Abstract

The electromagnetic energy stored inside a cylinder, which is irradiated by an electromagnetic plane wave, is calculated analytically. In view of their differing energy density functions, dispersive and nondispersive cylinders are treated separately. Numerical results show that the stored energy exhibits resonant enhancement near the extinction resonances of the cylinder. An application to the calculation of the transport velocity in a two-dimensional disordered medium is presented.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of fluorescence induced by microstructure resonances of a dielectric fiber,” Phys. Rev. Lett. 47, 1075–1078 (1981).
    [CrossRef]
  4. A. Bott, W. Zdunkowski, “Electromagnetic energy within dielectric spheres,” J. Opt. Soc. Am. A 4, 1361–1365 (1987).
    [CrossRef]
  5. R. Ruppin, “Electromagnetic energy in dispersive spheres,” J. Opt. Soc. Am. A 15, 524–527 (1998).
    [CrossRef]
  6. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  7. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
    [CrossRef]
  8. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  9. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  10. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  11. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1952).
  12. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
    [CrossRef]
  13. R. Ruppin, R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
    [CrossRef]
  14. K. L. Kliewer, R. Fuchs, “Theory of dynamical properties of dielectric surfaces,” in Advances in Chemical Physics, 1st ed., I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1974), pp. 355–541.
  15. R. Ruppin, “Spherical and cylindrical surface polaritons in solids,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, N.Y., 1982), Chap. 9.
  16. H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
    [CrossRef]
  17. J. C. Sutherland, E. T. Arakawa, R. N. Hamm, “Optical properties of sodium in the vacuum ultraviolet,” J. Opt. Soc. Am. 57, 645–650 (1967).
    [CrossRef]
  18. M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
    [CrossRef] [PubMed]
  19. B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
    [CrossRef]
  20. K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
    [CrossRef]

1998 (1)

1995 (1)

K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
[CrossRef]

1993 (1)

1992 (1)

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

1991 (1)

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

1987 (1)

1981 (3)

1970 (2)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

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

1967 (1)

1960 (1)

H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
[CrossRef]

Arakawa, E. T.

Barber, P. W.

Bilz, H.

H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
[CrossRef]

Bohren, C. F.

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

Bott, A.

Busch, K.

K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
[CrossRef]

Chang, R. K.

Dorain, P. B.

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of fluorescence induced by microstructure resonances of a dielectric fiber,” Phys. Rev. Lett. 47, 1075–1078 (1981).
[CrossRef]

Economou, E. N.

K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
[CrossRef]

Englman, R.

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

Fuchs, R.

K. L. Kliewer, R. Fuchs, “Theory of dynamical properties of dielectric surfaces,” in Advances in Chemical Physics, 1st ed., I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1974), pp. 355–541.

Genzel, L.

H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
[CrossRef]

Hamm, R. N.

Happ, M.

H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
[CrossRef]

Huffman, D. R.

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

Johnson, B. R.

Kerker, M.

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

Kliewer, K. L.

K. L. Kliewer, R. Fuchs, “Theory of dynamical properties of dielectric surfaces,” in Advances in Chemical Physics, 1st ed., I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1974), pp. 355–541.

Lagendijk, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

Messinger, B. J.

Owen, J. F.

Ruppin, R.

R. Ruppin, “Electromagnetic energy in dispersive spheres,” J. Opt. Soc. Am. A 15, 524–527 (1998).
[CrossRef]

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

R. Ruppin, “Spherical and cylindrical surface polaritons in solids,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, N.Y., 1982), Chap. 9.

Soukoulis, C. M.

K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
[CrossRef]

Stratton, J. A.

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

Sutherland, J. C.

Tip, A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

van Albada, M. P.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

van de Hulst, H. C.

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

van Tiggelen, B. A.

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

Watson, G. N.

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1952).

Zdunkowski, W.

J. Opt. Soc. Am. (1)

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

J. Phys. A (1)

R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

B. A. van Tiggelen, A. Lagendijk, M. P. van Albada, A. Tip, “Speed of light in random media,” Phys. Rev. B 45, 12233–12243 (1992).
[CrossRef]

K. Busch, C. M. Soukoulis, E. N. Economou, “Transport velocity in two-dimensional random media,” Phys. Rev. B 52, 10834–10840 (1995).
[CrossRef]

Phys. Rev. Lett. (2)

M. P. van Albada, B. A. van Tiggelen, A. Lagendijk, A. Tip, “Speed of propagation of classical waves in strongly scattering media,” Phys. Rev. Lett. 66, 3132–3135 (1991).
[CrossRef] [PubMed]

J. F. Owen, P. W. Barber, P. B. Dorain, R. K. Chang, “Enhancement of fluorescence induced by microstructure resonances of a dielectric fiber,” Phys. Rev. Lett. 47, 1075–1078 (1981).
[CrossRef]

Rep. Prog. Phys. (1)

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

Z. Phys. (1)

H. Bilz, L. Genzel, M. Happ, “Zur Ultrarotdispersion der Alkali-Halogenide,” Z. Phys. 160, 535–553 (1960).
[CrossRef]

Other (7)

K. L. Kliewer, R. Fuchs, “Theory of dynamical properties of dielectric surfaces,” in Advances in Chemical Physics, 1st ed., I. Prigogine, S. A. Rice, eds. (Wiley, New York, 1974), pp. 355–541.

R. Ruppin, “Spherical and cylindrical surface polaritons in solids,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, Chichester, N.Y., 1982), Chap. 9.

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

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

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

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

G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1952).

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Figures (8)

Fig. 1
Fig. 1

Normalized electromagnetic energy inside a cylinder with =5 in a medium with m=1, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Fig. 2
Fig. 2

Normalized electromagnetic energy inside a NaCl cylinder of radius 0.1 µm, in a medium with m=1, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Fig. 3
Fig. 3

Extinction width (in units of the geometric width) of a NaCl cylinder of radius 0.1 µm, in a medium with m=1, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Fig. 4
Fig. 4

Normalized electromagnetic energy inside a NaCl cylinder of radius 5 µm, in a medium with m=1, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Fig. 5
Fig. 5

Extinction width (in units of the geometric width) of a NaCl cylinder of radius 5 µm, in a medium with m=1, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Fig. 6
Fig. 6

Normalized electromagnetic energy inside a sodium cylinder in a medium with m=1, for perpendicular polarization, and for cylinder radii of 10 nm (solid curve), 30 nm (dashed curve), and 70 nm (dotted curve).

Fig. 7
Fig. 7

Extinction width (in units of the geometric width) of a sodium cylinder in a medium with m=1, for perpendicular polarization, and for cylinder radii of 10 nm (solid curve), 30 nm (dashed curve), and 70 nm (dotted curve).

Fig. 8
Fig. 8

Normalized energy-transport velocity in a medium containing cylinders with =5, at a volume fraction f=0.2, for perpendicular polarization (solid curve) and parallel polarization (dashed curve).

Equations (35)

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U¯=14(0|E|2+μμ0|H|2)
=+i,
(ω)=+0-1-ωωT2-iΓωTωωT,
(ω)=1-ωp2ω(ω+iΓ),
U¯=140+2ωΓ|E|2+μ0|H|2.
Mn=curl[aˆzZn(kr)exp(inθ)],
Nn=(1/k)curl Mn,
Et=(E0/k1)n=-incnNn(k1r),
Ht=-i(E0/ηk1)n=-incnMn(k1r),
cn=[Jn(x)+bnHn(x)]/Jn(y),
bn=-Jn(y)Jn(x)-mJn(y)Jn(x)Jn(y)Hn(x)-mJn(y)Hn(x).
IE=0R02π|Et|2rdrdθ,
IH=0R02π|Ht|2rdrdθ.
IE=2πE02n=-|cn|20R|Jn(k1r)|2rdr.
IE=2πR2E02S1II,
S1II=n=-|cn|2y2-y*2[y*Jn(y)Jn(y*)-yJn(y*)Jn(y)].
IH=πE02||/η2n=-|cn|20R[|Jn-1(k1r)|2+|Jn+1(k1r)|2]rdr.
IH=2πR2E02(||/η2)S2II,
S2II=n=- |cn|2y2-y*2[yIn(y)Jn(y*)-y*Jn(y*)Jn(y)].
W=W0[(/m)S1II+(||/m)S2II],
W0=(π/2)R2E02m0
S1II=n=-|cn|22y2[y2Jn2(y)+(y2-n2)Jn2(y)],
S2II=n=-|cn|22y2[2yJn(y)Jn(y)+y2Jn2(y)+(y2-n2)Jn2(y)].
W=W0{[(/m)+(2ω/mΓ)]S1II+(||/m)S2II}.
Et=i(E0/k1)n=-indnMn(k1r),
Ht=i(E0/ηk1r)n=-indnNn(k1r),
dn=[Jn(x)+anHn(x)]/Jn(y)
an=-Jn(y)Jn(x)-mJn(y)Jn(x)Jn(y)Hn(x)-mJn(y)Hn(x).
IE=2πR2E02S2,
IH=2πR2E02(||/η2)S1,
W=W0[(/m)S2+(||/m)S1],
W=W0{[(/m)+(2ω/mΓ)]S2+(||/m)S1}.
CE=-2k0Rn=- Re bn,
CE=-2k0Rn=- Re an
vE=c/[f(W/W0-1)+1],

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