19 research outputs found
A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures
In this paper, we develop a nested hybridizable discontinuous Galerkin (HDG)
method to numerically solve the Maxwell's equations coupled with the
hydrodynamic model for the conduction-band electrons in metals. By means of a
static condensation to eliminate the degrees of freedom of the approximate
solution defined in the elements, the HDG method yields a linear system in
terms of the degrees of freedom of the approximate trace defined on the element
boundaries. Furthermore, we propose to reorder these degrees of freedom so that
the linear system accommodates a second static condensation to eliminate a
large portion of the degrees of freedom of the approximate trace, thereby
yielding a much smaller linear system. For the particular metallic structures
considered in this paper, the resulting linear system obtained by means of
nested static condensations is a block tridiagonal system, which can be solved
efficiently. We apply the nested HDG method to compute the second harmonic
generation (SHG) on a triangular coaxial periodic nanogap structure. This
nonlinear optics phenomenon features rapid field variations and extreme
boundary-layer structures that span multiple length scales. Numerical results
show that the ability to identify structures which exhibit resonances at
and is paramount to excite the second harmonic response.Comment: 31 pages, 7 figure
Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits
With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. The plasmonic response in these extreme-scale gaps is significantly affected by nonlocal electrodynamics, quenching field enhancement and blue-shifting the resonance with respect to a purely local behavior. The extreme mismatch in lengthscales, ranging from millimeter-long wavelengths to atomic-scale charge distributions, poses a daunting computational challenge. In this paper, we perform computations of a single nanoslit using the hybridizable discontinuous Galerkin 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 the slit while accounting for the nonlocal interactions between electrons and the incident light. We study the impact of gap width, film thickness and electron motion model on the plasmon resonances of the slit for two different frequency regimes: (1) terahertz frequencies, which lead to 1000-fold field amplitude enhancements that saturate as the gap shrinks; and (2) the near- and mid-infrared regime, where we show that narrow gaps and thick films cluster Fabry-Pérot (FP) resonances towards lower frequencies, derive a dispersion relation for the first FP resonance, in addition to observing that nonlocality boosts transmittance and reduces enhancement
Computing parametrized solutions for plasmonic nanogap structures
The interaction of electromagnetic waves with metallic nanostructures
generates resonant oscillations of the conduction-band electrons at the metal
surface. These resonances can lead to large enhancements of the incident field
and to the confinement of light to small regions, typically several orders of
magnitude smaller than the incident wavelength. The accurate prediction of
these resonances entails several challenges. Small geometric variations in the
plasmonic structure may lead to large variations in the electromagnetic field
responses. Furthermore, the material parameters that characterize the optical
behavior of metals at the nanoscale need to be determined experimentally and
are consequently subject to measurement errors. It then becomes essential that
any predictive tool for the simulation and design of plasmonic structures
accounts for fabrication tolerances and measurement uncertainties.
In this paper, we develop a reduced order modeling framework that is capable
of real-time accurate electromagnetic responses of plasmonic nanogap structures
for a wide range of geometry and material parameters. The main ingredients of
the proposed method are: (i) the hybridizable discontinuous Galerkin method to
numerically solve the equations governing electromagnetic wave propagation in
dielectric and metallic media, (ii) a reference domain formulation of the
time-harmonic Maxwell's equations to account for geometry variations; and (iii)
proper orthogonal decomposition and empirical interpolation techniques to
construct an efficient reduced model. To demonstrate effectiveness of the
models developed, we analyze geometry sensitivities and explore optimal designs
of a 3D periodic annular nanogap structure.Comment: 28 pages, 9 figures, 4 tables, 2 appendice
Impact of surface roughness in nanogap plasmonic systems
Recent results have shown unprecedented control over separation distances
between two metallic elements hundreds of nanometers in size, underlying the
effects of free-electron nonlocal response also at mid-infrared wavelengths.
Most of metallic systems however, still suffer from some degree of
inhomogeneity due to fabrication-induced surface roughness. Nanoscale roughness
in such systems might hinder the understanding of the role of microscopic
interactions. Here we investigate the effect of surface roughness in coaxial
nanoapertures resonating at mid-infrared frequencies. We show that although
random roughness shifts the resonances in an unpredictable way, the impact of
nonlocal effects can still be clearly observed. Roughness-induced perturbation
on the peak resonance of the system shows a strong correlation with the
effective gap size of the individual samples. Fluctuations due to fabrication
imperfections then can be suppressed by performing measurements on structure
ensembles in which averaging over a large number of samples provides a precise
measure of the ideal system's optical properties
Simulation of the interaction of light with 3‐D metallic nanostructures using a proper orthogonal decomposition‐Galerkin reduced‐order discontinuous Galerkin time‐domain method
International audienc
Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft
Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations
We introduce a \textit{non-modal} analysis technique that characterizes the
diffusion properties of spectral element methods for linear
convection-diffusion systems. While strictly speaking only valid for linear
problems, the analysis is devised so that it can give critical insights on two
questions: (i) Why do spectral element methods suffer from stability issues in
under-resolved computations of nonlinear problems? And, (ii) why do they
successfully predict under-resolved turbulent flows even without a
subgrid-scale model? The answer to these two questions can in turn provide
crucial guidelines to construct more robust and accurate schemes for complex
under-resolved flows, commonly found in industrial applications. For
illustration purposes, this analysis technique is applied to the hybridized
discontinuous Galerkin methods as representatives of spectral element methods.
The effect of the polynomial order, the upwinding parameter and the P\'eclet
number on the so-called \textit{short-term diffusion} of the scheme are
investigated. From a purely non-modal analysis point of view, polynomial orders
between and with standard upwinding are well suited for under-resolved
turbulence simulations. For lower polynomial orders, diffusion is introduced in
scales that are much larger than the grid resolution. For higher polynomial
orders, as well as for strong under/over-upwinding, robustness issues can be
expected. The non-modal analysis results are then tested against under-resolved
turbulence simulations of the Burgers, Euler and Navier-Stokes equations. While
devised in the linear setting, our non-modal analysis succeeds to predict the
behavior of the scheme in the nonlinear problems considered