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Simulation of Second Harmonic Generation from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method

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Recent Trends in Computational Photonics

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 204))

Abstract

We apply the Discontinuous Galerkin Time Domain (DGTD) method for numerical simulations of the second harmonic generation from various metallic nanostructures. A Maxwell–Vlasov hydrodynamic model is used to describe the nonlinear effects in the motion of the excited free electrons in a metal. The results are compared with the corresponding experimental measurements for split-ring resonators and plasmonic gap antennas.

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References

  1. M. Kauranen, A.V. Zayats, Nat. Photonics 6, 737 (2012)

    Article  ADS  Google Scholar 

  2. H. Linnenbank, Y. Grynko, J. Foerstner, S. Linden, Light: Sci. Appl. 5 (2016)

    Google Scholar 

  3. J. Butet, K. Thyagarajan, O.J.F. Martin, Nano Lett. 13, 1787 (2013)

    Article  ADS  Google Scholar 

  4. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995)

    MATH  Google Scholar 

  5. P. Monk, Finite Element Methods for Maxwell’s Equations (Oxford Science Publications, Oxford, 2003)

    Book  MATH  Google Scholar 

  6. J. Niegemann, W. Pernice, K. Busch, J. Opt. A: Pure Appl. Opt. 11, 114015 (2009)

    Article  ADS  Google Scholar 

  7. B. Butrylo, F. Musy, L. Nicolas, R. Perrussel, R. Scorretti, Int. J. Comput. Electr. Electron. Eng. 23, 531 (2004)

    Article  Google Scholar 

  8. J. Hesthaven, T. Warburton, J. Comput. Phys. 181, 186 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  9. Y. Grynko, Y. Shkuratov, J. Förstner, Opt. Lett. 38, 5153 (2013)

    Article  ADS  Google Scholar 

  10. K. Busch, M. Knig, J. Niegemann, Laser Photon. Rev. 5, 773 (2011)

    Article  Google Scholar 

  11. A. Kloeckner, T. Warburton, J. Bridge, J. Hesthaven, J. Comput. Phys. 228, 7863 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Bernacki, L. Fezoui, S. Lanteri, S. Piperno, Appl. Math. Model. 30, 744 (2006)

    Article  Google Scholar 

  13. J. Niegemann, M. Koenig, K. Stannigel, K. Busch, Photon. Nanostruct. Fundam. Appl. 7, 2 (2009)

    Article  ADS  Google Scholar 

  14. K. Stannigel, M. König, J. Niegemann, K. Busch, Opt. Express 17, 14934 (2009)

    Article  ADS  Google Scholar 

  15. N. Feth, M. König, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, S. Linden, Opt. Express 18, 6545 (2010)

    Article  ADS  Google Scholar 

  16. Y. Grynko, J. Foerstner, T. Meier, A. Radke, T. Gissibl, P.V. Braun, H. Giessen, in AIP Conference Proceedings (2011), p. 1398

    Google Scholar 

  17. C. Matyssek, J. Niegemann, W. Hergert, K. Busch, Photon. Nanostruct.-Fundam. Appl. 9, 367 (2011)

    Article  ADS  Google Scholar 

  18. A. Hille, R. Kullock, S. Grafstrm, L.M. Eng, J. Comput. Theor. Nanosci. 7 (2010)

    Google Scholar 

  19. R. Kullock, A. Hille, A. Haußmann, S. Grafström, L.M. Eng, Opt. Express 19, 14426 (2011)

    Article  ADS  Google Scholar 

  20. A. Fallahi, F. Krtner, Journal of physics B: atomic. Mol. Opt. Phys. 47, 234015 (2014)

    Article  ADS  Google Scholar 

  21. J. Chen, Q.H. Liu, Proc. IEEE 101, 242 (2013)

    Article  Google Scholar 

  22. J.E. Sipe, V.C.Y. So, M. Fukui, G.I. Stegeman, Phys. Rev. B 21, 4389 (1980)

    Article  ADS  Google Scholar 

  23. N. Feth, S. Linden, M.W. Klein, M. Decker, F.B.P. Niesler, Y. Zeng, W. Hoyer, J. Liu, S.W. Koch, J.V. Moloney, M. Wegener, Opt. Lett. 33, 1975 (2008)

    Article  ADS  Google Scholar 

  24. Y. Zeng, W. Hoyer, J. Liu, S.W. Koch, J.V. Moloney, Phys. Rev. B 79, 235109 (2009)

    Article  ADS  Google Scholar 

  25. J. Liu, M. Brio, Y. Zeng, A.R. Zakharian, W. Hoyer, S.W. Koch, J.V. Moloney, J. Comput. Phys. 229, 5921 (2010)

    Article  ADS  Google Scholar 

  26. C. Ciracì, E. Poutrina, M. Scalora, D.R. Smith, Phys. Rev. B 86, 115451 (2012)

    Google Scholar 

  27. C. Ciracì, E. Poutrina, M. Scalora, D.R. Smith, Phys. Rev. B 85, 201403 (2012)

    Google Scholar 

  28. S. Linden, F.B.P. Niesler, J. Förstner, Y. Grynko, T. Meier, M. Wegener, Phys. Rev. Lett. 109, 015502 (2012)

    Google Scholar 

  29. Y. Grynko, T. Meier, S. Linden, F.B.P. Niesler, M. Wegener, J. Frstner, Proc. SPIE 8623, 86230L (2013)

    Article  ADS  Google Scholar 

  30. R. Chandrasekar, N.K. Emani, A. Lagutchev, V.M. Shalaev, C. Ciraci, D.R. Smith, A.V. Kildishev, in CLEO: QELS Fundamental Science, vol. 1 (2015), p. 1

    Google Scholar 

  31. A. Hille, M. Moeferdt, C. Wolff, C. Matyssek, R. Rodrguez-Oliveros, C. Prohm, J. Niegemann, S. Grafstrm, L.M. Eng, K. Busch, J. Phys. Chem. C 120, 1163 (2016)

    Article  Google Scholar 

  32. F.X. Wang, F.J. Rodríguez, W.M. Albers, R. Ahorinta, J.E. Sipe, M. Kauranen, Phys. Rev. B 80, 233402 (2009)

    Google Scholar 

  33. A. Benedetti, M. Centini, M. Bertolotti, C. Sibilia, Opt. Express 19, 26752 (2011)

    Article  ADS  Google Scholar 

  34. J.S. Hesthaven, T. Warburton, Nodal Discontinuous Galerkin Methods. Algorithms, Analysis, and Applications (Springer, New York, 2008)

    Google Scholar 

  35. J.S. Hesthaven, T. Warburton (2001), technical Report

    Google Scholar 

  36. J. Alvarez, L.D. Angulo, M.F. Pantoja, A.R. Bretones, S.G. Garcia, IEEE Trans. Antennas Propag. 58, 1997 (2010)

    Article  ADS  Google Scholar 

  37. T. Warburton, Dgtd codes, http://www.nudg.org

  38. Parmetis - parallel graph partitioning and fill-reducing matrix ordering, http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview

  39. H. Si, Tetgen - a quality tetrahedral mesh generator and a 3d delaunay triangulator, http://wias-berlin.de/software/tetgen/

  40. P.-O. Persson, G. Strang, SIAM Rev. 46, 329 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  41. L.A. Freitag, C. Ollivier-Gooch, Int. J. Numer. Methods Eng. 40, 3979 (1997)

    Article  Google Scholar 

  42. J. Niegemann, R. Diehl, K. Busch, J. Comput. Phys. 231, 364 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  43. A. Demirel, J. Niegemann, K. Busch, M. Hochbruck, J. Comput. Phys. 285, 133 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  44. L.D. Angulo, J. Alvarez, F.L. Teixeira, M.F. Pantoja, S.G. Garcia, J. Comput. Phys. 256, 678 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  45. G. Cohen, X. Ferrieres, S. Pernet, J. Comput. Phys. 217, 340 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  46. S. Piperno, ESAIM-Math. Model. Numer. Anal.-Model Math. Anal. Numer. 40, 815 (2006)

    Google Scholar 

  47. M. Dumbser, M. Kser, E.F. Toro, Geophys. J. Int. 171, 695 (2006)

    Article  ADS  Google Scholar 

  48. S. Schomann, N. Goedel, T. Warburton, M. Clemens, IEEE Trans. Magn. 46, 3504 (2010)

    Article  ADS  Google Scholar 

  49. N. Goedel, S. Schomann, T. Warburton, M. Clemens, IEEE Trans. Magn. 46, 2735 (2010)

    Article  ADS  Google Scholar 

  50. V. Dolean, H. Fahs, L. Fezoui, S. Lanteri, J. Comput. Phys. 229, 512 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  51. L. Moya, ESAIM: Math. Model. Numer. Anal. 46, 1225 (2012)

    Article  MathSciNet  Google Scholar 

  52. S. Descombes, S. Lanter, L. Moya, J. Sci. Comput. 65, 190 (2013)

    Article  Google Scholar 

  53. V. Alexiades, G. Amiez, P.-A. Gremaud, Commun. Numer. Methods Eng. 12, 31 (1996)

    Article  Google Scholar 

  54. C.D. Meyer, D.S. Balsara, T.D. Aslam, J. Comput. Phys. 257, Part A, 594 (2014)

    Google Scholar 

  55. M.W. Klein, C. Enkrich, M. Wegener, S. Linden, Science 313, 502 (2006)

    Article  ADS  Google Scholar 

  56. F.B.P. Niesler, N. Feth, S. Linden, M. Wegener, Opt. Lett. 36, 1533 (2011)

    Article  ADS  Google Scholar 

  57. J. Alberti, H. Linnenbank, S. Linden, Y. Grynko, J. Förstner, Appl. Phys. B 122, 1 (2016)

    Google Scholar 

  58. P. Biagioni, J.-S. Huang, B. Hecht, Rep. Prog. Phys. 75, 024402 (2012)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing (NIC) and provided on the supercomputer JUROPA at Jülich Supercomputing Centre (JSC) and Paderborn Center for Parallel Computing (PC2). This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) via TRR142.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Paderborn, Warburger Str. 100, 33098, Paderborn, Germany

    Y. Grynko & J. Förstner

Authors
  1. Y. Grynko
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  2. J. Förstner
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Correspondence to Y. Grynko .

Editor information

Editors and Affiliations

  1. Department of Electrical and Electronic Engineering, City, University of London, London, United Kingdom

    Arti Agrawal

  2. School of Electrical and Electronic Engineering, University of Nottingham, Nottingham, United Kingdom

    Trevor Benson

  3. School of Engineering, University of Glasgow, Glasgow, United Kingdom

    Richard M. De La Rue

  4. Department of Physics, King’s College, London, United Kingdom

    Gregory A. Wurtz

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Grynko, Y., Förstner, J. (2017). Simulation of Second Harmonic Generation from Photonic Nanostructures Using the Discontinuous Galerkin Time Domain Method. In: Agrawal, A., Benson, T., De La Rue, R., Wurtz, G. (eds) Recent Trends in Computational Photonics. Springer Series in Optical Sciences, vol 204. Springer, Cham. https://doi.org/10.1007/978-3-319-55438-9_9

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