Vol. 142
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2013-09-17
Hp-FEM and PML Analysis of Plasmonic Particles in Layered Media
By
Progress In Electromagnetics Research, Vol. 142, 523-544, 2013
Abstract
In this paper, we introduce a high order finite element (FEM) implementation using perfectly matched layer (PML) for the scattering by plasmonic structures inside layered media. The PML is proven to be very accurate and efficient by a comparative analysis with a commercial FEM software and the Multiple Multipole Program (MMP). A convergence analysis using hp-adaptive refinement inside the PML layer shows that adaptive mesh refinement inside the PML layer is most efficient. Based on this convergence analysis an hp-strategy is proposed, which shows a remarkable error reduction for small additional computational costs.
Citation
Mengyu Wang Kersten Schmidt Aytac Alparslan Christian V. Hafner , "Hp-FEM and PML Analysis of Plasmonic Particles in Layered Media," Progress In Electromagnetics Research, Vol. 142, 523-544, 2013.
doi:10.2528/PIER13081407
http://www.jpier.org/PIER/pier.php?paper=13081407
References

1. Bharadwaj, P., B. Deutsch, and L. Novotny, "Optical antennas," Advances in Optics and Photonics, Vol. 1, No. 3, 438-483, 2009.
doi:10.1364/AOP.1.000438

2. Novotny, L. and B. Hecht, Principles of Nano-optics, Cambridge University Press, 2012.
doi:10.1017/CBO9780511794193

3. Smajic, J., C. Hafner, and D. Erni, "Design and optimization of an achromatic photonic crystal bend," Opt. Express, Vol. 11, No. 12, 1378-1384, 2003.
doi:10.1364/OE.11.001378

4. Stewart, M. E., C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, "Nanostructured plasmonic sensors," Chemical Reviews, Vol. 108, No. 2, 494-521, 2008.
doi:10.1021/cr068126n

5. Sannomiya, T., C. Hafner, and J. Voros, "In situ sensing of single binding events by localized surface plasmon resonance," Nano Letters, Vol. 8, No. 10, 3450-3455, 2008.
doi:10.1021/nl802317d

6. Sannomiya, T., C. Hafner, and J. Voros, "Plasmonic nanoparticle based biosensing: Experiments and simulations," Proc. SPIE Plasmonics: Nanoimaging, Nanofabrication, and Their Applications V, Vol. 7395, 73950M, 2009.
doi:10.1117/12.824683

7. Kong, J. A., Electromagnetic Wave Theory, Wiley, New York, 1986.

8. Ihlenburg, F., Finite Element Analysis of Acoustic Scattering, Springer, Berlin & Heidelberg, Germany, 1998.
doi:10.1007/b98828

9. Givoli, D., Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam and New York, 1992.

10. Bonnet-BenDhia, A.-S., G. Dakhia, C. Hazard, and L. Chorfi, "Diffraction by a defect in an open waveguide: A mathematical analysis based on a modal radiation condition," SIAM J. Appl. Math., Vol. 70, No. 3, 677-693, Jul. 2009.

11. Ciraolo, G. and R. Magnanini, "A radiation condition for uniqueness in a wave propagation problem for 2-D open waveguides," Math. Meth. Appl. Sci., Vol. 32, No. 10, 1183-1206, 2009.
doi:10.1002/mma.1084

12. Bonnet-BenDhia, A.-S., B. Goursaud, and C. Hazard, "Mathematical analysis of the junction of two acoustic open waveguides," SIAM J. Appl. Math., Vol. 71, 2048-2071, 2011.

13. Jeresz-Hanckes, C. and J.-C. Nedelec, "Asymptotics for Helmoltz and Maxwell solutions in 3-D open waveguides," Commun. Comput. Phys., Vol. 11, No. 2, 629-646, Feb. 2012.

14. Schmidt, F., "A new approach to coupled interior-exterior Helmholtz-type problems: Theory and algorithms,", Habilitation Thesis, Free University Berlin, Germany, 2002.

15. Aksun, M. I. and G. Dural, "Clarification of issues on the closed-form Green's functions in stratified media," IEEE Transactions on Antennas and Propagation, Vol. 53, No. 11, 3644-3653, 2005.
doi:10.1109/TAP.2005.858571

16. Sauter, S. and C. Schwab, "Boundary Element Methods," Springer-Verlag, Heidelberg, 2011.

17. Alparslan, A., M. I. Aksun, and K. A. Michalski, "Closed-form Green's functions in planar layered media for all ranges and materials," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 3, 602-613, 2010.
doi:10.1109/TMTT.2010.2040354

18. Alparslan, A. and C. Hafner, "Using layered geometry Green's functions in the multiple multipole program," Journal of Computational and Theoretical Nanoscience, Vol. 8, No. 8, 1600-1608, 2011.
doi:10.1166/jctn.2011.1854

19. Berenger, J.-P., "A perfectly matched layer for the absorption of electromagnetic waves," Journal of Computational Physics, Vol. 114, No. 2, 185-200, 1994.
doi:10.1006/jcph.1994.1159

20. Jin, J.-M. and W. C. Chew, "Combining PML and ABC for the finite-element analysis of scattering problems," Microwave and Optical Technology Letters, Vol. 12, No. 4, 192-197, 1996.
doi:10.1002/(SICI)1098-2760(199607)12:4<192::AID-MOP4>3.0.CO;2-B

21. Chew, W. C., W. H. Weedon, and A. Sezginer, "A 3-D perfectly matched medium by coordinate stretching and its absorption of static fields," Applied Computational Electromagnetics Symposium Digest, Vol. 1, 482-489, Citeseer, 1995.

22. Bermudez, A., L. Hervella-Nieto, and A. Prieto, "An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems," Journal of Computational Physics, Vol. 223, No. 2, 469-488, 2007.
doi:10.1016/j.jcp.2006.09.018

23. Collino, F. and P. Monk, "The perfectly matched layer in curvilinear coordinat," SIAM Journal on Scientific Computing, Vol. 19, No. 6, 2061-2090, 1998.
doi:10.1137/S1064827596301406

24. Zschiedrich, L., R. Klose, A. SchÄadle, and F. Schmidt, "A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions," Journal of Computational and Applied Mathematics, Vol. 188, No. 1, 12-32, 2006.
doi:10.1016/j.cam.2005.03.047

25. Chen, Z. and H. Wu, "An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures," SIAM J. Numer. Anal., Vol. 41, No. 3, 799-826, 2003.
doi:10.1137/S0036142902400901

26. Bao, G., Z. Chen, and H. Wu, "Adaptive finite-element method for diffraction gratings," JOSA A, Vol. 22, No. 6, 1106-1114, 2005.
doi:10.1364/JOSAA.22.001106

27. Michler, C., L. Demkowicz, J. Kurtz, and D. Pardo, "Improving the performance of perfectly matched layers by means of hp-adaptivity," Numerical Methods for Partial Differential Equations, Vol. 23, No. 4, 832-858, 2007.
doi:10.1002/num.20252

28. Zschiedrich, L., "Transparent boundary conditions for Maxwell's equations,", Ph.D. Thesis, FU Berlin, Berlin, Germany, Nov. 2009.

29. Nannen, L. and A. Schadle, "Hardy space infinite elements for Helmholtz-type problems with unbounded inhomogeneities," Wave Motion, Vol. 48, No. 2, 116-129, 2011.
doi:10.1016/j.wavemoti.2010.09.004

30. Kettner, B. and F. Schmidt, "The pole condition as transparent boundary condition for resonance problems: Detection of spurious modes," Proc. SPIE, Vol. 7933, 79331B-1-79331B-11, 2011.

31. Kettner, B., "Detection of spurious modes in resonance mode computations --- Pole condition method,", Ph.D. Thesis, FU Berlin, Berlin, Germany, Jul. 2012.

32. Schwab, C., p- and hp-finite Element Methods: Theory and Applications in Solid and Fluid Mechanisms, Oxford University Press, Oxford, UK, 1998.

33. Ainsworth, M., "Discrete dispersion relation for hp-version finite element approximation at high wave number," SIAM J. Numer. Anal., Vol. 42, No. 2, 553-575, 2005.
doi:10.1137/S0036142903423460

34. Melenk, J. M. and S. Sauter, "Convergence analysis for finite element discretizations of the Helmholtz equation with Dirichletto-Neumann boundary conditions," Math. Comp., Vol. 79, No. 272, 1871-1914, 2010.
doi:10.1090/S0025-5718-10-02362-8

35. Melenk, J. M. and S. Sauter, "Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation," SIAM J. Numer. Anal., Vol. 49, No. 3, 1210-1243, 2011.
doi:10.1137/090776202

36. Babuska, I. and B. Q. Guo, "Approximation properties of the h-p version of the finite element method," Computer Methods in Appl. Mechanics Engineering, Vol. 133, 319-346, 1996.
doi:10.1016/0045-7825(95)00946-9

37. Schmidt, K. and P. Kauf, "Computation of the band structure of two-dimensional photonic crystals with hp finite elements," Computer Methods in Appl. Mechanics Engineering, Vol. 198, 1249-1259, Mar. 2009.
doi:10.1016/j.cma.2008.06.009

38. Babushka, I. and W. Rheinbolt, "A posteriori analysis for adaptive finite element computations," SIAM J. Numer. Anal., Vol. 15, 736-754, 1978.

39. Ainsworth, M. and J. T. Oden, "A posteriori error estimation in finite element analysis," Computer Methods in Appl. Mechanics Engineering, Vol. 142, No. 1-2, 1-88, 1997.
doi:10.1016/S0045-7825(96)01107-3

40. Ainsworth, M. and B. Senior, "An adaptive refinement strategy for hp-finite element computations," Appl. Numerical Mathematics, Vol. 26, 165-178, 1998.
doi:10.1016/S0168-9274(97)00083-4

41. Becker, R. and R. Rannacher, "An optimal control approach to a posteriori error estimation in finite element methods," Acta Numerica, Vol. 10, No. 1, 1-102, 2001.

42. Demkowicz, L., Computing with hp-adaptive Finite Elements: One and Two Dimensional Elliptic and Maxwell Problems,, Chapman and Hall/CRC Applied Mathematics and Nonlinear Science, 2006.
doi:10.1201/9781420011685

43. Schnepp, S. M. and T. Weiland, "Efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous Galerkin method," Journal of Computational and Applied Mathematics, Vol. 236, No. 18, 4909-4924, 2011.
doi:10.1016/j.cam.2011.12.005

44. Wihler, T. P., "An hp-adaptive strategy based on continuous Sobolev embeddings," Journal of Computational and Applied Mathematics, Vol. 235, No. 8, 2731-2739, 2011.
doi:10.1016/j.cam.2010.11.023

45. BÄurg, M. and W. Dofler, "Convergence of an adaptive hp finite element strategy in higher space-dimensions," Applied Numerical Mathematics, Vol. 61, No. 11, 1132-1146, 2011.
doi:10.1016/j.apnum.2011.07.008

46. Jackson, J. D., Classical Electrodynamics, 3rd Ed., John Wiley & Sons, 1999.

47. Fang, Y., N.-H. Seong, and D. D. Dlott, "Measurement of the distribution of site enhancements in surface-enhanced Raman scattering," Science, Vol. 321, No. 5887, 388-392, 2008.
doi:10.1126/science.1159499

48. Park, S. J. and R. E. Palmer, "Acoustic plasmon on the Au (111) surface," Physical Review Letters, Vol. 105, No. 1, 016801, 2010.
doi:10.1103/PhysRevLett.105.016801

49. Pohl, K., B. Diaconescu, G. Vercelli, L. Vattuone, V. M. Silkin, E. V. Chulkov, P. M. Echenique, and M. Rocca, "Acoustic surface plasmon on Cu (111)," EPL (Europhysics Letters), Vol. 90, No. 5, 57006, 2010.
doi:10.1209/0295-5075/90/57006

50. Vattuone, L., M. Smerieri, T. Langer, C. Tegenkamp, H. Pfnur, V. M. Silkin, E. V. Chulkov, P. M. Echenique, and M. Rocca, "Correlated motion of electrons on the Au (111) surface: Anomalous acoustic surface-plasmon dispersion and single-particle excitations," Physical Review Letters, Vol. 110, No. 12, 127405, 2013.
doi:10.1103/PhysRevLett.110.127405

51. Vattuone, L., G. Vercelli, M. Smerieri, L. Savio, and M. Rocca, "Acoustic surface plasmon dispersion on nanostructured Cu (111)," Plasmonics, Vol. 7, No. 2, 323-329, 2012.
doi:10.1007/s11468-011-9310-8

52. Politano, A., G. Chiarello, V. Formoso, R. G. Agostino, and E. Colavita, "Plasmon of shockley surface states in Cu (111): A high-resolution electron energy loss spectroscopy study," Physical Review B, Vol. 74, No. 8, 081401, 2006.
doi:10.1103/PhysRevB.74.081401

53. Politano, A., "Low-energy collective electronic mode at a noble metal interface," Plasmonics, Vol. 8, No. 2, 357-360, 2013.
doi:10.1007/s11468-012-9397-6

54. Schmidt, K. and R. Kappeler, "Efficient computation of photonic crystal waveguide modes with dispersive material," Optics Express, Vol. 18, No. 7, 7307-7322, 2010.
doi:10.1364/OE.18.007307

55. Frauenfelder, P. and C. Lage, "Concepts --- An object-oriented software package for partial differential equations," ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 36, No. 05, 937-951, 2002.
doi:10.1051/m2an:2002036

56. Ramos, J. S. and A. Huerta, "Efficient unstructured quadrilateral mesh generation," International Journal for Numerical Methods in Engineering, Vol. 49, 1327-1350, 2010.

57. EZ4U, Mesh Generation Environment, , www.lacan.upc.edu/ez4u.htm.

58. Hafner, C., MaX-1: A Visual Electromagnetics Platform for PCs, John Wiley & Sons, Chichester, UK, 1999.

59. Hafner, C., Post-modern Electromagnetics: Using Intelligent Maxwell Solvers, Wiley, 1999.

60. Alparslan, A. and C. Hafner, "Analysis of photonic structures by the multiple multipole program with complex origin layered geometry Green's functions," Journal of Computational and Theoretical Nanoscience, Vol. 9, No. 3, 479-485, 2012.
doi:10.1166/jctn.2012.2049

61., , COMSOL Multiphysics, http://www.comsol.com/.
doi:10.1166/jctn.2012.2049