Abstract
Nanophotonics is the field of science and technology which aimed at establishing and using the peculiar properties of light and light/matter interactions in various nanostructures. The numerical modeling of such interactions requires to solve the system of time-domain Maxwell equations possibly coupled to appropriate models of physical dispersion in metals such as the Drude and Drude-Lorentz models. In this paper, we discuss about the development of a high order discontinuous Galerkin time-domain solver for nanophotonics applications in the linear regime. For the numerical treatment of dispersion models in metals, we have adopted an Auxiliary Differential Equation (ADE) technique leading to solve the time-domain Maxwell equations coupled to a system of ODEs. We present numerical results that demonstrate the accuracy of the proposed numerical methodology for nanstructured settings involving curvilinear geometrical features.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
All the simulations are run in parallel on 16 CPUs.
References
K. Busch, M. König, J. Niegemann, Discontinuous Galerkin methods in nanophotonics. Laser Photonics Rev. 5, 1–37 (2011)
M. Carpenter, C. Kennedy, Fourth-order 2n-storage Runge-Kutta schemes. Tech. rep., NASA Technical Memorandum MM-109112 (1994)
T. Chung, S.Y. Lee, E.Y. Song, H. Chun, B. Lee, Plasmonic nanostructures for nanoscale biosensing. Sensors 11, 10907–10929 (2011)
H. Fahs, S. Lanteri, A high-order non-conforming discontinuous Galerkin method for time-domain electromagnetics. J. Comput. Appl. Math. 234, 1088–1096 (2010)
L. Fezoui, S. Lanteri, S. Lohrengel, S. Piperno, Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: Math. Model. Numer. Anal. 39(6), 1149–1176 (2005)
J. Hesthaven, T. Warburton, Nodal high-order methods on unstructured grids. I. Time-domain solution of Maxwell’s equations. J. Comput. Phys. 181(1), 186–221 (2002)
J. Huang, J.A. Encinar, Reflectarray Antennas (IEEE Press, New York, 2008)
H. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981)
F. Le, D.W. Brandl, Y.A. Urzhumov, H. Wang, J. Kundu, N.J. Halas, J. Aizpurua, P. Nordlander, Metallic nanoparticle arrays: a common substrate for both surface-enhanced Raman scattering and surface-enhanced infrared absorption. ACS Nano 2, 707–718 (2008)
B. Luk’yanchuk, N.I. Zheludev, S.A. Maier, N.J. Halas, P. Nordlander, H. Giessen, C.T. Chong, The Fano resonance in plasmonic nanostructures and metamaterials. Nat. Mater. 9, 707–715 (2010)
S. Maier, Plasmonics - Fundamentals and Applications (Springer, Berlin, 2007)
C. Matysseka, J. Niegemann, W. Hergertb, K. Busch, Computing electron energy loss spectra with the discontinuous Galerkin time-domain method. Photonics Nanostruct. 9(4), 367–373 (2011)
J. Niegemann, M. König, K. Stannigel, K. Busch, Higher-order time-domain methods for the analysis of nano-photonic systems. Photonics Nanostruct. 7, 2–11 (2009)
J. Niegemann, R. Diehl, K. Busch, Efficient low-storage Runge-Kutta schemes with optimized stability regions. J. Comput. Phys. 231(2), 364–372 (2012)
A. Taflove, S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edn. (Artech House Publishers, Boston, 2005)
J. Viquerat, Simulation of electromagnetic waves propagation in nano-optics with a high-order discontinuous Galerkin time-domain method. Ph.D. thesis, University of Nice-Sophia Antipolis (2015). https://tel.archives-ouvertes.fr/tel-01272010
J. Viquerat, C. Scheid, A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light-matter interactions. J. Comput. Appl. Math. 289, 37–50 (2015)
K. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14(3), 302–307 (1966)
L. Zou, M. Lopez-Garcia, W. Withayachumnankul, C.M. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, R. Oulton, M. Klemm, C. Fumeaux, Spectral and angular characteristics of dielectric resonator metasurface at optical frequencies. Appl. Phys. Lett. 105, 191, 109 (2014)
L. Zou, W. Withayachumnankul, C. Shah, A. Mitchell, M. Bhaskaran, S. Sriram, C. Fumeaux, Dielectric resonator nanoantennas at visible frequencies. Opt. Express 21, 1344–1352 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Lanteri, S., Scheid, C., Klemm, M., Viquerat, J. (2017). High Order DGTD Solver for the Numerical Modeling of Nanoscale Light/Matter Interaction. In: Bittencourt, M., Dumont, N., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016. Lecture Notes in Computational Science and Engineering, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-65870-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-319-65870-4_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-65869-8
Online ISBN: 978-3-319-65870-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)