## A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications |

JOSA A, Vol. 30, Issue 11, pp. 2175-2187 (2013)

http://dx.doi.org/10.1364/JOSAA.30.002175

Acrobat PDF (1376 KB)

### Abstract

In this paper we demonstrate that rigorous high-order perturbation of surfaces (HOPS) methods coupled with analytic continuation mechanisms are particularly well-suited for the assessment and design of nanoscale devices (e.g., biosensors) that operate based on surface plasmon resonances generated through the interaction of light with a periodic (metallic) grating. In this connection we explain that the characteristics of the latter are perfectly aligned with the optimal domain of applicability of HOPS schemes, as these procedures can be shown to be the methods of choice for low to moderate wavelengths of radiation and grating roughness that is representable by a few (e.g., tens of) Fourier coefficients. We argue that, in this context, the method can, for instance, produce full and precise reflectivity maps in computational times that are orders of magnitude faster than those of alternative numerical schemes (e.g., the popular “C-method,” finite differences, integral equations or finite elements). In this initial study we concentrate on the description of the basic principles that underlie the solution scheme, including those that relate to analytic continuation procedures. Within this framework, we explain how, in spite of conventional wisdom to the contrary, the resulting perturbative techniques can provide a most valuable tool for practical investigations in plasmonics. We demonstrate this with some examples that have been previously discussed in the literature (including treatments of the reflectivity and band gap structure of some simple geometries) and extend this to demonstrate the wider applicability of the proposed approach.

© 2013 Optical Society of America

## 1. INTRODUCTION

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5. T. W. Johnson, Z. J. Lapin, R. Beams, N. C. Lindquist, S. G. Rodrigo, L. Novotny, and S.-H. Oh, “Highly reproducible near-field optical imaging with sub-20-nm resolution based on template-stripped gold pyramids,” ACS Nano **6**, 9168–9174 (2012). [CrossRef]

6. F. J. García-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. **82**, 729–787 (2010). [CrossRef]

7. J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. **108**, 462–493 (2008). [CrossRef]

8. N. C. Lindquist, P. Nagpal, K. M. McPeak, D. J. Norris, and S.-H. Oh, “Engineering metallic nanostructures for plasmonics and nanophotonics,” Rep. Prog. Phys. **75**, 036501 (2012). [CrossRef]

9. D. Barchiesi, B. Guizal, and T. Grosges, “Accuracy of local field enhancement models: toward predictive models?” Appl. Phys. B **84**, 55–60 (2006). [CrossRef]

12. J. Smajic, C. Hafner, L. Raguin, K. Tavzarashvili, and M. Mishrikey, “Comparison of numerical methods for the analysis of plasmonic structures,” J. Comput. Theor. Nanosci. **6**, 763–774 (2009). [CrossRef]

13. A. Schädle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, “Domain decomposition method for Maxwell’s equations: scattering off periodic structures,” J. Comput. Phys. **226**, 477–493 (2007). [CrossRef]

17. O. Tsilipakos, A. Pitilakis, A. Tasolamprou, T. Yioultsis, and E. Kriezis, “Computational techniques for the analysis and design of dielectric-loaded plasmonic circuitry,” Opt. Quantum Electron. **42**, 541–555 (2011). [CrossRef]

18. D. Christensen and D. Fowers, “Modeling SPR sensors with the finite-difference time-domain method,” Biosens. Bioelectron. **11**, 677–684 (1996). [CrossRef]

23. A. Shahmansouri and B. Rashidian, “Comprehensive three-dimensional split-field finite-difference time-domain method for analysis of periodic plasmonic nanostructures: near- and far-field formulation,” J. Opt. Soc. Am. B **28**, 2690–2700 (2011). [CrossRef]

24. O. P. Bruno and M. C. Haslam, “Efficient high-order evaluation of scattering by periodic surfaces: deep gratings, high frequencies, and glancing incidences,” J. Opt. Soc. Am. A **26**, 658–668 (2009). [CrossRef]

31. M. Wang, C. Engstrom, K. Schmidt, and C. Hafner, “On high-order FEM applied to canonical scattering problems in plasmonics,” J. Comput. Theor. Nanosci. **8**, 1564–1572 (2011). [CrossRef]

*surface*discretizations and their formulation intrinsically encodes the outgoing character of diffracted waves. These advantages, however, are attained at the expense of introducing

*full*, i.e., not sparse, (impedance) matrices whose numerical inversion can render the methods uncompetitive, unless appropriate acceleration schemes are introduced (see, for instance, [24

24. O. P. Bruno and M. C. Haslam, “Efficient high-order evaluation of scattering by periodic surfaces: deep gratings, high frequencies, and glancing incidences,” J. Opt. Soc. Am. A **26**, 658–668 (2009). [CrossRef]

32. Y. Otani and N. Nishimura, “A periodic FMM for Maxwell’s equations in 3D and its applications to problems related to photonic crystals,” J. Comput. Phys. **227**, 4630–4652 (2008). [CrossRef]

33. A. D. Baczewski, N. C. Miller, and B. Shanker, “Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions,” J. Opt. Soc. Am. A **29**, 531–540 (2012). [CrossRef]

34. H. Kurkcu and F. Reitich, “Stable and efficient evaluation of periodized Green’s functions for the Helmholtz equation at high frequencies,” J. Comput. Phys. **228**, 75–95 (2009). [CrossRef]

55. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. **4**, 351–378 (1951). [CrossRef]

57. E. Rodriguez and Y. Kim, “A unified perturbation expansion for surface scattering,” Radio Sci. **27**, 79–93 (1992). [CrossRef]

58. C.-A. Guérin and A. Sentenac, “Second-order perturbation theory for scattering from heterogeneous rough surfaces,” J. Opt. Soc. Am. A **21**, 1251–1260 (2004). [CrossRef]

60. A. Trügler, J.-C. Tinguely, J. R. Krenn, A. Hohenau, and U. Hohenester, “Influence of surface roughness on the optical properties of plasmonic nanoparticles,” Phys. Rev. B **83**, 081412(R) (2011). [CrossRef]

61. A. A. Maradudin and E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. **32**, 3335–3343 (1993). [CrossRef]

65. H.-Y. Xie, M.-Y. Ng, and Y.-C. Chang, “Analytical solutions to light scattering by plasmonic nanoparticles with nearly spherical shape and nonlocal effect,” J. Opt. Soc. Am. A **27**, 2411–2422 (2010). [CrossRef]

36. T. Elfouhaily and C. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Wave Random Media **14**, R1–R40 (2004). [CrossRef]

66. J.-J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B **37**, 6436–6441 (1988). [CrossRef]

68. A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A **18**, 2778–2788 (2001). [CrossRef]

*complex analytic*functions of a parameter measuring (analytic) boundary deformations for values of this parameter that include a complex neighborhood of

*the entire real line*[69

69. O. P. Bruno and F. Reitich, “Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh , Sect. A **122**, 317–340 (1992). [CrossRef]

70. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A **10**, 1168–1175 (1993). [CrossRef]

70. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A **10**, 1168–1175 (1993). [CrossRef]

71. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A **10**, 2307–2316 (1993). [CrossRef]

74. L. Kazandjian, “A discussion of the properties of the Rayleigh perturbative solution in diffraction theory,” Wave Motion **42**, 169–176 (2005). [CrossRef]

36. T. Elfouhaily and C. Guérin, “A critical survey of approximate scattering wave theories from random rough surfaces,” Wave Random Media **14**, R1–R40 (2004). [CrossRef]

58. C.-A. Guérin and A. Sentenac, “Second-order perturbation theory for scattering from heterogeneous rough surfaces,” J. Opt. Soc. Am. A **21**, 1251–1260 (2004). [CrossRef]

## 2. PRELIMINARIES: MAXWELL’S EQUATIONS AND SURFACE PLASMONS

71. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A **10**, 2307–2316 (1993). [CrossRef]

*finite*number of reflected waves are propagating (namely, those corresponding to indices

78. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. **216**, 398–410 (1968). [CrossRef]

79. B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. **77**, 1889–1892 (1996). [CrossRef]

80. H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. **80**, 404–406 (2002). [CrossRef]

81. R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. **21**, 1530–1533 (1968). [CrossRef]

## 3. A FAST, HIGH-ORDER BOUNDARY PERTURBATION

70. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A **10**, 1168–1175 (1993). [CrossRef]

72. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A **10**, 2551–2562 (1993). [CrossRef]

71. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A **10**, 2307–2316 (1993). [CrossRef]

72. O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A **10**, 2551–2562 (1993). [CrossRef]

*explicit*nature of the solution in the case wherein the interface is entirely flat. This, in turn, suggests that this solution may be

*analytically*continued to that of an undulated surface. More precisely, for a normalized profile

**10**, 2307–2316 (1993). [CrossRef]

69. O. P. Bruno and F. Reitich, “Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh , Sect. A **122**, 317–340 (1992). [CrossRef]

*complex analytic*functions of the parameter

63. M. A. Demir and J. T. Johnson, “Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces,” J. Opt. Soc. Am. A **20**, 2330–2337 (2003). [CrossRef]

67. D. R. Jackson, D. P. Winebrenner, and A. Ishimaru, “Comparison of perturbation theories for rough-surface scattering,” J. Acoust. Soc. Am. **83**, 961–969 (1988). [CrossRef]

74. L. Kazandjian, “A discussion of the properties of the Rayleigh perturbative solution in diffraction theory,” Wave Motion **42**, 169–176 (2005). [CrossRef]

82. J. Uretsky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. **33**, 400–427 (1965). [CrossRef]

*converges*for small values of the parameter

69. O. P. Bruno and F. Reitich, “Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh , Sect. A **122**, 317–340 (1992). [CrossRef]

*complex analytic in a whole neighborhood of the real line*; see the example in Fig. 2 (here and throughout, and whenever appropriate, the axes denote measures in

*nanometers*).

**10**, 2307–2316 (1993). [CrossRef]

*recursion*:

*convolution*nature of the inner sums (that can therefore be effected with fast Fourier transforms), and to the relatively low orders

**10**, 2307–2316 (1993). [CrossRef]

*Padé approximants*that can be readily evaluated from knowledge of the Taylor coefficients

84. A. Rakic, A. Djurišic, J. Elazar, and M. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**, 5271–5283 (1998). [CrossRef]

85. Z. Chen, I. R. Hooper, and J. R. Sambles, “Low dispersion surface plasmon–polaritons on deep silver gratings,” J. Mod. Opt. **53**, 1569–1576 (2006). [CrossRef]

87. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

85. Z. Chen, I. R. Hooper, and J. R. Sambles, “Low dispersion surface plasmon–polaritons on deep silver gratings,” J. Mod. Opt. **53**, 1569–1576 (2006). [CrossRef]

91. T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. **81**, 665–668 (1998). [CrossRef]

93. I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B **65**, 165432 (2002). [CrossRef]

## 4. NUMERICAL RESULTS

### A. Analytic Continuation

41. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B **54**, 6227–6244 (1996). [CrossRef]

94. E. P. Da Silva, G. A. Farias, and A. A. Maradudin, “Analysis of three theories of scattering of electromagnetic radiation by gratings,” J. Opt. Soc. Am. A **4**, 2022–2024 (1987). [CrossRef]

94. E. P. Da Silva, G. A. Farias, and A. A. Maradudin, “Analysis of three theories of scattering of electromagnetic radiation by gratings,” J. Opt. Soc. Am. A **4**, 2022–2024 (1987). [CrossRef]

94. E. P. Da Silva, G. A. Farias, and A. A. Maradudin, “Analysis of three theories of scattering of electromagnetic radiation by gratings,” J. Opt. Soc. Am. A **4**, 2022–2024 (1987). [CrossRef]

*qualitatively*from more accurate representations corresponding to approximations of orders

**4**, 2022–2024 (1987). [CrossRef]

*several digits of accuracy*. Indeed, for instance, Fig. 4 shows the maximum

*relative*error in the value of

*accelerate*convergence to the exact solution. This is clearly exemplified in Fig. 4 which shows, for instance, that a Taylor approximation of order

*full double precision accuracy*.

*do not admit*a high-order representation in terms of Taylor series, and Padé approximation (or other analytic continuation mechanisms) are essential to attain convergence. The configuration is taken from the work of Chen

*et al.*[85

85. Z. Chen, I. R. Hooper, and J. R. Sambles, “Low dispersion surface plasmon–polaritons on deep silver gratings,” J. Mod. Opt. **53**, 1569–1576 (2006). [CrossRef]

**53**, 1569–1576 (2006). [CrossRef]

*diverges*for wavelengths in the vicinity of the resonances for heights that exceed approximately 15 nm.

### B. Reflection Data, Reflectivity Maps, and Electromagnetic Fields

*grooves*[rather than elliptical

*bumps*as in Fig. 7(a)]. As in the examples above, we use the polynomial dispersion relation [85

**53**, 1569–1576 (2006). [CrossRef]

### C. Photonic Energy Gaps (“band gaps”)

96. W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N. P. K. Cotter, and D. J. Nash, “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B **51**, 11164–11167 (1995). [CrossRef]

41. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B **54**, 6227–6244 (1996). [CrossRef]

*et al.*[94

**4**, 2022–2024 (1987). [CrossRef]

41. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B **54**, 6227–6244 (1996). [CrossRef]

*et al.*[39

39. J. Chandezon, M. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A **72**, 839–846 (1982). [CrossRef]

*not*for a (slight) perturbation that includes a second harmonic (in fact, the Taylor series

*diverges*in this case; see Fig. 14 below). As shown in Fig. 13, on the other hand, this latter behavior can be overcome with the use of Padé approximants of order [2/2], even though, as we have alluded to before, this uses

*precisely*the same information as that encoded in the first five terms of the Taylor series.

**54**, 6227–6244 (1996). [CrossRef]

**54**, 6227–6244 (1996). [CrossRef]

96. W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N. P. K. Cotter, and D. J. Nash, “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B **51**, 11164–11167 (1995). [CrossRef]

**54**, 6227–6244 (1996). [CrossRef]

39. J. Chandezon, M. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A **72**, 839–846 (1982). [CrossRef]

**54**, 6227–6244 (1996). [CrossRef]

*five*terms and, thus, in the form of a [2/2] Padé approximant, this approximate solution should be equally amenable to an analytic study as the (truncated)

39. J. Chandezon, M. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. A **72**, 839–846 (1982). [CrossRef]

**54**, 6227–6244 (1996). [CrossRef]

*maximum relative error*is less than 0.1% for Fig. 13(a) and about 3% for Fig. 13(b); a numerical convergence analysis is included in Fig. 14.

## 5. CONCLUSIONS

38. J. Chandezon, G. Raoult, and D. Maystre, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. **11**, 235–241 (1980). [CrossRef]

## ACKNOWLEDGMENTS

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50. | J. Bischoff and K. Hehl, “Perturbation approach applied to modal diffraction methods,” J. Opt. Soc. Am. A |

51. | M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A |

52. | M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A |

53. | L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A |

54. | J. Bischoff, “Prospects and limits of the Rayleigh Fourier approach for diffraction modelling in scatterometry and lithography,” Proc. SPIE |

55. | S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. |

56. | A. G. Voronovich, “Small-slope approximation in wave scattering by rough surfaces,” Sov. Phys. J. Exp. Theor. Phys. |

57. | E. Rodriguez and Y. Kim, “A unified perturbation expansion for surface scattering,” Radio Sci. |

58. | C.-A. Guérin and A. Sentenac, “Second-order perturbation theory for scattering from heterogeneous rough surfaces,” J. Opt. Soc. Am. A |

59. | D. Grieser, H. Uecker, S.-A. Biehs, O. Huth, F. Rüting, and M. Holthaus, “Perturbation theory for plasmonic eigenvalues,” Phys. Rev. B |

60. | A. Trügler, J.-C. Tinguely, J. R. Krenn, A. Hohenau, and U. Hohenester, “Influence of surface roughness on the optical properties of plasmonic nanoparticles,” Phys. Rev. B |

61. | A. A. Maradudin and E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. |

62. | K. A. O’Donnell, “High-order perturbation theory for light scattering from a rough metal surface,” J. Opt. Soc. Am. A |

63. | M. A. Demir and J. T. Johnson, “Fourth- and higher-order small-perturbation solution for scattering from dielectric rough surfaces,” J. Opt. Soc. Am. A |

64. | K. A. O’Donnell, “Small-amplitude perturbation theory for one-dimensionally rough surfaces,” in |

65. | H.-Y. Xie, M.-Y. Ng, and Y.-C. Chang, “Analytical solutions to light scattering by plasmonic nanoparticles with nearly spherical shape and nonlocal effect,” J. Opt. Soc. Am. A |

66. | J.-J. Greffet, “Scattering of electromagnetic waves by rough dielectric surfaces,” Phys. Rev. B |

67. | D. R. Jackson, D. P. Winebrenner, and A. Ishimaru, “Comparison of perturbation theories for rough-surface scattering,” J. Acoust. Soc. Am. |

68. | A. Soubret, G. Berginc, and C. Bourrely, “Backscattering enhancement of an electromagnetic wave scattered by two-dimensional rough layers,” J. Opt. Soc. Am. A |

69. | O. P. Bruno and F. Reitich, “Solution of a boundary value problem for the Helmholtz equation via variation of the boundary into the complex domain,” Proc. R. Soc. Edinburgh , Sect. A |

70. | O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A |

71. | O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A |

72. | O. P. Bruno and F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings,” J. Opt. Soc. Am. A |

73. | O. Bruno and F. Reitich, “High-order boundary perturbation methods,” in |

74. | L. Kazandjian, “A discussion of the properties of the Rayleigh perturbative solution in diffraction theory,” Wave Motion |

75. | J.-J. Greffet, “Introduction to surface plasmon theory,” in |

76. | D. Maystre, “Theory of Wood’s anomalies,” in |

77. | E. Kretschmann and H. Raether, “Radiative decay of non radiative surface plasmons excited by light,” Z. Naturforsch. A |

78. | A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. |

79. | B. Hecht, H. Bielefeldt, L. Novotny, Y. Inouye, and D. W. Pohl, “Local excitation, scattering, and interference of surface plasmons,” Phys. Rev. Lett. |

80. | H. Ditlbacher, J. R. Krenn, N. Felidj, B. Lamprecht, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Fluorescence imaging of surface plasmon fields,” Appl. Phys. Lett. |

81. | R. H. Ritchie, E. T. Arakawa, J. J. Cowan, and R. N. Hamm, “Surface-plasmon resonance effect in grating diffraction,” Phys. Rev. Lett. |

82. | J. Uretsky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. |

83. | G. A. Baker and P. Graves-Morris, |

84. | A. Rakic, A. Djurišic, J. Elazar, and M. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. |

85. | Z. Chen, I. R. Hooper, and J. R. Sambles, “Low dispersion surface plasmon–polaritons on deep silver gratings,” J. Mod. Opt. |

86. | D. J. Nash and J. R. Sambles, “Surface plasmon–polariton study of the optical dielectric function of silver,” J. Mod. Opt. |

87. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

88. | D. W. Lynch and W. R. Hunter, “Comments on the optical constants of metals and an introduction to the data for several metals,” in |

89. | J. Homola, |

90. | Z. Chen, “Grating coupled surface plasmons in metallic structures,” Ph.D. dissertation (University of Exeter, 2007). |

91. | T. López-Rios, D. Mendoza, F. J. García-Vidal, J. Sánchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic gratings,” Phys. Rev. Lett. |

92. | F. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Rios, T. Fournier, and B. Pannetier, “Localized surface plasmons in lamellar metallic gratings,” J. Lightwave Technol. |

93. | I. R. Hooper and J. R. Sambles, “Dispersion of surface plasmon polaritons on short-pitch metal gratings,” Phys. Rev. B |

94. | E. P. Da Silva, G. A. Farias, and A. A. Maradudin, “Analysis of three theories of scattering of electromagnetic radiation by gratings,” J. Opt. Soc. Am. A |

95. | A. J. Jerri, ed., |

96. | W. L. Barnes, T. W. Preist, S. C. Kitson, J. R. Sambles, N. P. K. Cotter, and D. J. Nash, “Photonic gaps in the dispersion of surface plasmons on gratings,” Phys. Rev. B |

97. | A. Taflove and S. Hagness, |

98. | A. Malcolm and D. P. Nicholls, “A field expansions method for scattering by periodic multilayered media,” J. Acoust. Soc. Am. |

**OCIS Codes**

(240.6680) Optics at surfaces : Surface plasmons

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Optics at Surfaces

**History**

Original Manuscript: June 17, 2013

Manuscript Accepted: August 22, 2013

Published: October 3, 2013

**Virtual Issues**

Vol. 9, Iss. 1 *Virtual Journal for Biomedical Optics*

October 29, 2013 *Spotlight on Optics*

**Citation**

Fernando Reitich, Timothy W. Johnson, Sang-Hyun Oh, and Gary Meyer, "A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications," J. Opt. Soc. Am. A **30**, 2175-2187 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-11-2175

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