Abstract

We investigate the T-matrix approach for the simulation of light scattering by an oblate particle near a planar interface. Its validity has been in question if the interface intersects the particle’s circumscribing sphere, where the spherical wave expansion of the scattered field can diverge. However, the plane wave expansion of the scattered field converges everywhere below the particle, and in particular at the planar interface. We demonstrate that the particle-interface scattering interaction is correctly accounted for through a plane wave expansion in combination with Fresnel reflection at the planar interface. We present an in-depth analysis of the involved convergence mechanisms, which are governed by the transformation properties between spherical and plane waves. The method is illustrated with the cases of spherical and oblate spheroidal nanoparticles near a perfectly conducting interface, and its accuracy is demonstrated for different scatterer arrangements and materials.

© 2016 Optical Society of America

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  1. L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
    [Crossref]
  2. Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
    [Crossref]
  3. G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
    [Crossref]
  4. P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812, (1965).
    [Crossref]
  5. M. Mishchenko, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf.,  55(5), 535–575, (1996).
    [Crossref]
  6. N. G. Khlebtsov, “T-matrix method in plasmonics: An overview,” J. Quant. Spectrosc. Radiat. Transf. 123, 184–217, (2013).
    [Crossref]
  7. G. Kristensson, “Electromagnetic scattering from buried inhomogeneities–a general three-dimensional formalism,” J. Appl. Phys. 51(7), 3486 (1980).
    [Crossref]
  8. G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8(3), 483 (1991).
    [Crossref]
  9. G. Videen, “Light scattering from a sphere on or near a surface: errata,” J. Opt. Soc. Am. A 9(5), 844–845 (1992)
    [Crossref]
  10. D. W. Mackowski, “Exact solution for the scattering and absorption properties of sphere clusters on a plane surface,” J. Quant. Spectrosc. Radiat. Transf. 109(5), 770–788 (2008).
    [Crossref]
  11. A. Egel and U. Lemmer, “Dipole emission in stratified media with multiple spherical scatterers: enhanced outcoupling from OLEDs,” J. Quant. Spectrosc. Radiat. Transf. 148, 165–176 (2014).
    [Crossref]
  12. 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(4),266–277 (1999).
    [Crossref]
  13. M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
    [Crossref]
  14. For a collection of computer codes, see for example: www.scattport.org .
  15. R.H.T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23(8), 605–623 (1975).
    [Crossref]
  16. T. Hansen and A. D. Yaghjian, Plane-wave theory of time-domain fields: near-field scanning applications (IEEE Press, 1999).
    [Crossref]
  17. C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
    [Crossref]
  18. K. A. Fuller, “Optical resonances and two-sphere systems,” Appl. Opt. 30(33), 4716–4731 (1991).
    [Crossref] [PubMed]
  19. D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266 (1996).
    [Crossref]
  20. A. Boström, G. Kristensson, and S. Ström, “Transformation properties of plane, spherical and cylindrical scalar and vector wave functions,” in Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds. (Elsevier, 1991).
  21. D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
    [Crossref]
  22. A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
    [Crossref]
  23. G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115(1), 1–7 (1995)
    [Crossref]
  24. COMSOL Multiphysics, ver. 5.2, www.comsol.com .

2016 (1)

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

2014 (1)

A. Egel and U. Lemmer, “Dipole emission in stratified media with multiple spherical scatterers: enhanced outcoupling from OLEDs,” J. Quant. Spectrosc. Radiat. Transf. 148, 165–176 (2014).
[Crossref]

2013 (1)

N. G. Khlebtsov, “T-matrix method in plasmonics: An overview,” J. Quant. Spectrosc. Radiat. Transf. 123, 184–217, (2013).
[Crossref]

2011 (1)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

2008 (2)

D. W. Mackowski, “Exact solution for the scattering and absorption properties of sphere clusters on a plane surface,” J. Quant. Spectrosc. Radiat. Transf. 109(5), 770–788 (2008).
[Crossref]

C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
[Crossref]

2004 (1)

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

2003 (1)

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

1999 (1)

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(4),266–277 (1999).
[Crossref]

1997 (1)

D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
[Crossref]

1996 (2)

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266 (1996).
[Crossref]

M. Mishchenko, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf.,  55(5), 535–575, (1996).
[Crossref]

1995 (1)

G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115(1), 1–7 (1995)
[Crossref]

1992 (1)

1991 (2)

1980 (1)

G. Kristensson, “Electromagnetic scattering from buried inhomogeneities–a general three-dimensional formalism,” J. Appl. Phys. 51(7), 3486 (1980).
[Crossref]

1975 (1)

R.H.T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23(8), 605–623 (1975).
[Crossref]

1965 (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812, (1965).
[Crossref]

Babenko, V. A.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

Bates, R.H.T.

R.H.T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23(8), 605–623 (1975).
[Crossref]

Boström, A.

A. Boström, G. Kristensson, and S. Ström, “Transformation properties of plane, spherical and cylindrical scalar and vector wave functions,” in Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds. (Elsevier, 1991).

Breinbjerg, O.

C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
[Crossref]

Cappellin, C.

C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
[Crossref]

Cho, S.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Dalling, R.

D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
[Crossref]

Do, Y. R.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Doicu, A.

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(4),266–277 (1999).
[Crossref]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
[Crossref]

Egel, A.

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

A. Egel and U. Lemmer, “Dipole emission in stratified media with multiple spherical scatterers: enhanced outcoupling from OLEDs,” J. Quant. Spectrosc. Radiat. Transf. 148, 165–176 (2014).
[Crossref]

Eremin, Y. A.

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(4),266–277 (1999).
[Crossref]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
[Crossref]

Frandsen, A.

C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
[Crossref]

Fuller, K. A.

Gomard, G.

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

Hansen, T.

T. Hansen and A. D. Yaghjian, Plane-wave theory of time-domain fields: near-field scanning applications (IEEE Press, 1999).
[Crossref]

Huh, J.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Khlebtsov, N. G.

N. G. Khlebtsov, “T-matrix method in plasmonics: An overview,” J. Quant. Spectrosc. Radiat. Transf. 123, 184–217, (2013).
[Crossref]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

Kim, G.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Kim, S.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Kim, Y.-C.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Kristensson, G.

G. Kristensson, “Electromagnetic scattering from buried inhomogeneities–a general three-dimensional formalism,” J. Appl. Phys. 51(7), 3486 (1980).
[Crossref]

A. Boström, G. Kristensson, and S. Ström, “Transformation properties of plane, spherical and cylindrical scalar and vector wave functions,” in Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds. (Elsevier, 1991).

Lee, Y.-H.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Lee, Y.-J.

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

Lemmer, U.

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

A. Egel and U. Lemmer, “Dipole emission in stratified media with multiple spherical scatterers: enhanced outcoupling from OLEDs,” J. Quant. Spectrosc. Radiat. Transf. 148, 165–176 (2014).
[Crossref]

Mackowski, D. W.

D. W. Mackowski, “Exact solution for the scattering and absorption properties of sphere clusters on a plane surface,” J. Quant. Spectrosc. Radiat. Transf. 109(5), 770–788 (2008).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266 (1996).
[Crossref]

Mishchenko, M.

M. Mishchenko, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf.,  55(5), 535–575, (1996).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

D. W. Mackowski and M. I. Mishchenko, “Calculation of the T matrix and the scattering matrix for ensembles of spheres,” J. Opt. Soc. Am. A 13(11), 2266 (1996).
[Crossref]

Ngo, D.

D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
[Crossref]

Novotny, L.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

Preinfalk, J.

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

Ström, S.

A. Boström, G. Kristensson, and S. Ström, “Transformation properties of plane, spherical and cylindrical scalar and vector wave functions,” in Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds. (Elsevier, 1991).

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

Videen, G.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
[Crossref]

G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115(1), 1–7 (1995)
[Crossref]

G. Videen, “Light scattering from a sphere on or near a surface: errata,” J. Opt. Soc. Am. A 9(5), 844–845 (1992)
[Crossref]

G. Videen, “Light scattering from a sphere on or near a surface,” J. Opt. Soc. Am. A 8(3), 483 (1991).
[Crossref]

Waterman, P. C.

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812, (1965).
[Crossref]

Wriedt, T.

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[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(4),266–277 (1999).
[Crossref]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
[Crossref]

Yaghjian, A. D.

T. Hansen and A. D. Yaghjian, Plane-wave theory of time-domain fields: near-field scanning applications (IEEE Press, 1999).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y.-J. Lee, S.-H. Kim, J. Huh, G.-H. Kim, Y.-H. Lee, S.-H. Cho, Y.-C. Kim, and Y. R. Do, “A high-extraction-efficiency nanopatterned organic light-emitting diode,” Appl. Phys. Lett. 82(21), 3779–3781 (2003).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

R.H.T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23(8), 605–623 (1975).
[Crossref]

J. Appl. Phys. (1)

G. Kristensson, “Electromagnetic scattering from buried inhomogeneities–a general three-dimensional formalism,” J. Appl. Phys. 51(7), 3486 (1980).
[Crossref]

J. Opt. Soc. Am. A (3)

J. Photon. Energy (1)

G. Gomard, J. Preinfalk, A. Egel, and U. Lemmer, “Photon management in solution-processed organic light-emitting diodes: a review of light outcoupling micro- and nanostructures,” J. Photon. Energy 6(3), 030901 (2016).
[Crossref]

J. Quant. Spectrosc. Radiat. Transf. (5)

M. Mishchenko, “T-matrix computations of light scattering by nonspherical particles: a review,” J. Quant. Spectrosc. Radiat. Transf.,  55(5), 535–575, (1996).
[Crossref]

N. G. Khlebtsov, “T-matrix method in plasmonics: An overview,” J. Quant. Spectrosc. Radiat. Transf. 123, 184–217, (2013).
[Crossref]

D. W. Mackowski, “Exact solution for the scattering and absorption properties of sphere clusters on a plane surface,” J. Quant. Spectrosc. Radiat. Transf. 109(5), 770–788 (2008).
[Crossref]

A. Egel and U. Lemmer, “Dipole emission in stratified media with multiple spherical scatterers: enhanced outcoupling from OLEDs,” J. Quant. Spectrosc. Radiat. Transf. 148, 165–176 (2014).
[Crossref]

M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, “T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database,” J. Quant. Spectrosc. Radiat. Transf. 88(1–3), 357–406 (2004).
[Crossref]

Nat. Photonics (1)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5(2), 83–90 (2011).
[Crossref]

Opt. Commun. (2)

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(4),266–277 (1999).
[Crossref]

G. Videen, “Light scattering from a particle on or near a perfectly conducting surface,” Opt. Commun. 115(1), 1–7 (1995)
[Crossref]

Phys. Lett. A (1)

D. Ngo, G. Videen, and R. Dalling, “Chaotic light scattering from a system of osculating, conducting spheres,” Phys. Lett. A 227(3), 197–202 (1997)
[Crossref]

Proc. IEEE (1)

P. C. Waterman, “Matrix formulation of electromagnetic scattering,” Proc. IEEE 53(8), 805–812, (1965).
[Crossref]

Radio Sci. (1)

C. Cappellin, O. Breinbjerg, and A. Frandsen, “Properties of the transformation from the spherical wave expansion to the plane wave expansion,” Radio Sci. 43(1), RS1012 (2008).
[Crossref]

Other (5)

A. Boström, G. Kristensson, and S. Ström, “Transformation properties of plane, spherical and cylindrical scalar and vector wave functions,” in Acoustic, Electromagnetic and Elastic Wave Scattering, Field Representations and Introduction to Scattering, V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds. (Elsevier, 1991).

For a collection of computer codes, see for example: www.scattport.org .

T. Hansen and A. D. Yaghjian, Plane-wave theory of time-domain fields: near-field scanning applications (IEEE Press, 1999).
[Crossref]

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
[Crossref]

COMSOL Multiphysics, ver. 5.2, www.comsol.com .

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Figures (8)

Fig. 1
Fig. 1

Oblate scattering particle near a planar surface

Fig. 2
Fig. 2

The expansion of ES (r) in outgoing spherical waves is valid for r > rmax. The expansion in downgoing plane waves is valid for z < zmin. In the dashed white region, the expansion in downgoing plane waves is thus valid, even if the expansion in outgoing spherical waves does not converge. The plane z = z0 is inside the domain of validity for both expansions.

Fig. 3
Fig. 3

Scattering of a downward propagating plane wave at five dielectric spheres in free space. A: The norm of the exact scattered near-field. B: Error of the field constructed with the superposition T-matrix for the composite particle, truncated at ltrunc = 20. C: Error of the field constructed with the superposition T-matrix, truncated at ltrunc = 20, then transformed into the angular spectrum representation, Eq. (8), truncated at κtrunc = 2 k. D: The same as C, but with κtrunc = 50 k. The dashed circles and lines indicate the boundary of the domains of validity for the SWE and the PWE, respectively. The color scale reaches from 0 (dark blue) to 0.8 (dark red).

Fig. 4
Fig. 4

Plane wave expansion of the scattered field for five spheres in free space. The y-axis shows the weight of the respective partial plane waves to the scattered electric field evaluated at 1.5R below the particle centers, |T (κêx) exp(1.5ikz R)|. The solid curve corresponds to the exact PWE constructed from the reference solution. The dashed, dotted and dash-dotted lines correspond to the PWE in the composite-particle approach for different truncation multipole orders ltrunc in the right hand side of Eq. (8). The vertical grey lines indicate the location of κ1 and κ2 for the respective truncation multipole orders. We have also marked the points up to which the PWE was considered in the evaluation of the scattered fields shown in Figs. 3(C) and (D), respectively, as black dots.

Fig. 5
Fig. 5

Five dielectric spheres near a perfectly conducting substrate.

Fig. 6
Fig. 6

A) Achieved accuracy as a function of the truncation in-plane wavenumber and truncation multipole order. The distance between the particles and the planar interface was fixed to Δz = R. B) Minimal error (i.e., for optimal κtrunc), as a function of the distance between the particle centers and the planar interface. The lines refer to different truncation multipole orders (see annotation). The dashed grey line refers to the accuracy that results from the image method for the composite particle for ltrunc = 15.

Fig. 7
Fig. 7

Oblate spheroid near a perfectly conducting substrate.

Fig. 8
Fig. 8

Scattered far field intensity in the xz-plane as a function of the polar angle for a dielectric (n = 2.4, left column) or perfectly conducting (right column) oblate spheroid near a perfectly conducting substrate. The particles are illuminated under normal incidence by a plane wave set at 550 nm. Each row of graphs corresponds to a fixed particle-substrate distance. We compare T-matrix results with a PWE truncation of κtrunc = 3 k (solid line) and 20 k (dash-dotted line) to FEM results (black dots). In addition, T-matrix results using the image method are shown, too (dashed line). For Δz = 0, the results for the image method and for κtrunc = 20 k have been scaled down to fit into the axes box.

Equations (22)

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E ( r ) = E 0 ( r ) + E S ( r ) + E S R ( r ) ,
E in ( r ) = E 0 ( r ) + E S R ( r ) = n a n M n ( 1 ) ( r ) .
E S ( r ) = n b n M n ( 3 ) ( r ) .
b n = n T n n a n .
a n = a 0 , n + a S , n R ,
E S ( r ) = n j b n 2 π 2 d 2 k k z k B n j ( k z / k ) E j ( κ , α ; r ) e i m α
E S R ( r ) = n j b n 2 π 2 d 2 k ρ j ( κ ) e 2 i k z z I k z k B n j ( k z / k ) E j + ( κ , α ; r ) e i m α .
E S R ( r ) = 4 n n j δ m m b n 0 d κ κ ρ j ( κ ) e 2 i k z z I k z k B n j ( k z / k ) B n j ( k z / k ) M n ( 1 ) ( r )
E S R ( r ) = n a S , n R M n ( 1 ) ( r )
a S , n R = n W n n R b n
W n n R = 4 j δ m m 0 d κ κ ρ j ( κ ) e 2 i k z z I k z k B n j ( k z / k ) B n j ( k z / k ) .
b n = n T n n ( a 0 , n + a 0 , n R + n W n n R b n ) ,
E S ( r ) = j 2 d 2 k k z k n b n 2 π B n j ( k z / k ) E j ( κ , α ; r ) e i m α for z = z 0 .
E S ( r ) = 2 d 2 k T ( k ) e i k r
T ( k ) = j n b n 2 π B n j ( k z / k ) k z k e i m α e ^ j .
relative error = b b exact b exact ,
M l m 1 ( ν ) ( r ) = 1 2 l ( l + 1 ) × ( r z l ( ν ) ( k r ) P l | m | ( cos θ ) e i m ϕ ) M l m 2 ( ν ) ( r ) = 1 k × M m l 1 ( ν ) ( r )
E j ± ( κ , α ; r ) = exp ( i k ± r ) e ^ j
M n ( 3 ) ( r ) = 1 2 π 2 d 2 k 1 k z k j = 1 2 B n j ( ± k z / k ) E j ± ( κ , α ; r ) e i m α for z 0
E j ± ( κ , α ; r ) = 4 n e i m α B n j ( ± k z / k ) M n ( 1 ) ( r ) ,
B n j ( x ) = 1 i l + 1 1 2 l ( l + 1 ) ( i δ j 1 + δ j 2 ) ( δ p j τ l | m | ( x ) + ( 1 δ p j ) m π l | m | ( x ) )
π l m ( cos θ ) = P l m ( cos θ ) sin θ τ l m ( cos θ ) = θ P l m ( cos θ ) .

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