A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

Schmitt, Nikolai; Scheid, Claire; Lanteri, Stéphane; Moreau, Antoine; Viquerat, Jonathan

doi:10.1016/j.jcp.2016.04.020

Cited by 50 publications

(42 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution across elements is discontinuous, and continuity of the flux is enforced weakly across element interfaces. The DG method with explicit time integration was applied to solve the time-domain Maxwell's equations [27], and has been further developed to simulate wave propagation phenomena through metamaterials at the nanoscale [11], as well as for dispersive media [31,35,37] and more recently for 2D dimers using the hydrodynamic model [59]. DG methods face disadvantages when used for practical 3D applications in the frequency domain or in the time domain with implicit time integration, due to the computational burden that arises from nodal duplication at the interfaces.…”

Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures

Vidal-Codina

Nguyen

et al. 2018

Journal of Computational Physics

View full text Add to dashboard Cite

The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light in deep-subwavelength regions, thereby leading to large nearfield enhancements. The simulation of plasmon resonances presents notable challenges. From the modeling perspective, the realistic behavior of conduction-band electrons in metallic nanostructures is not captured by Maxwell's equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization demands efficient and accurate numerical methods.In this paper, we develop the hybridizable discontinuous Galerkin (HDG) method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of plasmonic nanostructures while accounting for the nonlocal interactions between electrons and the incident light. We introduce a novel postprocessing scheme to recover superconvergent solutions and demonstrate the convergence of the proposed HDG method for the simulation of a 2D gold nanowire and a 3D periodic annular nanogap structure. The results of the hydrodynamic model are compared to those of a simplified local response model, showing that differences between them can be significant at the nanoscale.

show abstract

Section: Introductionmentioning

confidence: 99%

A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures

Vidal-Codina

Nguyen

et al. 2018

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…In contrast to earlier works [6,7], timedomain approaches provide direct access to the nonlinear properties of the hydrodynamic Drude model by solving the full set of nonlinear equations [17,18,21], without making any further assumptions about the nonlinear source terms. In particular, the Discontinuous Galerkin Time-Domain (DGTD) method [22], a time-dependent finite-element framework, has shown good performance characteristics both for nonlocal and nonlinear properties [17,23].…”

Section: Introductionmentioning

confidence: 99%

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

Moeferdt

Kiel

Sproll³

et al. 2018

Phys. Rev. B

View full text Add to dashboard Cite

A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a Discontinuous Galerkin Time-Domain approach and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, secondharmonic generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interprete the physical mechanisms that lead to corresponding field distributions, the associated linear quasi-electrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes, both in the linear and the nonlinear regime. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nano-antenna systems.

show abstract

“…We hope this work will help the community to assess much more easily the influence of nonlocality on the response of metallic structures with nanometer-sized features -especially in cases that are both numerically expensive and the most likely to be influenced by spatial dispersion [6], like the computation of the Purcell effect [32,33] when emitters are placed under an optical patch antenna [34]. Our study actually suggests that, when using advanced simulation tools for complicated geometries [35,36], it is not necessary to use the hydrodynamic model to describe the response of the metal beyond a boundary layer of 2.7 nm in the visible. This is likely to make such simulations less expensive, an obvious need [16] of the community.…”

mentioning

confidence: 95%

Fresnel coefficients and Fabry-Perot formula for spatially dispersive metallic layers

et al. 2017

Self Cite

View full text Add to dashboard Cite

The repulsion between free electrons inside a metal makes its optical response spatially dispersive, so that it is not described by Drude's model but by a hydrodynamic model. We give here fully analytic results for a metallic slab in this framework, thanks to a two-modes cavity formalism leading to a Fabry-Perot formula, and show that a simplification can be made that preserves the accuracy of the results while allowing much simpler analytic expressions. For metallic layers thicker than 2.7 nm modified Fresnel coefficients can actually be used to accurately predict the response of any multilayer with spatially dispersive metals (for reflection, transmission or the guided modes). Finally, this explains why adding a small dielectric layer [Y. Luo et al., Phys. Rev. Lett. 111, 093901 (2013)] allows to reproduce the effects of nonlocality in many cases, and especially for multilayers. Drude's model, where the electromagnetic response of metals is summarized in a local permittivity, has been very successful in describing the optical response of metals even at the scale of a few nanometers. Electrons are however repulsing each other, making the response of metals spatially dispersive -a phenomenon that is completely overlooked in Drude's model. The response is then said to be non-local because the metal can not be described by a simple permittivity any more. This subject has attracted a lot of interest from a theoretical point of view in the seventies and eighties[1, 2], but an experimental evidence that the Drude model could be inaccurate even in the optical domain has been produced only very recently for very narrow gaps between two metals [3,4]. The hydrodynamic model with hard-wall boundaries[5-7] is a sufficiently accurate framework to take these nonlocal effects into account -even if more complex models taking spill-out corrections have very rencently been proposed [8]. It appears now that nonlocal effects have an impact on metallo-dielectric multilayers with deeply subwavelength thicknesses of dielectric or metal[9] for instance when guided modes are supported [6,10] or when trying to design all kinds of plasmonic flat lenses [11][12][13]. The hydrodynamic model is particularly interesting in the framework of multilayers because the fields have analytic expressions in that case [6,10,12,14,15]. Taking nonlocality into account can be complicated for more complex structures, and there is clearly a need for simpler approaches: it has been recently shown [16], spurring debate [17,18], that adding a very thin dielectric layer could yield results that match very well with the prediction of the hydrodynamic model.In the present work, we first obtain simple analytic expressions using a generalized cavity formalism for a single metallic slab. We then show that a simple assumption, which is valid as soon as the metallic layer is thicker than 2.7 nm in the visible range and 5-6 nm in the near UV, can greatly reduce the complexity of the calculus of the nonlocal response. Using our assumption, simpler * antoine.moreau@uca....

show abstract

A DGTD method for the numerical modeling of the interaction of light with nanometer scale metallic structures taking into account non-local dispersion effects

Abstract: International audienc

Cited by 50 publications

References 56 publications

A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures

A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

Fresnel coefficients and Fabry-Perot formula for spatially dispersive metallic layers

Contact Info

Product

Resources

About