Resonance expansions are an intuitive approach to capture the interaction of an optical resonator with light. Herein, a quasinormal mode expansion approach for quadratic observables is presented. The ...approach exploits the rigorous Riesz projection method. A numerical implementation of a state‐of‐the‐art quantum light source demonstrates the applicability with emphasis on modal expansions outside the underlying nanophotonic resonator.
Herein, a quasinormal mode expansion approach for quadratic observables is presented. The approach exploits the rigorous Riesz projection method. A numerical implementation of a state‐of‐the‐art quantum light source demonstrates the applicability with emphasis on modal expansions outside the underlying nanophotonic resonator.
Nonlocal material response distinctively changes the optical properties of nano-plasmonic scatterers and waveguides. It is described by the nonlocal hydrodynamic Drude model, which – in frequency ...domain – is given by a coupled system of equations for the electric field and an additional polarization current of the electron gas modeled analogous to a hydrodynamic flow. Recent attempt to simulate such nonlocal model using the finite difference time domain method encountered difficulties in dealing with the grad–div operator appearing in the governing equation of the hydrodynamic current. Therefore, in these studies the model has been simplified with the curl-free hydrodynamic current approximation; but this causes spurious resonances. In this paper we present a rigorous weak formulation in the Sobolev spaces H(curl) for the electric field and H(div) for the hydrodynamic current, which directly leads to a consistent discretization based on Nédélec’s finite element spaces. Comparisons with the Mie theory results agree well. We also demonstrate the capability of the method to handle any arbitrary shaped scatterer.
We report on an auxiliary field approach for solving nonlinear eigenvalue problems occurring in nano-optical systems with material dispersion. The material dispersion can be described by a rational ...function for the frequency-dependent permittivity, e.g., by a Drude-Lorentz model or a rational function fit to measured material data. The approach is applied to compute plasmonic resonances of a metallic grating.
We discuss an approach for modal expansion of optical far-field quantities based on quasinormal modes (QNMs). The issue of the exponential divergence of QNMs is circumvented by contour integration of ...the far-field quantities involving resonance poles with negative and positive imaginary parts. A numerical realization of the approach is demonstrated by convergence studies for a nanophotonic system.
Many nanophotonic devices rely on the excitation of photonic resonances to enhance light-matter interaction. The understanding of the resonances is therefore of a key importance to facilitate the ...design of such devices. These resonances may be analyzed by use of the quasi-normal mode (QNM) theory. Here, we illustrate how QNM analysis may help study and design resonant nanophotonic devices. We will in particular use the QNM expansion of far-field quantities based on Riesz projection to design optical antennas.
Abstract
Resonances are omnipresent in physics and essential for the description of wave phenomena. We present an approach for computing eigenfrequency sensitivities of resonances. The theory is ...based on Riesz projections and the approach can be applied to compute partial derivatives of the complex eigenfrequencies of any resonance problem. Here, the method is derived for Maxwell’s equations. Its numerical realization essentially relies on direct differentiation of scattering problems. We use a numerical implementation to demonstrate the performance of the approach compared to differentiation using finite differences. The method is applied for the efficient optimization of the quality factor of a nanophotonic resonator.
Dimensional microscopy is an essential tool for non-destructive and fast inspection of manufacturing processes. Standard approaches process only the measured images. By modelling the imaged structure ...and solving an inverse problem, the uncertainty on dimensional estimates can be reduced by orders of magnitude. At the same time, the inverse problem needs to be solved in a timely manner. Here we present a method of accelerating the inverse problem by reducing images to their elementary features, thereby extracting the relevant information and distinguishing it from noise. The resulting reduction in complexity allows the inverse problem to be solved more efficiently by utilize cutting edge machine learning based optimization techniques. By employing the techniques presented here, we are able to perform for highly accurate and fast dimensional microscopy.
•Contour integral method numerically solves nonlinear eigenvalue problems.•Riesz-projection-based method allows for computation of physically relevant eigensolutions.•Applications to nanophotonic and ...nanoplasmonic problems are demonstrated.
We propose an algorithm for general nonlinear eigenvalue problems to compute physically relevant eigenvalues within a chosen contour. Eigenvalue information is explored by contour integration incorporating different weight functions. The gathered information is processed by solving a nonlinear system of equations of small dimension prioritizing eigenvalues with high physical impact. No auxiliary functions have to be introduced since linearization is not used. The numerical implementation is straightforward as the evaluation of the integrand can be regarded as a blackbox. We apply the method to a quantum mechanical problem and to two nanophotonic systems.
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