Semi analytical numerical analysis of plasmonic structures in layered geometries

Alparslan, Aytac; Hafner, Christian

doi:10.1117/12.891056

Cited by 4 publications

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“…(4.8) 3 If we take n = 3 (R 3 ), l = 2, m = 1, and rename u ∈ Λ 1 (R 3 ) as u : R 3 → C 3 and α, γ as M −1 µ , −ω 2 M : R 3 → C 3,3 , we obtain the ungauged version of (1.3):…”

Section: Coupling Through An (L − 1)-formmentioning

confidence: 99%

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Coupling finite elements and auxiliary sources

Casati¹,

Hiptmair²

2019

Computers & Mathematics with Applications

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We propose a hybrid method to solve time-harmonic Maxwell's equations in R 3 through the Finite Element Method (FEM) in a bounded region encompassing parameter inhomogeneities, coupled with the Multiple Multipole Program (MMP) in the unbounded complement.FEM and MMP enjoy complementary capabilities. FEM requires a mesh of the computational domain of interest. This is expensive, but can treat inhomogeneous materials, shapes with corners, or other singularities. Moreover, FEM allows a purely local construction of the discrete system of equations.On the other hand, MMP belongs to the class of methods of auxiliary sources and of Trefftz methods, as it employs point sources that are exact solutions of the homogeneous equations as (global) basis functions: one only needs to evaluate them on hypersurfaces to obtain the discrete problem, and the resulting linear combination is valid in the whole domain where the equations hold, which can be unbounded. MMP performs well where the electromagnetic field is smooth, i.e. in the free space far from physical sources and material interfaces.Thus, a natural way to combine the strengths of these methods arises when one needs to simulate the electromagnetic field of components with inhomogeneous parameters or nonsmooth shapes surrounded by free space: use FEM on a mesh defined on the components and MMP in the unbounded domain outside. The boundary between the FEM and MMP domains can be nonphysical if one surrounds the components by a conforming mesh of an "airbox" also modeled by FEM.The interface conditions on the surface of the FEM domain are key to accurate coupled FEM-MMP solutions. Integrating by parts the variational form solved by FEM, surface integrals appear, through which one can impose interface conditions by substituting the ansatz of MMP.iii However, one interface condition (for example, the continuity of the tangential trace for Maxwell's equations) cannot be imposed in this way.To include this additional condition, we derive four methods from Lagrangian functionals that enforce both the variational form in the FEM domain and all the interface conditions between different discretizations:1. Least-squares-based coupling using techniques from PDE-constrained optimization. This approach optimizes a functional for the additional condition, subject to a constraint expressed by the variational form of FEM.2. Discontinuous Galerkin (DG) between the meshed FEM domain and the single-entity "MMP mesh", interpreting MMP as FEM with special basis functions.3. Multi-field variational formulation in the spirit of mortar finite element methods, relying on the same interpretation of MMP as the DG-based coupling.4. Coupling through the Dirichlet-to-Neumann operator : here we introduce a weak formulation of the additional condition where MMP basis functions are used as test functions. This approach is generalized to couple MMP with any numerical method based on volume meshes that fits co-chain calculus.Furthermore, to minimize the meshed region and for the sake of generalization, we as...

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Section: Coupling Through An (L − 1)-formmentioning

confidence: 99%

“…BlockInstruct A is the base class of these three types. 3 The DG-based coupling, being arguably the most difficult strategy to implement out of Chapter 3, has the largest number of BlockInstruct classes, also to consider the differences between its scalar (Section 1.1.1) and vector implementations (Section 1.1.3).…”

Section: Librariesmentioning

confidence: 99%

Coupling finite elements and auxiliary sources

Casati¹,

Hiptmair²

2019

Computers & Mathematics with Applications

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“…The electromagnetic fields caused by dipoles in stratified media are a well-studied subject [11,12,13]. We took advantage of this knowledge and implemented the layered dipole expansion in MMP [14] which saves us from explicitly discretizing the boundaries of layers and therefore reduces the memory requirements and the computational cost signifi-cantly. Since the computation of such a layered dipole expansion is fairly involved, we now present the most important steps in more detail.…”

Section: Dipoles In Layered Mediamentioning

confidence: 99%

MMP Simulation of Plasmonic Particles on Substrate Under E-Beam Illumination

Koch

Niegemann

Hafner

et al. 2018

Springer Series on Atomic, Optical, and Plasma Physics

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A novel numerical approach to investigate the resonance behavior of plasmonic particles on a substrate under e-beam illumination is presented. The method is based on the Multiple Multipole Program (MMP), a generalized point matching technique, and is augmented by the ability to compute layered media and electron energy loss spectroscopy (EELS) measurements. Furthermore, the whole framework is complemented by a mesh-based method that automatically places the multipole expansions and matching points for arbitrary three-dimensional geometries. The performance of our technique is analyzed by a series of numerical experiments. The EELS responses of a plasmonic split-ring resonator in free space and a plasmonic disk dimer on a membrane, as well as the resonant modes, are simulated. Finally, our implementation is compared to the established discontinuous Galerkin time domain (DGTD) method with respect to its computational efficiency. We show significantly improved performance especially for the computation of EELS resonance maps.

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“…By using the automatic expansion distribution routines of OpenMaXwell for the MMP solution, we obtain the results in an efficient and robust way for all the different optimization parameter combinations (the boundary condition mismatch error measured on the scatterers is less than 0.1 percent for the numerical results presented in Section 6). For a detailed description of MMP analysis for layered media, refer to [24][25][26].…”

Section: Boundary Discretization -Mmpmentioning

confidence: 99%

Optimization of a Plasmon-Assisted Waveguide Coupler Using Fem and MMP

Wang¹,

Alparslan²,

Schnepp³

et al. 2014

PIER B

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Abstract-In this paper, we focus on the problem of optimizing plasmonic structures. A plasmonassisted waveguide coupler is considered as a test problem, which leads to a five-dimensional optimization problem carried out by an evolution strategy (ES). The optimization results are verified by a comparative analysis between different solvers, i.e., the finite element package CONCEPTs and the multiple multipole program (MMP). We also compared with results obtained using a deterministic optimization algorithm, namely the Nedler-Mead method as implemented in the commercial software package COMSOL Multiphysics. Some issues concerning deterministic versus evolutionary optimization, in particular, in the field of plasmonics have been discussed.

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Semi analytical numerical analysis of plasmonic structures in layered geometries

Cited by 4 publications

References 0 publications

Coupling finite elements and auxiliary sources

Coupling finite elements and auxiliary sources

MMP Simulation of Plasmonic Particles on Substrate Under E-Beam Illumination

Optimization of a Plasmon-Assisted Waveguide Coupler Using Fem and MMP

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