Abstract

The classical electromagnetic scattering theory for a circular cylinder that is irradiated by a normally incident plane wave is extended to the case of a spatially dispersive cylinder. A dielectric constant that applies in the vicinity of an excitonic spectral line is used, and the size quantization of the exciton motion is taken into account through the boundary conditions that are employed at the surface of the cylinder. Examples of calculated extinction spectra are presented, and it is found that the excitonic absorption peaks shift to higher energies with decreasing cylinder radius.

© 1989 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. E. L. Ivchenko, “Spatial dispersion effects in the exciton resonance region,” in Excitons, E. I. Rashba and M. D. Sturge, eds. (North-Holland, Amsterdam, 1982).
  3. R. Ruppin, “Optical properties of spatially dispersive dielectric spheres,” J. Opt. Soc. Am. 71, 755–758 (1981).
    [CrossRef]
  4. A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).
  5. S. Hayashi and K. Yamamoto, “Exciton absorption in gas evaporated CuCl microcrystals,” J. Phys. Soc. Jpn. 56, 2229–2230 (1987).
    [CrossRef]
  6. T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
    [CrossRef]
  7. B. G. Potter and J. H. Simmons, “Quantum size effects in optical properties of CdS-glass composites,” Phys. Rev. B 37, 10838–10845 (1988).
    [CrossRef]
  8. H. Sakaki, “Scattering suppression and high mobility effect of size quantized electrons in ultrafine semiconductor wire structures,” Jpn. J. Appl. Phys. 19, L735–L738 (1980).
    [CrossRef]
  9. P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
    [CrossRef]
  10. H. H. Hassan and H. N. Spector, “Interband optical absorption in thin semiconducting quantum well wires,” J. Vac. Sci. Technol. A 3, 22–28 (1985).
    [CrossRef]
  11. J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
    [CrossRef]
  12. H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
    [CrossRef]
  13. R. Perez-Alvarez and P. Pajon-Suarez, “Optical absorption coefficient in cylindrical quantum wells,” Phys. Status Solidi B 147, 547–552 (1988).
    [CrossRef]
  14. H. Heinrich, G. Bauer, and F. Kucher, eds., Physics and Technology of Submicron Structures (Springer-Verlag, Berlin, 1988).
    [CrossRef]
  15. S. I. Pekar, “Dispersion of light in the exciton absorption region of crystals,” Sov. Phys. JETP 7, 813–822 (1958).
  16. 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).
    [CrossRef]
  17. F. Patella, F. Evangelisti, and M. Capizzi, “Experimental reflectivity spectra and additional boundary conditions in CdS,” Solid State Commun. 20, 23–25 (1976).
    [CrossRef]
  18. P. Halevi and R. Fuchs, “Generalised additional boundary condition for non-local dielectrics: I. Reflectivity,” J. Phys. C 17, 3869–3888 (1984).
    [CrossRef]
  19. K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
    [CrossRef]
  20. T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
    [CrossRef]
  21. R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
    [CrossRef]
  22. Al. L. Efros and A. L. Efros, “Interband absorption of light in a semiconductor sphere,” Sov. Phys. Semicond. 16, 772–775 (1982).

1988 (3)

T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
[CrossRef]

B. G. Potter and J. H. Simmons, “Quantum size effects in optical properties of CdS-glass composites,” Phys. Rev. B 37, 10838–10845 (1988).
[CrossRef]

R. Perez-Alvarez and P. Pajon-Suarez, “Optical absorption coefficient in cylindrical quantum wells,” Phys. Status Solidi B 147, 547–552 (1988).
[CrossRef]

1987 (2)

S. Hayashi and K. Yamamoto, “Exciton absorption in gas evaporated CuCl microcrystals,” J. Phys. Soc. Jpn. 56, 2229–2230 (1987).
[CrossRef]

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

1986 (1)

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

1985 (3)

H. H. Hassan and H. N. Spector, “Interband optical absorption in thin semiconducting quantum well wires,” J. Vac. Sci. Technol. A 3, 22–28 (1985).
[CrossRef]

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[CrossRef]

1984 (1)

P. Halevi and R. Fuchs, “Generalised additional boundary condition for non-local dielectrics: I. Reflectivity,” J. Phys. C 17, 3869–3888 (1984).
[CrossRef]

1982 (2)

Al. L. Efros and A. L. Efros, “Interband absorption of light in a semiconductor sphere,” Sov. Phys. Semicond. 16, 772–775 (1982).

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

1981 (1)

1980 (2)

T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
[CrossRef]

H. Sakaki, “Scattering suppression and high mobility effect of size quantized electrons in ultrafine semiconductor wire structures,” Jpn. J. Appl. Phys. 19, L735–L738 (1980).
[CrossRef]

1976 (1)

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

1970 (1)

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
[CrossRef]

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).
[CrossRef]

1958 (1)

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

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).
[CrossRef]

Cho, K.

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[CrossRef]

Chu, S. N. G.

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

Cibert, J.

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

Dolan, G. J.

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

Efros, A. L.

Al. L. Efros and A. L. Efros, “Interband absorption of light in a semiconductor sphere,” Sov. Phys. Semicond. 16, 772–775 (1982).

Efros, Al. L.

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

Al. L. Efros and A. L. Efros, “Interband absorption of light in a semiconductor sphere,” Sov. Phys. Semicond. 16, 772–775 (1982).

Ekimov, A. I.

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

English, J. H.

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

Englman, R.

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
[CrossRef]

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).
[CrossRef]

Fuchs, R.

P. Halevi and R. Fuchs, “Generalised additional boundary condition for non-local dielectrics: I. Reflectivity,” J. Phys. C 17, 3869–3888 (1984).
[CrossRef]

Gossard, A. C.

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

Halevi, P.

P. Halevi and R. Fuchs, “Generalised additional boundary condition for non-local dielectrics: I. Reflectivity,” J. Phys. C 17, 3869–3888 (1984).
[CrossRef]

Hassan, H. H.

H. H. Hassan and H. N. Spector, “Interband optical absorption in thin semiconducting quantum well wires,” J. Vac. Sci. Technol. A 3, 22–28 (1985).
[CrossRef]

Hayashi, S.

S. Hayashi and K. Yamamoto, “Exciton absorption in gas evaporated CuCl microcrystals,” J. Phys. Soc. Jpn. 56, 2229–2230 (1987).
[CrossRef]

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).
[CrossRef]

Itoh, T.

T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
[CrossRef]

Ivchenko, E. L.

E. L. Ivchenko, “Spatial dispersion effects in the exciton resonance region,” in Excitons, E. I. Rashba and M. D. Sturge, eds. (North-Holland, Amsterdam, 1982).

Iwabuchi, Y.

T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
[CrossRef]

Kataoka, M.

T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
[CrossRef]

Kawata, M.

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[CrossRef]

Logan, R. A.

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

Mita, T.

T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
[CrossRef]

Onushchenko, A. A.

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

Pajon-Suarez, P.

R. Perez-Alvarez and P. Pajon-Suarez, “Optical absorption coefficient in cylindrical quantum wells,” Phys. Status Solidi B 147, 547–552 (1988).
[CrossRef]

Panish, M. B.

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

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).
[CrossRef]

Pearton, S. J.

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

Pekar, S. I.

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

Perez-Alvarez, R.

R. Perez-Alvarez and P. Pajon-Suarez, “Optical absorption coefficient in cylindrical quantum wells,” Phys. Status Solidi B 147, 547–552 (1988).
[CrossRef]

Petroff, P. M.

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

Plyukhin, A. G.

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

Potter, B. G.

B. G. Potter and J. H. Simmons, “Quantum size effects in optical properties of CdS-glass composites,” Phys. Rev. B 37, 10838–10845 (1988).
[CrossRef]

Ruppin, R.

R. Ruppin, “Optical properties of spatially dispersive dielectric spheres,” J. Opt. Soc. Am. 71, 755–758 (1981).
[CrossRef]

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
[CrossRef]

Sakaki, H.

H. Sakaki, “Scattering suppression and high mobility effect of size quantized electrons in ultrafine semiconductor wire structures,” Jpn. J. Appl. Phys. 19, L735–L738 (1980).
[CrossRef]

Simmons, J. H.

B. G. Potter and J. H. Simmons, “Quantum size effects in optical properties of CdS-glass composites,” Phys. Rev. B 37, 10838–10845 (1988).
[CrossRef]

Sotome, K.

T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
[CrossRef]

Spector, H. N.

H. H. Hassan and H. N. Spector, “Interband optical absorption in thin semiconducting quantum well wires,” J. Vac. Sci. Technol. A 3, 22–28 (1985).
[CrossRef]

Temkin, H.

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

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).
[CrossRef]

Ueta, M.

T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Wiegmann, W.

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

Yamamoto, K.

S. Hayashi and K. Yamamoto, “Exciton absorption in gas evaporated CuCl microcrystals,” J. Phys. Soc. Jpn. 56, 2229–2230 (1987).
[CrossRef]

Appl. Phys. Lett. (3)

J. Cibert, P. M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, “Optically detected carrier confinement to one and zero dimension in GaAs quantum well wires and boxes,” Appl. Phys. Lett. 49, 1275–1277 (1986).
[CrossRef]

H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, “Low temperature photoluminescence from InGaAs/InP quantum wires and boxes,” Appl. Phys. Lett. 50, 413–415 (1987).
[CrossRef]

P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, “Toward quantum well wires: fabrication and optical properties,” Appl. Phys. Lett. 41, 635–638 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. C (1)

P. Halevi and R. Fuchs, “Generalised additional boundary condition for non-local dielectrics: I. Reflectivity,” J. Phys. C 17, 3869–3888 (1984).
[CrossRef]

J. Phys. Soc. Jpn. (2)

K. Cho and M. Kawata, “Theoretical analysis of polariton interference in a thin platelet of CuCl. I. Additional boundary condition,” J. Phys. Soc. Jpn. 54, 4431–4443 (1985).
[CrossRef]

S. Hayashi and K. Yamamoto, “Exciton absorption in gas evaporated CuCl microcrystals,” J. Phys. Soc. Jpn. 56, 2229–2230 (1987).
[CrossRef]

J. Vac. Sci. Technol. A (1)

H. H. Hassan and H. N. Spector, “Interband optical absorption in thin semiconducting quantum well wires,” J. Vac. Sci. Technol. A 3, 22–28 (1985).
[CrossRef]

Jpn. J. Appl. Phys. (1)

H. Sakaki, “Scattering suppression and high mobility effect of size quantized electrons in ultrafine semiconductor wire structures,” Jpn. J. Appl. Phys. 19, L735–L738 (1980).
[CrossRef]

Phys. Rev. (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).
[CrossRef]

Phys. Rev. B (1)

B. G. Potter and J. H. Simmons, “Quantum size effects in optical properties of CdS-glass composites,” Phys. Rev. B 37, 10838–10845 (1988).
[CrossRef]

Phys. Status Solidi B (2)

T. Itoh, Y. Iwabuchi, and M. Kataoka, “Study on the size and shape of CuCl microcrystals embedded in alkali-chloride matrices and their correlation with exciton confinement,” Phys. Status Solidi B 145, 567–577 (1988).
[CrossRef]

R. Perez-Alvarez and P. Pajon-Suarez, “Optical absorption coefficient in cylindrical quantum wells,” Phys. Status Solidi B 147, 547–552 (1988).
[CrossRef]

Rep. Prog. Phys. (1)

R. Ruppin and R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
[CrossRef]

Solid State Commun. (2)

T. Mita, K. Sotome, and M. Ueta, “Exciton spatial dispersion determined through the two-photon Raman scattering via excitonic molecule state at large wave vectors in CuCl,” Solid State Commun. 33, 1135–1138 (1980).
[CrossRef]

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

Sov. Phys. JETP (2)

A. I. Ekimov, A. A. Onushchenko, A. G. Plyukhin, and Al. L. Efros, “Size quantization of excitons and determination of the parameters of their energy spectrum in CuCl,” Sov. Phys. JETP 61, 891–897 (1985).

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

Sov. Phys. Semicond. (1)

Al. L. Efros and A. L. Efros, “Interband absorption of light in a semiconductor sphere,” Sov. Phys. Semicond. 16, 772–775 (1982).

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

E. L. Ivchenko, “Spatial dispersion effects in the exciton resonance region,” in Excitons, E. I. Rashba and M. D. Sturge, eds. (North-Holland, Amsterdam, 1982).

H. Heinrich, G. Bauer, and F. Kucher, eds., Physics and Technology of Submicron Structures (Springer-Verlag, Berlin, 1988).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Calculated extinction width of a CuCl cylinder of radius 100 Å. The upper curves are for E || z and the lower ones for Ez. The dashed curves show the results of the local theory.

Fig. 2
Fig. 2

Calculated extinction width of a CuCl cylinder of radius 30 Å. The upper curves are for E || z and the lower ones for Ez. The dashed curves show the results of the local theory.

Fig. 3
Fig. 3

Calculated extinction width of a CuCl cylinder of radius 60 Å, with γ = 0.002ωT (solid curves) and γ = 0.001ωT (dashed curves). The upper curves are for E || z and the lower ones for Ez.

Fig. 4
Fig. 4

Size dependence of the main excitonic peak of CuCl cylinders: (a) E || z, (b) Ez.

Fig. 5
Fig. 5

Calculated extinction width of a CuCl cylinder of radius 30 Å in a medium with m = 2.36. The upper curve is for E || z and the lower one for Ez.

Equations (35)

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

( ω , k ) = 0 + ω p 2 ω T 2 + D k 2 - ω 2 - i γ ω .
P ( a ) = 0 ,
M n = × [ a ^ z Z n ( k r ) exp ( i n θ ) ] ,
N n = ( 1 / k ) × M n ,
L n = [ Z n ( k r ) exp ( i n θ ) ] ,
E i = a ^ z exp ( i k 0 x ) = ( 1 / k 0 ) n = - i n N n ( k 0 r ) ,
H i = - a ^ y m exp ( i k 0 x ) = - i ( m / k 0 ) n = - i n M n ( k 0 r ) .
E t = n = - i n [ c n k t 1 N n ( k t 1 r ) + d n k t 2 N n ( k t 2 r ) ] ,
H t = - i ( m / k 0 ) n = - i n [ c n M n ( k t 1 r ) + d n M n ( k t 2 r ) ] .
E s = ( 1 / k 0 ) n = - i n b n N n ( k 0 r ) ,
H s = - i ( m / k 0 ) n = - i n b n M n ( k 0 r ) .
c n J n ( k t 1 a ) + d n J n ( k t 2 a ) = b n H n ( k 0 a ) + J n ( k 0 a ) ,
c n t 1 J n ( k t 1 a ) + d n t 2 J n ( k t 2 a ) = b n m H n ( k 0 a ) + m J n ( k 0 a ) ,
c n ( t 1 - 0 ) J n ( k t 1 a ) + d n ( t 2 - 0 ) J n ( k t 2 a ) = 0.
b n = - R n / S n ,
R n = J n ( k 0 a ) [ ( t 1 - 0 ) t 2 J n ( k t 1 a ) J n ( k t 2 a ) - ( t 2 - 0 ) t 1 J n ( k t 1 a ) J n ( k t 2 a ) ] + m J n ( k 0 a ) J n ( k t 1 a ) J n ( k t 2 a ) ( t 2 - t 1 ) ,
S n = H n ( k 0 a ) [ ( t 1 - 0 ) t 2 J n ( k t 1 a ) J n ( k t 2 a ) - ( t 2 - 0 ) t 1 J n ( k t 1 a ) J n ( k t 2 a ) ] + m H n ( k 0 a ) J n ( k t 1 a ) J n ( k t 2 a ) ( t 2 - t 1 ) .
C e = - ( 2 / k 0 a ) n = - Re b n .
E i = a ^ y exp ( i k 0 x ) = ( i / k 0 ) n = - i n M n ( k 0 r ) ,
H i = a ^ z m exp ( i k 0 x ) = ( m / k 0 ) n = - i n N n ( k 0 r ) .
E t = i n = - i n [ f n k t 1 M n ( k t 1 r ) + g n k t 2 M n ( k t 2 r ) ] ,
H t = ( m / k 0 ) n = - i n [ f n N n ( k t 1 r ) + g n N n ( k t 2 r ) ] .
E l = ( i / k 0 ) n = - i n h n L n ( k l r ) .
E s = ( i / k 0 ) n = - i n a n M n ( k 0 r ) ,
H s = ( m / k 0 ) n = - i n a n N n ( k 0 r ) .
f n J n ( k t 1 a ) + g n J n ( k t 2 a ) - h n ( i n / k 0 a ) J n ( k l a ) = a n H n ( k 0 a ) + J n ( k 0 a ) ,
f n k t 1 J n ( k t 1 a ) + g n k t 2 J n ( k t 2 a ) = a n k 0 H n ( k 0 a ) + k 0 J n ( k 0 a ) .
f n ( t 1 - 0 ) J n ( k t 1 a ) + g n ( t 2 - 0 ) J n ( k t 2 a ) + h n ( i n 0 / k 0 a ) J n ( k l a ) = 0 ,
f n ( t 1 - 0 ) ( i n / k t 1 a ) J n ( k t 1 a ) + g n ( t 2 - 0 ) ( i n / k t 2 a ) J n ( k t 2 a ) - h n 0 ( k l / k 0 ) J n ( k l a ) = 0.
a n = - P n / Q n ,
P n = α n J n ( k 0 a ) - β n J n ( k 0 a ) ,
Q n = α n H n ( k 0 a ) - β n H n ( k 0 a ) ,
α n = ( k t 1 / k 0 ) ( t 2 - 0 ) 0 J n ( k t 1 a ) [ J n ( k t 2 a ) ( k l / k 0 ) J n ( k l a ) - ( n 2 / k t 2 a ) J n ( k t 2 a ) J n ( k l a ) / k 0 a ] - ( k t 2 / k 0 ) ( t 1 - 0 ) 0 J n ( k t 2 a ) [ J n ( k t 1 a ) ( k l / k 0 ) J n ( k l a ) - ( n 2 / k t 1 a ) J n ( k t 1 a ) J n ( k l a ) / k 0 a ] ,
β n = ( t 2 - 0 ) 0 J n ( k t 1 a ) [ ( k l / k 0 ) J n ( k t 2 a ) J n ( k l a ) - ( n 2 / k t 2 a ) J n ( k t 2 a ) J n ( k l a ) / k 0 a ] - ( t 1 - 0 ) 0 J n ( k t 2 a ) [ ( k l / k 0 ) J n ( k t 1 a ) J n ( k l a ) - ( n 2 / k t 1 a ) J n ( k t 1 a ) J n ( k l a ) / k 0 a ] - ( n 2 / k 0 a ) ( t 1 - 0 ) ( t 2 - 0 ) J n ( k l a ) [ J n ( k t 1 a ) J n ( k t 2 a ) / k t 2 a - J n ( k t 2 a ) J n ( k t 1 a ) / k t 1 a ] .
C e = - ( 2 / k 0 a ) n = - Re a n .

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