrum of resonances of non-hermitian operators and dissipative systems, like two-dimensional photonic crystal made of absorbing Drude metal, can be investigated in detail. The method is used to reveal unexpected features of their complex band structures., Comment: to be submitted for publication