Abstract

Use of the Finite-Difference Time-Domain (FDTD) method to model nanoplasmonic structures continues to rise – more than 2700 papers have been published in 2014 on FDTD simulations of surface plasmons. However, a comprehensive study on the convergence and accuracy of the method for nanoplasmonic structures has yet to be reported. Although the method may be well-established in other areas of electromagnetics, the peculiarities of nanoplasmonic problems are such that a targeted study on convergence and accuracy is required. The availability of a high-performance computing system (a massively parallel IBM Blue Gene/Q) allows us to do this for the first time. We consider gold and silver at optical wavelengths along with three “standard” nanoplasmonic structures: a metal sphere, a metal dipole antenna and a metal bowtie antenna – for the first structure comparisons with the analytical extinction, scattering, and absorption coefficients based on Mie theory are possible. We consider different ways to set-up the simulation domain, we vary the mesh size to very small dimensions, we compare the simple Drude model with the Drude model augmented with two critical points correction, we compare single-precision to double-precision arithmetic, and we compare two staircase meshing techniques, per-component and uniform. We find that the Drude model with two critical points correction (at least) must be used in general. Double-precision arithmetic is needed to avoid round-off errors if highly converged results are sought. Per-component meshing increases the accuracy when complex geometries are modeled, but the uniform mesh works better for structures completely fillable by the Yee cell (e.g., rectangular structures). Generally, a mesh size of 0.25 nm is required to achieve convergence of results to ∼ 1%. We determine how to optimally setup the simulation domain, and in so doing we find that performing scattering calculations within the near-field does not necessarily produces large errors but reduces the computational resources required.

© 2015 Optical Society of America

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References

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2014 (5)

J. Hamm, F. Renn, and O. Hess, “Dispersive Media Subcell Averaging in the FDTD Method Using Corrective Surface Currents,” IEEE Trans. Antennas Propag. 62(2), 832–838 (2014).
[Crossref]

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).
[Crossref]

M. Fujii, “Fundamental correction of Mie’s scattering theory for the analysis of the plasmonic resonance of a metal nanosphere,” Phys. Rev. A 89(3), 033805 (2014).
[Crossref]

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

2013 (3)

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

K. P. Prokopidis and D. C. Zografopoulos, “A Unified FDTD/PML Scheme Based on Critical Points for Accurate Studies of Plasmonic Structures,” J. Lightwave Technol. 31(15), 2467–2476 (2013).
[Crossref]

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

2012 (2)

N. Okada and J. B. Cole, “Effective Permittivity for FDTD Calculation of Plasmonic Materials,” Micromachines 3(1), 168–179 (2012).
[Crossref]

A. Calà Lesina, A. Vaccari, and A. Bozzoli, “A novel RC-FDTD algorithm for the Drude dispersion analysis,” Prog. Electromagn. Res. M 24, 251–264 (2012).
[Crossref]

2011 (2)

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

2009 (2)

M. A. Alsunaidi and A. A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett. 21(12), 817–819 (2009).
[Crossref]

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanos. 6(9), 2040–2053 (2009).
[Crossref]

2008 (2)

A. Mohammadi, T. Jalali, and M. Agio, “Dispersive contour-path algorithm for the two-dimensional finite-difference time-domain method,” Opt. Express 16(10), 7397–7406 (2008).
[Crossref] [PubMed]

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008).
[Crossref]

2007 (4)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: [26],” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
[Crossref]

A. Deinega and I. Valuev, “Subpixel smoothing for conductive and dispersive media in the finite-difference time-domain method,” Opt. Lett. 32(23), 3429–3431 (2007).
[Crossref] [PubMed]

I. Laakso, S. Ilvonen, and T. Uusitupa, “Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations,” Phys. Med. Biol. 52(23), 7183–7192 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (1)

2001 (1)

W. Yu and R. Mittra, “A conformal finite difference time domain technique for modeling curved dielectric surfaces,” IEEE Microw. Compon. Lett. 11(1), 25–27 (2001).
[Crossref]

2000 (1)

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000).
[Crossref]

1991 (1)

R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antennas Propag. 39(1), 29–34 (1991).
[Crossref]

1982 (1)

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24(4), 397–405 (1982).
[Crossref]

1980 (1)

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27(6), 1829–1833 (1980).
[Crossref]

1975 (1)

A. Taflove and M. E. Brodwin, “Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

1967 (1)

R. Courant, K. O. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev. 11(2), 215–234 (1967).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s Equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

1908 (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 25(3), 377–445 (1908).

Agio, M.

Ai, X.

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

Al-Jabr, A. A.

M. A. Alsunaidi and A. A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett. 21(12), 817–819 (2009).
[Crossref]

Alsunaidi, M. A.

M. A. Alsunaidi and A. A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett. 21(12), 817–819 (2009).
[Crossref]

Attinella, J.

J. Attinella, S. Miller, and G. Lakner, IBM System Blue Gene Solution: Blue Gene/Q Code Development and Tools Interface (IBM, 2013).

Barchiesi, D.

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).
[Crossref]

Berini, P.

Bermel, P.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[Crossref]

Bozzoli, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Calà Lesina, A. Vaccari, and A. Bozzoli, “A novel RC-FDTD algorithm for the Drude dispersion analysis,” Prog. Electromagn. Res. M 24, 251–264 (2012).
[Crossref]

Brodwin, M. E.

A. Taflove and M. E. Brodwin, “Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

Buckley, R.

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanos. 6(9), 2040–2053 (2009).
[Crossref]

Burr, G. W.

Calà Lesina, A.

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Calà Lesina, A. Vaccari, and A. Bozzoli, “A novel RC-FDTD algorithm for the Drude dispersion analysis,” Prog. Electromagn. Res. M 24, 251–264 (2012).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

Calliari, L.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

Chiappini, A.

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Chun, K.

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

Chung, Y.

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

Cole, J. B.

N. Okada and J. B. Cole, “Effective Permittivity for FDTD Calculation of Plasmonic Materials,” Micromachines 3(1), 168–179 (2012).
[Crossref]

Courant, R.

R. Courant, K. O. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev. 11(2), 215–234 (1967).
[Crossref]

Crema, L.

Cristoforetti, L.

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

Cui, Z.

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

Deinega, A.

Dridi, M.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Etchegoin, P. G.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: [26],” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Farjadpour, A.

Ferrari, M.

Fisher, R.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27(6), 1829–1833 (1980).
[Crossref]

Friedrichs, K. O.

R. Courant, K. O. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev. 11(2), 215–234 (1967).
[Crossref]

Fujii, M.

M. Fujii, “Fundamental correction of Mie’s scattering theory for the analysis of the plasmonic resonance of a metal nanosphere,” Phys. Rev. A 89(3), 033805 (2014).
[Crossref]

Gedney, S. D.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000).
[Crossref]

Gilge, M.

M. Gilge, IBM System Blue Gene Solution Blue Gene/Q Application Development (IBM, 2013).

Grosges, T.

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).
[Crossref]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3. (Artech House, 2005).

Hamm, J.

J. Hamm, F. Renn, and O. Hess, “Dispersive Media Subcell Averaging in the FDTD Method Using Corrective Surface Currents,” IEEE Trans. Antennas Propag. 62(2), 832–838 (2014).
[Crossref]

Han, Y.

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

Hess, O.

J. Hamm, F. Renn, and O. Hess, “Dispersive Media Subcell Averaging in the FDTD Method Using Corrective Surface Currents,” IEEE Trans. Antennas Propag. 62(2), 832–838 (2014).
[Crossref]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[Crossref]

Hunsberger, F.

R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antennas Propag. 39(1), 29–34 (1991).
[Crossref]

Ibanescu, M.

Ilvonen, S.

I. Laakso, S. Ilvonen, and T. Uusitupa, “Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations,” Phys. Med. Biol. 52(23), 7183–7192 (2007).
[Crossref] [PubMed]

Jalali, T.

Joannopoulos, J. D.

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Johnson, S. G.

Kim, H.

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

Kunz, K. S.

R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antennas Propag. 39(1), 29–34 (1991).
[Crossref]

Laakso, I.

I. Laakso, S. Ilvonen, and T. Uusitupa, “Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations,” Phys. Med. Biol. 52(23), 7183–7192 (2007).
[Crossref] [PubMed]

Lakner, G.

J. Attinella, S. Miller, and G. Lakner, IBM System Blue Gene Solution: Blue Gene/Q Code Development and Tools Interface (IBM, 2013).

Laroche, T.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008).
[Crossref]

Le Cunff, L.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Le Ru, E. C.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: [26],” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Lewy, H.

R. Courant, K. O. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev. 11(2), 215–234 (1967).
[Crossref]

Luebbers, R. J.

R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antennas Propag. 39(1), 29–34 (1991).
[Crossref]

Merewether, D. E.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27(6), 1829–1833 (1980).
[Crossref]

Meyer, M.

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: [26],” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 25(3), 377–445 (1908).

Miller, S.

J. Attinella, S. Miller, and G. Lakner, IBM System Blue Gene Solution: Blue Gene/Q Code Development and Tools Interface (IBM, 2013).

Mittra, R.

W. Yu and R. Mittra, “A conformal finite difference time domain technique for modeling curved dielectric surfaces,” IEEE Microw. Compon. Lett. 11(1), 25–27 (2001).
[Crossref]

Mohammadi, A.

Nadgaran, H.

Okada, N.

N. Okada and J. B. Cole, “Effective Permittivity for FDTD Calculation of Plasmonic Materials,” Micromachines 3(1), 168–179 (2012).
[Crossref]

Oskooi, A.

A. Taflove, S. G. Johnson, and A. Oskooi, Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology (Artech House, 2013).

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

Pontalti, R.

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

Prokopidis, K. P.

Prudenzano, F.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Ramunno, L.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

Renn, F.

J. Hamm, F. Renn, and O. Hess, “Dispersive Media Subcell Averaging in the FDTD Method Using Corrective Surface Currents,” IEEE Trans. Antennas Propag. 62(2), 832–838 (2014).
[Crossref]

Roden, J. A.

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000).
[Crossref]

Rodriguez, A.

Roundy, D.

Shi, X.-W.

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

Smith, F. W.

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27(6), 1829–1833 (1980).
[Crossref]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Taflove, A.

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24(4), 397–405 (1982).
[Crossref]

A. Taflove and M. E. Brodwin, “Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

A. Taflove, S. G. Johnson, and A. Oskooi, Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology (Artech House, 2013).

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3. (Artech House, 2005).

Tian, Y.

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

Umashankar, K.

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24(4), 397–405 (1982).
[Crossref]

Uusitupa, T.

I. Laakso, S. Ilvonen, and T. Uusitupa, “Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations,” Phys. Med. Biol. 52(23), 7183–7192 (2007).
[Crossref] [PubMed]

Vaccari, A.

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, A. Chiappini, L. Crema, L. Calliari, L. Ramunno, P. Berini, and M. Ferrari, “Light-opals interaction modeling by direct numerical solution of Maxwell’s equations,” Opt. Express 22(22), 27739–27749 (2014).
[Crossref] [PubMed]

A. Calà Lesina, A. Vaccari, and A. Bozzoli, “A novel RC-FDTD algorithm for the Drude dispersion analysis,” Prog. Electromagn. Res. M 24, 251–264 (2012).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

Valuev, I.

Vial, A.

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008).
[Crossref]

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s Equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

Yu, W.

W. Yu and R. Mittra, “A conformal finite difference time domain technique for modeling curved dielectric surfaces,” IEEE Microw. Compon. Lett. 11(1), 25–27 (2001).
[Crossref]

Zografopoulos, D. C.

Annalen der Physik (1)

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Annalen der Physik 25(3), 377–445 (1908).

Appl. Phys. A (1)

A. Vial, T. Laroche, M. Dridi, and L. Le Cunff, “A new model of dispersion for metals leading to a more accurate modeling of plasmonic structures using the FDTD method,” Appl. Phys. A 103(3), 849–853 (2011).
[Crossref]

Appl. Phys. B (1)

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93(1), 139–143 (2008).
[Crossref]

IBM J. Res. Dev. (1)

R. Courant, K. O. Friedrichs, and H. Lewy, “On the partial difference equations of mathematical physics,” IBM J. Res. Dev. 11(2), 215–234 (1967).
[Crossref]

IEEE Microw. Compon. Lett. (1)

W. Yu and R. Mittra, “A conformal finite difference time domain technique for modeling curved dielectric surfaces,” IEEE Microw. Compon. Lett. 11(1), 25–27 (2001).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. A. Alsunaidi and A. A. Al-Jabr, “A general ADE-FDTD algorithm for the simulation of dispersive structures,” IEEE Photon. Technol. Lett. 21(12), 817–819 (2009).
[Crossref]

IEEE Trans. Antennas Propag. (3)

R. J. Luebbers, F. Hunsberger, and K. S. Kunz, “A frequency-dependent finite-difference time-domain formulation for transient propagation in plasma,” IEEE Trans. Antennas Propag. 39(1), 29–34 (1991).
[Crossref]

J. Hamm, F. Renn, and O. Hess, “Dispersive Media Subcell Averaging in the FDTD Method Using Corrective Surface Currents,” IEEE Trans. Antennas Propag. 62(2), 832–838 (2014).
[Crossref]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s Equations in isotropic media,” IEEE Trans. Antennas Propag. 14(3), 302–307 (1966).
[Crossref]

IEEE Trans. Electromagn. Compat. (1)

K. Umashankar and A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24(4), 397–405 (1982).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

A. Taflove and M. E. Brodwin, “Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell’s Equations,” IEEE Trans. Microwave Theory Tech. 23, 623–630 (1975).
[Crossref]

IEEE Trans. Nucl. Sci. (1)

D. E. Merewether, R. Fisher, and F. W. Smith, “On implementing a numeric Huygen’s source scheme in a finite difference program to illuminate scattering bodies,” IEEE Trans. Nucl. Sci. 27(6), 1829–1833 (1980).
[Crossref]

J. Chem. Phys. (2)

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “An analytic model for the optical properties of gold,” J. Chem. Phys. 125(16), 164705 (2006).
[Crossref] [PubMed]

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, “Erratum: [26],” J. Chem. Phys. 127(18), 189901 (2007).
[Crossref]

J. Comput. Theor. Nanos. (1)

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanos. 6(9), 2040–2053 (2009).
[Crossref]

J. Lightwave Technol. (1)

J. Nanophotonics (1)

D. Barchiesi and T. Grosges, “Fitting the optical constants of gold, silver, chromium, titanium, and aluminum in the visible bandwidth,” J. Nanophotonics 8(1), 083097 (2014).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

A. Vial, “Implementation of the critical points model in the recursive convolution method for modelling dispersive media with the finite-difference time domain method,” J. Opt. A: Pure Appl. Opt. 9(7), 745–748 (2007).
[Crossref]

Micromachines (1)

N. Okada and J. B. Cole, “Effective Permittivity for FDTD Calculation of Plasmonic Materials,” Micromachines 3(1), 168–179 (2012).
[Crossref]

Microw. Opt. Technol. Lett. (1)

J. A. Roden and S. D. Gedney, “Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media,” Microw. Opt. Technol. Lett. 27(5), 334–339 (2000).
[Crossref]

Opt. Eng. (1)

A. Vaccari, L. Cristoforetti, A. Calà Lesina, L. Ramunno, A. Chiappini, F. Prudenzano, A. Bozzoli, and L. Calliari, “Parallel finite-difference time-domain modeling of an opal photonic crystal,” Opt. Eng. 53(7), 071809 (2014).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Med. Biol. (1)

I. Laakso, S. Ilvonen, and T. Uusitupa, “Performance of convolutional PML absorbing boundary conditions in finite-difference time-domain SAR calculations,” Phys. Med. Biol. 52(23), 7183–7192 (2007).
[Crossref] [PubMed]

Phys. Rev. A (1)

M. Fujii, “Fundamental correction of Mie’s scattering theory for the analysis of the plasmonic resonance of a metal nanosphere,” Phys. Rev. A 89(3), 033805 (2014).
[Crossref]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370 (1972).
[Crossref]

Prog. Electromagn. Res. (3)

X. Ai, Y. Tian, Z. Cui, Y. Han, and X.-W. Shi, “A dispersive conformal FDTD technique for accurate modeling electromagnetic scattering of THz waves by inhomogeneous plasma cylinder array,” Prog. Electromagn. Res. 142, 353–368 (2013).
[Crossref]

K. Chun, H. Kim, H. Kim, and Y. Chung, “PLRC and ADE implementations of Drude-critical point dispersive model for the FDTD method,” Prog. Electromagn. Res. 135, 373–390 (2013).
[Crossref]

A. Vaccari, A. Calà Lesina, L. Cristoforetti, and R. Pontalti, “Parallel implementation of a 3D subgridding FDTD algorithm for large simulations,” Prog. Electromagn. Res. 120, 263–292 (2011).
[Crossref]

Prog. Electromagn. Res. M (1)

A. Calà Lesina, A. Vaccari, and A. Bozzoli, “A novel RC-FDTD algorithm for the Drude dispersion analysis,” Prog. Electromagn. Res. M 24, 251–264 (2012).
[Crossref]

Other (13)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

http://www.lumerical.com/solutions/innovation/fdtd_conformal_mesh_whitepaper.html

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3. (Artech House, 2005).

A. Taflove, S. G. Johnson, and A. Oskooi, Advances in FDTD Computational Electrodynamics: Photonics and Nanotechnology (Artech House, 2013).

Lumerical Solutions, www.lumerical.com

Google Scholar, searching “FDTD and plasmonics”

http://docs.lumerical.com/en/layout_analysis_test_convergence_fdtd.html

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
[Crossref]

M. Gilge, IBM System Blue Gene Solution Blue Gene/Q Application Development (IBM, 2013).

SciNet, https://support.scinet.utoronto.ca/wiki/index.php/BGQ

J. Attinella, S. Miller, and G. Lakner, IBM System Blue Gene Solution: Blue Gene/Q Code Development and Tools Interface (IBM, 2013).

MPI Forum, http://www.mpi-forum.org

Supplementary Material (3)

» Media 1: AVI (13698 KB)     
» Media 2: AVI (13625 KB)     
» Media 3: AVI (13506 KB)     

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Figures (12)

Fig. 1
Fig. 1 (a) Yee FDTD cell and per-component meshing technique illustration (not in scale). (b) FDTD simulation domain setup: (A) CPML thickness, (B) TF/SF position, (C) Ssca position, (D) physical box length, and (E) Sabs position.
Fig. 2
Fig. 2 Simulation setup for silver sphere: (a) Ssca position effect and (b) Sabs position effect.
Fig. 3
Fig. 3 Scalability study.
Fig. 4
Fig. 4 Light-nanostructure interaction: (a) silver sphere (left, Media 1), (b) gold dipole (middle, Media 2), and (c) gold bowtie (right, Media 3).
Fig. 5
Fig. 5 Per-component silver sphere Cext convergence: (a) and (b) spectra, (c) errors.
Fig. 6
Fig. 6 Per-component silver sphere Csca convergence: (a) and (b) spectra, (c) errors.
Fig. 7
Fig. 7 Per-component silver sphere Cabs convergence: (a) and (b) spectra, (c) errors.
Fig. 8
Fig. 8 Uniform staircase silver sphere Cext convergence: (a) and (b) spectra, (c) errors.
Fig. 9
Fig. 9 Single-precision silver sphere Cext convergence: (a) and (b) spectra, (c) errors.
Fig. 10
Fig. 10 Single Drude silver sphere Cext convergence: (a) and (b) spectra, (c) errors.
Fig. 11
Fig. 11 Gold dipole Cext convergence: per-component (top) and uniform staircase (bottom).
Fig. 12
Fig. 12 Gold bowtie Cext convergence: per-component (top) and uniform staircase (bottom).

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

χ ( ω ) = ω D 2 ω ( ω + i γ ) + p = 1 2 A p Ω p ( e i ϕ p Ω p ω i Γ p + e i ϕ p Ω p + ω + i Γ p ) ,
Q e x t = 2 π k 2 2 R e n = 1 ( 2 n + 1 ) ( a n r + b n r ) ,
Q s c a = 2 π k 2 2 R e n = 1 ( 2 n + 1 ) ( | a n r | 2 + | b n r | 2 ) ,
Q a b s = Q e x t = Q s c a ,
C s c a = S s c a < S > n ^ d S < S i n c > A g e o m ,
C a b s = V σ ( ω ) N m i δ i E i 2 d V < S i n c > A g e o m ,
% e r r o r = 100 × | n u m e r i c a l # a n a l y t i c # a n a l y t i c # | ,
< % e r r o r > = 1 N λ = 1 N % e r r o r ,
m % e d = 1 N λ = 1 N | % e r r o r a s y m p t o t i c % e r r o r | ,

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