Discontinuous Galerkin methods for nano-photonics
18 May 2011-pp 1-2
TL;DR: Together with advanced material models, Discontinuous Galerkin methods represent an ideal tool for the quantitative analysis of nano-photonic systems and lead to highly efficient explicit time-stepping schemes.
Abstract: We present our results regarding the modeling and simulation of nano-photonic elements using Discontinuous Galerkin Finite-Element techniques. Just like ordinary finite-element approaches, these methods provide an adaptive spatial resolution. However, in contrast to ordinary finite elements, these methods lead to highly efficient explicit time-stepping schemes. Together with advanced material models, Discontinuous Galerkin methods represent an ideal tool for the quantitative analysis of nano-photonic systems. We demonstrate this by investigating certain prototypical nano-photonic elements such as micro-resonators.
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18 Dec 2007
TL;DR: The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations.
Abstract: The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEs, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEs, e.g., Maxwells equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations. These developments are done in detail inone and two dimensions on general unstructured grids with high-order elements and all essential routines for 3D extensions are also included and discussed briefly. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters.
2,014 citations
TL;DR: In this article, a high-Q micro-resonator made of low-loss, thermoplastic polymer poly(methyl methacrylate) (PMMA) directly processed on a silicon substrate is presented.
Abstract: We report on the fabrication of high-Q microresonators made of low-loss, thermoplastic polymer poly(methyl methacrylate) (PMMA) directly processed on a silicon substrate. Using this polymer-on-silicon material in combination with a thermal reflow step enables cavities of conical geometry with an ultrasmooth surface. The cavity Q factor of these PMMA resonators is above 2×106 in the 1300 nm wavelength range. Finite element simulations show the existence of a variety of “whispering gallery” modes in these resonators explaining the complexity of the measured transmission spectra.
115 citations
TL;DR: Numerical calculations based on a Discontinuous Galerkin Time-Domain approach are in good agreement with the experiments and support the physical interpretation of the findings.
Abstract: Extinction cross-section spectra of split-ring-resonator dimers have been measured at near-infrared frequencies with a sensitive spatial modulation technique. The resonance frequency of the dimer's coupled mode as well as its extinction cross-section and its quality factor depend on the relative orientation and separation of the two split-ring resonators. The findings can be interpreted in terms of electric and magnetic dipole-dipole interaction. Numerical calculations based on a Discontinuous Galerkin Time-Domain approach are in good agreement with the experiments and support our physical interpretation.
79 citations
"Discontinuous Galerkin methods for ..." refers background in this paper
...As a result, realistic computations, also for metallic nanostructures come within reach [4, 6 ]....
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TL;DR: A novel way to accurately implement delta-like point sources is proposed and a detailed study on the performance of PMLs within the DG framework is presented, demonstrating that the PML-performance may be substantially improved through an appropriate choice of the absorption profile.
Abstract: In thiswork, we investigate the use of higher-order Discontinuous Galerkin (DG) methods for time-domain computations of nano-photonic systems. We briefly discuss the implementation of such methods and comment on several important extensions such as Perfectly Matched Layers (PMLs), sources and dispersive materials. In particular, we propose a novel way to accurately implement delta-like point sources and we present a detailed study on the performance of PMLs within the DG framework. We demonstrate that the PML-performance may be substantially improved through an appropriate choice of the absorption profile. Finally, we employ our specific version of the DG method to certain plasmonic systems such as silver cylinders and nano-structured metallic films.
76 citations
TL;DR: The three-dimensional Discontinuous-Galerkin Time-Domain method is applied to the investigation of the optical properties of bar- and V-shaped metallic nanostructures on dielectric substrates and finds significant deviations from the quasi-static theory.
Abstract: We apply the three-dimensional Discontinuous-Galerkin Time-Domain method to the investigation of the optical properties of bar- and V-shaped metallic nanostructures on dielectric substrates. A flexible finite element-like mesh together with an expansion into high-order basis functions allows for an accurate resolution of complex geometries and strong field gradients. In turn, this provides accurate results on the optical response of realistic structures. We study in detail the influence of particle size and shape on resonance frequencies as well as on scattering and absorption efficiencies. Beyond a critical size which determines the onset of the quasi-static limit we find significant deviations from the quasi-static theory. Furthermore, we investigate the influence of the excitation by comparing normal illumination and attenuated total internal reflection setups. Finally, we examine the possibility of coherently controlling the local field enhancement of V-structures via chirped pulses.
62 citations
"Discontinuous Galerkin methods for ..." refers background or methods in this paper
...We have applied our Discontinuous Galerkin Time-Domain (DGTD) framework to a number of nano-photonic systems that include dielectric resonators and metallic nano-particles [ 1-4 ]....
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...As a result, realistic computations, also for metallic nanostructures come within reach [ 4 ,6]....
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