Abstract

We present the study of a spectral-domain near-field-to-far-field (NFTFF) transformation, taking into account an interface in the vicinity of a particle. This technique is associated with a three-dimensional finite-difference time-domain (FDTD) model, which solves the Maxwell equations in the time domain. Moreover, material properties are considered with the use of dispersion models. First, particular attention is paid to the description of the modeling, especially concerning the NFTFF transformation using the dyadic Green tensors. Second, several simulation cases are considered to evaluate the ability of the developed technique to model the scattering by different kinds of “particles/interface” configurations and for various illuminating waves. Then validation test cases are used in order to assess the model accuracy through comparisons with T-matrix simulations. Finally, perspectives to this work and its application to near-field detection devices are discussed.

© 2011 Optical Society of America

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  1. H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1957).
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  3. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  4. T. Martin and L. Pettersson, “FDTD time domain near- to far-zone transformation above a lossy dielectric half-space,” Appl. Comput. Electromagn. Soc. J. 16, 45-52 (2001).
  5. A. Zayats and D. Richards, Nano-Optics and Near-Field Optical Microscopy (Artech, 2009).
  6. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8, 483-489 (1991).
    [CrossRef]
  7. G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110-117 (1993).
    [CrossRef]
  8. B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
    [CrossRef]
  9. T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376-384 (1998).
    [CrossRef]
  10. A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
    [CrossRef]
  11. A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).
  12. C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, 1990).
  13. Y. A. Eremin and A. G. Sveshnikov, “The discrete sources method for investigating three-dimensional electromagnetic scattering problems,” Electromagnetics 13, 1-22 (1993).
    [CrossRef]
  14. Y. A. Eremin and N. V. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599-6604(1996).
    [CrossRef] [PubMed]
  15. A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
    [CrossRef]
  16. A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
    [CrossRef]
  17. A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
    [CrossRef]
  18. A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
    [CrossRef]
  19. Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
    [CrossRef]
  20. Y. Eremin and T. Wriedt, “Large dielectric non-spherical particle in an evanescent wave field near a plane surface,” Opt. Commun. 214, 39-45 (2002).
    [CrossRef]
  21. Y. Eremin and T. Wriedt, “Discrete sources method model for evanescent waves scattering analysis,” J. Quant. Spectrosc. Radiat. Transfer 89, 53-65 (2004).
    [CrossRef]
  22. Y. Eremin and N. Grishina, “Modeling of nanoshells spectra in evanescent wave field via discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 100, 122-130 (2006).
    [CrossRef]
  23. E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
    [CrossRef]
  24. E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
    [CrossRef]
  25. E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
    [CrossRef]
  26. A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from composite objects,” Opt. Commun. 190, 13-17 (2001).
    [CrossRef]
  27. N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
    [CrossRef]
  28. J. Jung and T. Sondergaard, “Green's function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008).
    [CrossRef]
  29. E. Purcell and C. Pennypacker, “Scattering and adsorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
    [CrossRef]
  30. T. Sondergaard, “Modeling of plasmonic nanostructures: Green's function integral equation methods,” Phys. Status Solidi (b) 244, 3448-3462 (2007).
    [CrossRef]
  31. A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
    [CrossRef]
  32. B. T. Draine and P. Flatau, “The discrete dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491-1499(1994).
    [CrossRef]
  33. P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
    [CrossRef]
  34. P. C. Chaumet and M. Nieto-Vesperinas, “Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate,” Phys. Rev. B 61, 14119-14127 (2000).
    [CrossRef]
  35. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, 2005).
  36. A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from layered scatterers,” Comput. Phys. Commun. 138, 136-142 (2001).
    [CrossRef]
  37. K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
    [CrossRef]
  38. I. Capoglu and G. Smith, “A direct time-domain FDTD near-field-to-far-field transform in the presence of an infinite grounded dielectric slab,” IEEE Trans. Antennas Propag. 54, 3805-3814(2006).
    [CrossRef]
  39. C. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  40. J. Sipe, “New Green-function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481-489 (1987).
    [CrossRef]
  41. F. Arnoldus and J. Foley, “Transmission of dipole radiation through interfaces and the phenomenon of anti-critical angles,” J. Opt. Soc. Am. A 21, 1109-1117 (2004).
    [CrossRef]
  42. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
    [CrossRef] [PubMed]

2009 (1)

A. Zayats and D. Richards, Nano-Optics and Near-Field Optical Microscopy (Artech, 2009).

2008 (1)

J. Jung and T. Sondergaard, “Green's function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008).
[CrossRef]

2007 (4)

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

T. Sondergaard, “Modeling of plasmonic nanostructures: Green's function integral equation methods,” Phys. Status Solidi (b) 244, 3448-3462 (2007).
[CrossRef]

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
[CrossRef]

2006 (5)

Y. Eremin and N. Grishina, “Modeling of nanoshells spectra in evanescent wave field via discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 100, 122-130 (2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
[CrossRef]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).

I. Capoglu and G. Smith, “A direct time-domain FDTD near-field-to-far-field transform in the presence of an infinite grounded dielectric slab,” IEEE Trans. Antennas Propag. 54, 3805-3814(2006).
[CrossRef]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

2005 (2)

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

E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
[CrossRef]

2004 (2)

Y. Eremin and T. Wriedt, “Discrete sources method model for evanescent waves scattering analysis,” J. Quant. Spectrosc. Radiat. Transfer 89, 53-65 (2004).
[CrossRef]

F. Arnoldus and J. Foley, “Transmission of dipole radiation through interfaces and the phenomenon of anti-critical angles,” J. Opt. Soc. Am. A 21, 1109-1117 (2004).
[CrossRef]

2002 (1)

Y. Eremin and T. Wriedt, “Large dielectric non-spherical particle in an evanescent wave field near a plane surface,” Opt. Commun. 214, 39-45 (2002).
[CrossRef]

2001 (7)

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
[CrossRef]

Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from composite objects,” Opt. Commun. 190, 13-17 (2001).
[CrossRef]

B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
[CrossRef]

T. Martin and L. Pettersson, “FDTD time domain near- to far-zone transformation above a lossy dielectric half-space,” Appl. Comput. Electromagn. Soc. J. 16, 45-52 (2001).

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from layered scatterers,” Comput. Phys. Commun. 138, 136-142 (2001).
[CrossRef]

2000 (2)

A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, “Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate,” Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

1999 (2)

A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

1998 (2)

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376-384 (1998).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

1996 (2)

Y. A. Eremin and N. V. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599-6604(1996).
[CrossRef] [PubMed]

K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
[CrossRef]

1994 (1)

1993 (2)

Y. A. Eremin and A. G. Sveshnikov, “The discrete sources method for investigating three-dimensional electromagnetic scattering problems,” Electromagnetics 13, 1-22 (1993).
[CrossRef]

G. Videen, “Light scattering from a sphere behind a surface,” J. Opt. Soc. Am. A 10, 110-117 (1993).
[CrossRef]

1991 (1)

1990 (1)

C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, 1990).

1989 (1)

C. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

1987 (1)

1983 (1)

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

1973 (1)

E. Purcell and C. Pennypacker, “Scattering and adsorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

1969 (1)

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

1957 (1)

H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1957).

Arnoldus, F.

Balanis, C.

C. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Bechinger, C.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Capoglu, I.

I. Capoglu and G. Smith, “A direct time-domain FDTD near-field-to-far-field transform in the presence of an infinite grounded dielectric slab,” IEEE Trans. Antennas Propag. 54, 3805-3814(2006).
[CrossRef]

Carminati, R.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Chaumet, P. C.

P. C. Chaumet and M. Nieto-Vesperinas, “Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate,” Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

Chen, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

de Fornel, F.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

de la Peña, J.

B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
[CrossRef]

De Wilde, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Demarest, K.

K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
[CrossRef]

Doicu, A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from composite objects,” Opt. Commun. 190, 13-17 (2001).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from layered scatterers,” Comput. Phys. Commun. 138, 136-142 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376-384 (1998).
[CrossRef]

Draine, B.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Draine, B. T.

Dufour, J.-P.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

Eremin, Y.

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
[CrossRef]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
[CrossRef]

Y. Eremin and N. Grishina, “Modeling of nanoshells spectra in evanescent wave field via discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 100, 122-130 (2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
[CrossRef]

Y. Eremin and T. Wriedt, “Discrete sources method model for evanescent waves scattering analysis,” J. Quant. Spectrosc. Radiat. Transfer 89, 53-65 (2004).
[CrossRef]

Y. Eremin and T. Wriedt, “Large dielectric non-spherical particle in an evanescent wave field near a plane surface,” Opt. Commun. 214, 39-45 (2002).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
[CrossRef]

Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

Eremin, Y. A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

Y. A. Eremin and N. V. Orlov, “Simulation of light scattering from a particle upon a wafer surface,” Appl. Opt. 35, 6599-6604(1996).
[CrossRef] [PubMed]

Y. A. Eremin and A. G. Sveshnikov, “The discrete sources method for investigating three-dimensional electromagnetic scattering problems,” Electromagnetics 13, 1-22 (1993).
[CrossRef]

Eremina, E.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
[CrossRef]

Flatau, P.

Foley, J.

Formanek, F.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Gralak, B.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Greffet, J.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Grishina, N.

Y. Eremin and N. Grishina, “Modeling of nanoshells spectra in evanescent wave field via discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 100, 122-130 (2006).
[CrossRef]

Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
[CrossRef]

Hafner, C.

C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, 1990).

Hagness, S.

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

Helden, L.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

Hertlein, C.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

Hirleman, E.

B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
[CrossRef]

Hoekstra, A.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Huang, Z.

K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
[CrossRef]

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Joulain, K.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Jung, J.

J. Jung and T. Sondergaard, “Green's function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Lemoine, P.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Lumme, K.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Martin, T.

T. Martin and L. Pettersson, “FDTD time domain near- to far-zone transformation above a lossy dielectric half-space,” Appl. Comput. Electromagn. Soc. J. 16, 45-52 (2001).

Muinonen, K.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Mulet, J.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Nebeker, B.

B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
[CrossRef]

Nieto-Vesperinas, M.

P. C. Chaumet and M. Nieto-Vesperinas, “Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate,” Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

Orlov, N. V.

Pennypacker, C.

E. Purcell and C. Pennypacker, “Scattering and adsorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Penttila, A.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Pettersson, L.

T. Martin and L. Pettersson, “FDTD time domain near- to far-zone transformation above a lossy dielectric half-space,” Appl. Comput. Electromagn. Soc. J. 16, 45-52 (2001).

Plumb, R.

K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
[CrossRef]

Purcell, E.

E. Purcell and C. Pennypacker, “Scattering and adsorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

Rahola, J.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Richards, D.

A. Zayats and D. Richards, Nano-Optics and Near-Field Optical Microscopy (Artech, 2009).

Riefler, N.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

Shkuratov, Y.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Sipe, J.

Smith, G.

I. Capoglu and G. Smith, “A direct time-domain FDTD near-field-to-far-field transform in the presence of an infinite grounded dielectric slab,” IEEE Trans. Antennas Propag. 54, 3805-3814(2006).
[CrossRef]

Sondergaard, T.

J. Jung and T. Sondergaard, “Green's function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008).
[CrossRef]

T. Sondergaard, “Modeling of plasmonic nanostructures: Green's function integral equation methods,” Phys. Status Solidi (b) 244, 3448-3462 (2007).
[CrossRef]

Stover, J.

Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
[CrossRef]

Sveshnikov, A. G.

Y. A. Eremin and A. G. Sveshnikov, “The discrete sources method for investigating three-dimensional electromagnetic scattering problems,” Electromagnetics 13, 1-22 (1993).
[CrossRef]

Taflove, A.

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

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1957).

Videen, G.

Wriedt, T.

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
[CrossRef]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).

E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
[CrossRef]

Y. Eremin and T. Wriedt, “Discrete sources method model for evanescent waves scattering analysis,” J. Quant. Spectrosc. Radiat. Transfer 89, 53-65 (2004).
[CrossRef]

Y. Eremin and T. Wriedt, “Large dielectric non-spherical particle in an evanescent wave field near a plane surface,” Opt. Commun. 214, 39-45 (2002).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from composite objects,” Opt. Commun. 190, 13-17 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from layered scatterers,” Comput. Phys. Commun. 138, 136-142 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376-384 (1998).
[CrossRef]

Yurkin, M.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Zayats, A.

A. Zayats and D. Richards, Nano-Optics and Near-Field Optical Microscopy (Artech, 2009).

Zubko, E.

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Appl. Comput. Electromagn. Soc. J. (1)

T. Martin and L. Pettersson, “FDTD time domain near- to far-zone transformation above a lossy dielectric half-space,” Appl. Comput. Electromagn. Soc. J. 16, 45-52 (2001).

Appl. Opt. (1)

Astrophys. J. (1)

E. Purcell and C. Pennypacker, “Scattering and adsorption of light by nonspherical dielectric grains,” Astrophys. J. 186, 705-714 (1973).
[CrossRef]

Comput. Phys. Commun. (2)

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a particle on or near a plane surface,” Comput. Phys. Commun. 134, 1-10 (2001).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from layered scatterers,” Comput. Phys. Commun. 138, 136-142 (2001).
[CrossRef]

Electromagnetics (1)

Y. A. Eremin and A. G. Sveshnikov, “The discrete sources method for investigating three-dimensional electromagnetic scattering problems,” Electromagnetics 13, 1-22 (1993).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

K. Demarest, Z. Huang, and R. Plumb, “An FDTD near- to far-zone transformation for scatterers buried in stratified grounds,” IEEE Trans. Antennas Propag. 44, 1150-1156 (1996).
[CrossRef]

I. Capoglu and G. Smith, “A direct time-domain FDTD near-field-to-far-field transform in the presence of an infinite grounded dielectric slab,” IEEE Trans. Antennas Propag. 54, 3805-3814(2006).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

J. Quant. Spectrosc. Radiat. Transfer (6)

B. Nebeker, J. de la Peña, and E. Hirleman, “Comparisons of the discrete-dipole approximation and modified double interaction model methods to predict light scattering from small features on surfaces,” J. Quant. Spectrosc. Radiat. Transfer 70, 749-759(2001).
[CrossRef]

Y. Eremin and T. Wriedt, “Discrete sources method model for evanescent waves scattering analysis,” J. Quant. Spectrosc. Radiat. Transfer 89, 53-65 (2004).
[CrossRef]

Y. Eremin and N. Grishina, “Modeling of nanoshells spectra in evanescent wave field via discrete sources method,” J. Quant. Spectrosc. Radiat. Transfer 100, 122-130 (2006).
[CrossRef]

A. Penttila, E. Zubko, K. Lumme, K. Muinonen, M. Yurkin, B. Draine, J. Rahola, A. Hoekstra, and Y. Shkuratov, “Comparison between discrete dipole implementations and exact techniques,” J. Quant. Spectrosc. Radiat. Transfer 106, 417-436(2007).
[CrossRef]

Y. Eremin, J. Stover, and N. Grishina, “Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate,” J. Quant. Spectrosc. Radiat. Transfer 70, 421-431(2001).
[CrossRef]

N. Riefler, E. Eremina, C. Hertlein, L. Helden, Y. Eremin, T. Wriedt, and C. Bechinger, “Comparison of T-matrix method with discrete sources method applied for total internal reflection microscopy,” J. Quant. Spectrosc. Radiat. Transfer 106, 464-474(2007).
[CrossRef]

Nature (1)

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. Lemoine, K. Joulain, J. Mulet, Y. Chen, and J. Greffet, “Thermal radiation scanning tunnelling microscopy,” Nature 444, 740-743(2006).
[CrossRef] [PubMed]

Opt. Commun. (10)

Y. Eremin and T. Wriedt, “Large dielectric non-spherical particle in an evanescent wave field near a plane surface,” Opt. Commun. 214, 39-45 (2002).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Discrete sources method for simulation of resonance spectra of nonspherical nanoparticles on a plane surface,” Opt. Commun. 246, 405-413(2005).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method,” Opt. Commun. 267, 524-529(2006).
[CrossRef]

E. Eremina, Y. Eremin, and T. Wriedt, “Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method,” Opt. Commun. 273, 278-285 (2007).
[CrossRef]

A. Doicu and T. Wriedt, “Null-field method with discrete sources to electromagnetic scattering from composite objects,” Opt. Commun. 190, 13-17 (2001).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Non-axisymmetric models for light scattering from a particle on or near a plane surface,” Opt. Commun. 182, 281-288 (2000).
[CrossRef]

A. Doicu, Y. Eremin, and T. Wriedt, “Scattering of evanescent waves by a sensor tip near a plane interface,” Opt. Commun. 190, 5-12 (2001).
[CrossRef]

T. Wriedt and A. Doicu, “Light scattering from a particle on or near a surface,” Opt. Commun. 152, 376-384 (1998).
[CrossRef]

A. Doicu, Y. A. Eremin, and T. Wriedt, “Convergence of the T-matrix method for light scattering from a particle on or near a surface,” Opt. Commun. 159, 266-277 (1999).
[CrossRef]

Phys. Rev. B (3)

J. Jung and T. Sondergaard, “Green's function surface integral equation method for theoretical analysis of scatterers close to a metal interface,” Phys. Rev. B 77, 245310 (2008).
[CrossRef]

P. C. Chaumet, A. Rahmani, F. de Fornel, and J.-P. Dufour, “Evanescent light scattering: the validity of the dipole approximation,” Phys. Rev. B 58, 2310-2315 (1998).
[CrossRef]

P. C. Chaumet and M. Nieto-Vesperinas, “Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate,” Phys. Rev. B 61, 14119-14127 (2000).
[CrossRef]

Phys. Status Solidi (b) (1)

T. Sondergaard, “Modeling of plasmonic nanostructures: Green's function integral equation methods,” Phys. Status Solidi (b) 244, 3448-3462 (2007).
[CrossRef]

Other (8)

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

C. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs (Springer, 2006).

C. Hafner, The Generalized Multiple Multipole Technique for Computational Electromagnetics (Artech, 1990).

A. Zayats and D. Richards, Nano-Optics and Near-Field Optical Microscopy (Artech, 2009).

H. C. Van de Hulst, Light Scattering by Small Particles(Dover, 1957).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Supplementary Material (3)

» Media 1: MOV (658 KB)     
» Media 2: MOV (663 KB)     
» Media 3: MOV (508 KB)     

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Figures (11)

Fig. 1
Fig. 1

Discretization and simulation domains: (a) electric and magnetic fields in the Yee cell and (b) calculation domains.

Fig. 2
Fig. 2

Surface equivalence theorem description.

Fig. 3
Fig. 3

Sipe formalism.

Fig. 4
Fig. 4

Dipole near an infinite dielectric plane. (a)  D dipole / surface = 5 × Δ z ; Δ z = λ 0 / 50 . (b)  D dipole / surface = 100 × Δ z ; Δ z = λ 0 / 50 . Polar variations of the electric component E θ ff in the far field for two dipole/interface spacing: red circles, NFTFF calculation; blue solid curve, analytical result.

Fig. 5
Fig. 5

Snapshots of | E y nf ( x , z ) | at times t = 300 × Δ t , 600 × Δ t , 900 × Δ t , 1200 × Δ t , and 1500 × Δ t . Δ t = λ 0 / ( 200 × c ) = 0.21 fs (Media 1).

Fig. 6
Fig. 6

Far-field variations of the electric field scattered by a sphere above an interface illuminated by a plane wave with an angle of incidence θ i = 45 ° : red circles, NFTFF calculation; blue solid curve, T-matrix. (a) Electric far field over 4 π sr above and below the interface. (b) Electric far field in the plane ϕ = 90 ° .

Fig. 7
Fig. 7

Far-field variations of the electric field scattered by a sphere above an interface illuminated by a plane wave with angle of incidence θ i = 0 ° : red circles, NFTFF calculation; blue solid curve, T-matrix. (a) Electric far field over 4 π sr above and below the interface. (b) Electric far field in the plane ϕ = 90 ° (Media 2).

Fig. 8
Fig. 8

Snapshots of | E x nf ( x , z ) | at times t = 350 × Δ t , 500 × Δ t , 650 × Δ t , 1000 × Δ t , and 1300 × Δ t . Δ t = λ 0 / ( 200 × c ) = 0.21 fs (Media 3).

Fig. 9
Fig. 9

Far-field variations of the electric field scattered by a sphere above an interface illuminated by an evanescent wave created by a plane wave in total reflection with an angle of incidence θ i = 45 ° , red circles, NFTFF calculation; blue solid curve, T-matrix. (a) Electric far field over 4 π sr above and below the interface. (b) Electric far field in the plane ϕ = 90 ° .

Fig. 10
Fig. 10

Far-field variations of the electric field scattered by a cube lined up with the mesh above an interface illuminated by a plane wave with an angle of incidence θ i = 45 ° . (a) Electric far field over 4 π sr above and below the interface. (b) Electric far field in the plane ϕ = 90 ° .

Fig. 11
Fig. 11

Far-field variations of the electric field scattered by a cube rotated around the z axis with an angle of 45 ° above an interface illuminated by a plane wave with an angle of incidence θ i = 45 ° . (a) Electric far field over 4 π sr above and below the interface. (b) Electric far field in the plane ϕ = 90 ° .

Equations (20)

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

ϵ 0 ϵ i , j + 1 / 2 , k + 1 / 2 ( E x | i , j + 1 / 2 , k + 1 / 2 n + 1 / 2 E x | i , j + 1 / 2 , k + 1 / 2 n 1 / 2 ) = Δ t Δ y [ H z | i , j + 1 , k + 1 / 2 n H z | i , j , k + 1 / 2 n ] Δ t Δ z [ H y | i , j + 1 / 2 , k + 1 n H y | i , j + 1 / 2 , k n ] ,
μ 0 ( H x | i 1 / 2 , j + 1 , k + 1 n + 1 H x | i 1 / 2 , j + 1 , k + 1 n ) = Δ t Δ z [ E y | i 1 / 2 , j + 1 , k + 3 / 2 n E y | i 1 / 2 , j + 1 , k + 1 / 2 n ] Δ t Δ y [ E z | i 1 / 2 , j + 3 / 2 , k + 1 n + 1 / 2 E z | i 1 / 2 , j + 1 / 2 , k + 1 n + 1 / 2 ] ,
E ˜ ( r , ω ) = 0 E ( r , t ) exp ( j ω t ) d t n E ( r , n × Δ t ) exp [ j ω ( n × Δ t ) ] Δ t ,
H ˜ ( r , ω ) = 0 H ( r , t ) exp ( j ω t ) d t n H ( r , ( n + 1 2 ) × Δ t ) exp [ j ω ( ( n + 1 2 ) × Δ t ) ] Δ t .
E ˜ ( ω , K , z 0 ) = E ( ω , R , z 0 ) exp ( j K · R ) d R ,
E ˜ ( ω , K , z 0 ) = Σ G ˜ E ( ω , K , z 0 , z ) J E ( ω , r ) exp ( j K · R ) d S + Σ G ˜ H ( ω , K , z 0 , z ) J H ( ω , r ) exp ( j K · R ) d S ,
G f ( ω , r , r ) = 1 ( 2 π ) 2 G ˜ f ( ω , K , z 0 , z ) exp ( j K · ( R R ) ) exp ( j w ( z 0 z ) ) d K .
G ˜ E up ( ω , K , z 0 , z ) = ω 2 w 1 [ ( s ^ s ^ + p ^ 1 + p ^ 1 + ) exp ( j w 1 | z 0 z | ) + ( s ^ r 12 s s ^ + p ^ 1 + r 12 p p ^ 1 ) exp ( j w 1 | z 0 + z | ) ] ,
G ˜ H up ( ω , K , z 0 , z ) = n 1 ω 2 w 1 [ ( p ^ 1 + s ^ s ^ p ^ 1 + ) exp ( j w 1 | z 0 z | ) + ( p ^ 1 + r 12 p s ^ s ^ r 12 s p ^ 1 ) exp ( j w 1 | z 0 + z | ) ] ,
r 12 s = w 1 w 2 w 1 + w 2 and r 12 p = ϵ 2 w 1 ϵ 1 w 2 ϵ 2 w 1 + ϵ 1 w 2 .
G ˜ E up ( ω , K , z 0 , z ) = ω 2 w 2 ( s ^ t 21 s s ^ + p ^ 1 + t 21 p p ^ 1 + ) exp [ j ( w 1 z 0 w 2 z ) ] ,
G ˜ H up ( ω , K , z 0 , z ) = n 2 ω 2 w 2 ( p ^ 1 + t 21 p s ^ s ^ t 21 s p ^ 1 + ) exp [ j ( w 1 z 0 w 2 z ) ] .
t 21 s = 2 w 2 w 1 + w 2 and t 21 p = 2 n 1 n 2 w 2 ϵ 2 w 1 + ϵ 1 w 2 .
E ff ( r , θ , ϕ ) = j k 0 exp ( j k 0 r ) 2 π r exp ( j k 0 z 0 cos θ ) × [ F θ ( θ , ϕ ) e θ + F ϕ ( θ , ϕ ) e ϕ ] ,
F ( θ , ϕ ) = | F θ ( θ , ϕ ) = ( cos ϕ e x + sin ϕ e y ) · E ˜ ( K , z 0 ) F ϕ ( θ , ϕ ) = ( sin ϕ cos θ e x + cos ϕ cos θ e y ) · E ˜ ( K , z 0 ) ,
K ( θ , ϕ ) = k · ( cos ϕ sin θ e x + sin ϕ sin θ e y ) .
E up θ ( θ ) 1 k 1 [ 1 + r 12 p exp ( 2 j w 1 d ) ] sin ( θ ) ,
E down θ ( θ ) w 2 k 1 w 1 [ t 12 p exp ( j ( w 2 w 1 ) d ) ] sin ( θ ) ,
E inc ( x , y , z , t ) = e x E 0 g ( ω ) exp ( j ω t ) exp ( j ( k s sin θ i y + k s cos θ i z ) ) d ω .
g ( ω ) = exp [ ( ω ω 0 ) 2 ( Δ ω ) 2 ] ,

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