Abstract

The classical Mie theory for the scattering and absorption of electromagnetic radiation by a sphere is extended to the case of a spatially dispersive sphere. Three alternative extensions, based on three different types of additional boundary conditions, are derived. Extinction spectra of small ZnSe spheres are calculated, and it is found that the frequency of the main resonance exhibits a strong dependence on the choice of the additional boundary conditions.

© 1981 Optical Society of America

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  1. G. Mie, "Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen," Ann. Phys. 25, 377–445 (1908).
  2. R. Clanget, "Der Einfluss von Plasmawellen auf die optischen Eigenschaften leitender Schichten und metallischer Kolloide," Optik (Stuttgart) 35, 180–194 (1972).
  3. R. Ruppin, "Optical properties of small metal spheres," Phys. Rev. B 11, 2871–2876 (1975).
  4. S. I. Pekar, "Dispersion of light in the exciton absorption region of crystals," Sov. Phys. JETP 7, 813–822 (1958).
  5. J. J. Hopfield and D. G. Thomas, "Theoretical and experimental effects of spatial dispersion on the optical properties of crystals," Phys. Rev. 132, 563–572 (1963).
  6. G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).
  7. J. L. Birman and J. J. Sein, "Optics of polaritons in bounded media," Phys. Rev. B 6, 2482–2490 (1972).
  8. T. Skettrup, "Exciton spectra with spatial dispersion in case of non-normal incidence," Phys. Status Solidi B 60, 695–705 (1973).
  9. A. A. Maradudin and D. L. Mills, "Effect of spatial dispersion on the properties of a semi-infinite dielectric," Phys. Rev. B 7, 2787–2810 (1973).
  10. G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).
  11. P. R. Rimbey and G. D. Mahan, "Surface impedance of a spatially dispersive medium," Solid State Commun. 15, 35–37 (1974).
  12. C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).
  13. F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).
  14. M. J. Frankel and J. L. Birman, "Electrodynamics of nonlocal bounded dielectrics," Phys. Rev. B 13, 2587–2595 (1976).
  15. M. R. Philpott, "Polaritons in a spatially dispersive dielectric half space," Phys. Rev. B 14, 3471–3487 (1976).
  16. P. R. Rimbey, "Polariton Green's functions for semi-infinite spatially dispersive media with applications to molecular crystal reflectivity spectra," J. Chem. Phys. 67, 698–709 (1977).
  17. F. Garcia-Moliner and F. Flores, "Classical electrodynamics of non-specular dielectric surfaces," J. Phys. 38, 851–862 (1977).
  18. I. Broser et al., "A quantitative study of excitonic polariton reflectance in CdS," Phys. Status Solidi B 90, 77–91 (1978).
  19. P. Halevi and R. Fuchs, "The generalized additional boundary conditions for nonlocal dielectrics," Phys. Rev. B (in press).
  20. J. T. Foley and D. N. Pattanayak, "Electromagnetic scattering from a spatially dispersive sphere," Opt. Commun. 12, 113–117 (1974).
  21. R. Ruppin, "Mie theory with spatial dispersion," Opt. Commun. 30, 380–382 (1979).
  22. K. L. Kliewer and R. Fuchs, "Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence," Phys. Rev. 172, 607–624 (1968).
  23. R. Fuchs and K. L. Kliewer, "Surface plasmon in a semi-infinite free-electron gas," Phys. Rev. B 3, 2270–2278 (1971).
  24. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  25. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  26. H. Fröhlich, Theory of Dielectrics (Clarendon, Oxford, 1949).
  27. R. Ruppin and R. Engiman, "Optical phonons of small crystals," Rep. Prog. Phys. 33, 149–196 (1970).

1979 (1)

R. Ruppin, "Mie theory with spatial dispersion," Opt. Commun. 30, 380–382 (1979).

1978 (1)

I. Broser et al., "A quantitative study of excitonic polariton reflectance in CdS," Phys. Status Solidi B 90, 77–91 (1978).

1977 (2)

P. R. Rimbey, "Polariton Green's functions for semi-infinite spatially dispersive media with applications to molecular crystal reflectivity spectra," J. Chem. Phys. 67, 698–709 (1977).

F. Garcia-Moliner and F. Flores, "Classical electrodynamics of non-specular dielectric surfaces," J. Phys. 38, 851–862 (1977).

1976 (3)

F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).

M. J. Frankel and J. L. Birman, "Electrodynamics of nonlocal bounded dielectrics," Phys. Rev. B 13, 2587–2595 (1976).

M. R. Philpott, "Polaritons in a spatially dispersive dielectric half space," Phys. Rev. B 14, 3471–3487 (1976).

1975 (2)

C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).

R. Ruppin, "Optical properties of small metal spheres," Phys. Rev. B 11, 2871–2876 (1975).

1974 (3)

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).

P. R. Rimbey and G. D. Mahan, "Surface impedance of a spatially dispersive medium," Solid State Commun. 15, 35–37 (1974).

J. T. Foley and D. N. Pattanayak, "Electromagnetic scattering from a spatially dispersive sphere," Opt. Commun. 12, 113–117 (1974).

1973 (2)

T. Skettrup, "Exciton spectra with spatial dispersion in case of non-normal incidence," Phys. Status Solidi B 60, 695–705 (1973).

A. A. Maradudin and D. L. Mills, "Effect of spatial dispersion on the properties of a semi-infinite dielectric," Phys. Rev. B 7, 2787–2810 (1973).

1972 (2)

R. Clanget, "Der Einfluss von Plasmawellen auf die optischen Eigenschaften leitender Schichten und metallischer Kolloide," Optik (Stuttgart) 35, 180–194 (1972).

J. L. Birman and J. J. Sein, "Optics of polaritons in bounded media," Phys. Rev. B 6, 2482–2490 (1972).

1971 (2)

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).

R. Fuchs and K. L. Kliewer, "Surface plasmon in a semi-infinite free-electron gas," Phys. Rev. B 3, 2270–2278 (1971).

1970 (1)

R. Ruppin and R. Engiman, "Optical phonons of small crystals," Rep. Prog. Phys. 33, 149–196 (1970).

1968 (1)

K. L. Kliewer and R. Fuchs, "Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence," Phys. Rev. 172, 607–624 (1968).

1963 (1)

J. J. Hopfield and D. G. Thomas, "Theoretical and experimental effects of spatial dispersion on the optical properties of crystals," Phys. Rev. 132, 563–572 (1963).

1958 (1)

S. I. Pekar, "Dispersion of light in the exciton absorption region of crystals," Sov. Phys. JETP 7, 813–822 (1958).

1908 (1)

G. Mie, "Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen," Ann. Phys. 25, 377–445 (1908).

Agarwal, G. S.

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).

Birman, J. L.

M. J. Frankel and J. L. Birman, "Electrodynamics of nonlocal bounded dielectrics," Phys. Rev. B 13, 2587–2595 (1976).

C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).

J. L. Birman and J. J. Sein, "Optics of polaritons in bounded media," Phys. Rev. B 6, 2482–2490 (1972).

Broser, I.

I. Broser et al., "A quantitative study of excitonic polariton reflectance in CdS," Phys. Status Solidi B 90, 77–91 (1978).

Capizzi, M.

F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).

Clanget, R.

R. Clanget, "Der Einfluss von Plasmawellen auf die optischen Eigenschaften leitender Schichten und metallischer Kolloide," Optik (Stuttgart) 35, 180–194 (1972).

Engiman, R.

R. Ruppin and R. Engiman, "Optical phonons of small crystals," Rep. Prog. Phys. 33, 149–196 (1970).

Evangelisti, F.

F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).

Flores, F.

F. Garcia-Moliner and F. Flores, "Classical electrodynamics of non-specular dielectric surfaces," J. Phys. 38, 851–862 (1977).

Foley, J. T.

J. T. Foley and D. N. Pattanayak, "Electromagnetic scattering from a spatially dispersive sphere," Opt. Commun. 12, 113–117 (1974).

Frankel, M. J.

M. J. Frankel and J. L. Birman, "Electrodynamics of nonlocal bounded dielectrics," Phys. Rev. B 13, 2587–2595 (1976).

Frankel, M. M.

C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).

Fröhlich, H.

H. Fröhlich, Theory of Dielectrics (Clarendon, Oxford, 1949).

Fuchs, R.

R. Fuchs and K. L. Kliewer, "Surface plasmon in a semi-infinite free-electron gas," Phys. Rev. B 3, 2270–2278 (1971).

K. L. Kliewer and R. Fuchs, "Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence," Phys. Rev. 172, 607–624 (1968).

P. Halevi and R. Fuchs, "The generalized additional boundary conditions for nonlocal dielectrics," Phys. Rev. B (in press).

Garcia-Moliner, F.

F. Garcia-Moliner and F. Flores, "Classical electrodynamics of non-specular dielectric surfaces," J. Phys. 38, 851–862 (1977).

Halevi, P.

P. Halevi and R. Fuchs, "The generalized additional boundary conditions for nonlocal dielectrics," Phys. Rev. B (in press).

Hopfield, J. J.

J. J. Hopfield and D. G. Thomas, "Theoretical and experimental effects of spatial dispersion on the optical properties of crystals," Phys. Rev. 132, 563–572 (1963).

Kerker, M.

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

Kliewer, K. L.

R. Fuchs and K. L. Kliewer, "Surface plasmon in a semi-infinite free-electron gas," Phys. Rev. B 3, 2270–2278 (1971).

K. L. Kliewer and R. Fuchs, "Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence," Phys. Rev. 172, 607–624 (1968).

Mahan, G. D.

P. R. Rimbey and G. D. Mahan, "Surface impedance of a spatially dispersive medium," Solid State Commun. 15, 35–37 (1974).

Maradudin, A. A.

A. A. Maradudin and D. L. Mills, "Effect of spatial dispersion on the properties of a semi-infinite dielectric," Phys. Rev. B 7, 2787–2810 (1973).

Mie, G.

G. Mie, "Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen," Ann. Phys. 25, 377–445 (1908).

Mills, D. L.

A. A. Maradudin and D. L. Mills, "Effect of spatial dispersion on the properties of a semi-infinite dielectric," Phys. Rev. B 7, 2787–2810 (1973).

Patella, F.

F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).

Pattanayak, D. N.

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).

J. T. Foley and D. N. Pattanayak, "Electromagnetic scattering from a spatially dispersive sphere," Opt. Commun. 12, 113–117 (1974).

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).

Pekar, S. I.

S. I. Pekar, "Dispersion of light in the exciton absorption region of crystals," Sov. Phys. JETP 7, 813–822 (1958).

Philpott, M. R.

M. R. Philpott, "Polaritons in a spatially dispersive dielectric half space," Phys. Rev. B 14, 3471–3487 (1976).

Rimbey, P. R.

P. R. Rimbey, "Polariton Green's functions for semi-infinite spatially dispersive media with applications to molecular crystal reflectivity spectra," J. Chem. Phys. 67, 698–709 (1977).

P. R. Rimbey and G. D. Mahan, "Surface impedance of a spatially dispersive medium," Solid State Commun. 15, 35–37 (1974).

Ruppin, R.

R. Ruppin, "Mie theory with spatial dispersion," Opt. Commun. 30, 380–382 (1979).

R. Ruppin, "Optical properties of small metal spheres," Phys. Rev. B 11, 2871–2876 (1975).

R. Ruppin and R. Engiman, "Optical phonons of small crystals," Rep. Prog. Phys. 33, 149–196 (1970).

Sein, J. J.

J. L. Birman and J. J. Sein, "Optics of polaritons in bounded media," Phys. Rev. B 6, 2482–2490 (1972).

Skettrup, T.

T. Skettrup, "Exciton spectra with spatial dispersion in case of non-normal incidence," Phys. Status Solidi B 60, 695–705 (1973).

Stratton, J. A.

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

Thomas, D. G.

J. J. Hopfield and D. G. Thomas, "Theoretical and experimental effects of spatial dispersion on the optical properties of crystals," Phys. Rev. 132, 563–572 (1963).

Ting, C. S.

C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).

Wolf, E.

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).

Ann. Phys. (1)

G. Mie, "Beitrage zur Optik trüber Medien, speziell kolloidaler Metallösungen," Ann. Phys. 25, 377–445 (1908).

J. Chem. Phys. (1)

P. R. Rimbey, "Polariton Green's functions for semi-infinite spatially dispersive media with applications to molecular crystal reflectivity spectra," J. Chem. Phys. 67, 698–709 (1977).

J. Phys. (1)

F. Garcia-Moliner and F. Flores, "Classical electrodynamics of non-specular dielectric surfaces," J. Phys. 38, 851–862 (1977).

Opt. Commun. (3)

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Refraction and reflection on a spatially dispersive medium," Opt. Commun. 4, 255–259 (1971).

J. T. Foley and D. N. Pattanayak, "Electromagnetic scattering from a spatially dispersive sphere," Opt. Commun. 12, 113–117 (1974).

R. Ruppin, "Mie theory with spatial dispersion," Opt. Commun. 30, 380–382 (1979).

Optik Stuttgart (1)

R. Clanget, "Der Einfluss von Plasmawellen auf die optischen Eigenschaften leitender Schichten und metallischer Kolloide," Optik (Stuttgart) 35, 180–194 (1972).

Phys. Rev. (6)

A. A. Maradudin and D. L. Mills, "Effect of spatial dispersion on the properties of a semi-infinite dielectric," Phys. Rev. B 7, 2787–2810 (1973).

G. S. Agarwal, D. N. Pattanayak, and E. Wolf, "Electromagnetic fields in spatially dispersive media," Phys. Rev. B 10, 1447–1475 (1974).

J. L. Birman and J. J. Sein, "Optics of polaritons in bounded media," Phys. Rev. B 6, 2482–2490 (1972).

K. L. Kliewer and R. Fuchs, "Anomalous skin effect for specular electron scattering and optical experiments at non-normal angles of incidence," Phys. Rev. 172, 607–624 (1968).

R. Fuchs and K. L. Kliewer, "Surface plasmon in a semi-infinite free-electron gas," Phys. Rev. B 3, 2270–2278 (1971).

J. J. Hopfield and D. G. Thomas, "Theoretical and experimental effects of spatial dispersion on the optical properties of crystals," Phys. Rev. 132, 563–572 (1963).

Phys. Rev. B (3)

M. J. Frankel and J. L. Birman, "Electrodynamics of nonlocal bounded dielectrics," Phys. Rev. B 13, 2587–2595 (1976).

M. R. Philpott, "Polaritons in a spatially dispersive dielectric half space," Phys. Rev. B 14, 3471–3487 (1976).

R. Ruppin, "Optical properties of small metal spheres," Phys. Rev. B 11, 2871–2876 (1975).

Phys. Status Solidi (1)

T. Skettrup, "Exciton spectra with spatial dispersion in case of non-normal incidence," Phys. Status Solidi B 60, 695–705 (1973).

Phys. Status Solidi B (1)

I. Broser et al., "A quantitative study of excitonic polariton reflectance in CdS," Phys. Status Solidi B 90, 77–91 (1978).

Rep. Prog. Phys. (1)

R. Ruppin and R. Engiman, "Optical phonons of small crystals," Rep. Prog. Phys. 33, 149–196 (1970).

Solid State Commun. (3)

P. R. Rimbey and G. D. Mahan, "Surface impedance of a spatially dispersive medium," Solid State Commun. 15, 35–37 (1974).

C. S. Ting, M. M. Frankel, and J. L. Birman, "Electrodynamics of bounded spatially dispersive media: the additional boundary conditions," Solid State Commun. 17, 1285–1289 (1975).

F. Patella, F. Evangelisti, and M. Capizzi, "Experimental reflectivity spectra and additional boundary conditions in CdS," Solid State Commun. 20, 23–25 (1976).

Sov. Phys. JETP (1)

S. I. Pekar, "Dispersion of light in the exciton absorption region of crystals," Sov. Phys. JETP 7, 813–822 (1958).

Other (4)

P. Halevi and R. Fuchs, "The generalized additional boundary conditions for nonlocal dielectrics," Phys. Rev. B (in press).

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

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

H. Fröhlich, Theory of Dielectrics (Clarendon, Oxford, 1949).

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