Abstract

Analytic expressions for the time-averaged electromagnetic energy within a dispersive and absorbing sphere on which a plane wave is incident are derived. Numerical results are presented for diatomic ionic crystal spheres and for metallic, nearly free-electron-like spheres. It is found that the stored energy exhibits resonant enhancement near resonances of the sphere’s extinction cross section. In the Rayleigh region the energy increase at resonance may amount to more than three orders of magnitude. The energy formula is applied to the calculation of the energy transport velocity in a disordered medium containing dispersive spheres.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  4. R. Loudon, “The propagation of electromagnetic energy through an absorbing dielectric,” J. Phys. A 3, 233–245 (1970).
    [CrossRef]
  5. G. Mie, “Beitrag zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
    [CrossRef]
  6. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
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    [CrossRef]
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    [CrossRef]
  9. R. Ruppin, R. Englman, “Optical phonons of small crystals,” Rep. Prog. Phys. 33, 149–196 (1970).
    [CrossRef]
  10. H. Fröhlich, Theory of Dielectrics (Clarendon, Oxford, 1949).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1993 (1)

Y. Kuga, A. Ishimaru, D. Rice, “Velocity of coherent and incoherent electromagnetic waves in a dense strongly scattering medium,” Phys. Rev. B 48, 13155–13158 (1993).
[CrossRef]

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)

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]

1968 (1)

1967 (1)

1960 (1)

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

1908 (1)

G. Mie, “Beitrag zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Arakawa, E. T.

Bilz, H.

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

Bott, A.

Englman, R.

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

Fröhlich, H.

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

Fuchs, R.

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]

Ishimaru, A.

Y. Kuga, A. Ishimaru, D. Rice, “Velocity of coherent and incoherent electromagnetic waves in a dense strongly scattering medium,” Phys. Rev. B 48, 13155–13158 (1993).
[CrossRef]

Kliewer, K. L.

Kuga, Y.

Y. Kuga, A. Ishimaru, D. Rice, “Velocity of coherent and incoherent electromagnetic waves in a dense strongly scattering medium,” Phys. Rev. B 48, 13155–13158 (1993).
[CrossRef]

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]

Mie, G.

G. Mie, “Beitrag zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Rice, D.

Y. Kuga, A. Ishimaru, D. Rice, “Velocity of coherent and incoherent electromagnetic waves in a dense strongly scattering medium,” Phys. Rev. B 48, 13155–13158 (1993).
[CrossRef]

Ruppin, R.

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

Zdunkowski, W.

Ann. Phys. (1)

G. Mie, “Beitrag zur Optik truber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Phys. A (1)

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

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]

Y. Kuga, A. Ishimaru, D. Rice, “Velocity of coherent and incoherent electromagnetic waves in a dense strongly scattering medium,” Phys. Rev. B 48, 13155–13158 (1993).
[CrossRef]

Phys. Rev. Lett. (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]

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 (3)

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

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

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

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Figures (7)

Fig. 1
Fig. 1

Normalized electromagnetic energy inside a NaCl sphere of radius 1 µm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 2
Fig. 2

Extinction cross section, in units of the geometric cross section, of a NaCl sphere of radius 1 µm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 3
Fig. 3

Normalized electromagnetic energy inside a NaCl sphere of radius 5 µm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 4
Fig. 4

Extinction cross section, in units of the geometric cross section, of a NaCl sphere of radius 5 µm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 5
Fig. 5

Normalized electromagnetic energy inside a Na sphere of radius 30 nm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 6
Fig. 6

Extinction cross section, in units of the geometric cross section, of a Na sphere of radius 30 nm, for M=1 (solid curve) and M=2.31 (dashed curve).

Fig. 7
Fig. 7

Normalized energy transport velocity in a medium containing NaCl spheres of radius 5 µm, at a volume fraction f=0.05, with M=1 (solid curve) and M=2.31 (dashed curve).

Equations (16)

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U¯=14(0|E|2+μμ0|H|2)
=+i,
(ω)=+0-1-(ω/ωT)2-i(Γ/ωT)(ω/ωT),
(ω)=1-ωp2ω(ω+iΓ),
U¯=140+2ωΓ|E|2+μ0|H|2.
Et=E0 exp(-iωt)n=1in 2n+1n(n+1)×(antM01n(1)-ibntNe1n(1)),
Ht=-k1ωμ0E0 exp(-iωt)n=1in 2n+1n(n+1)×(bntMe1n(1)+iantNo1n(1)),
W=140π02π0a0+2ωΓ|Et|2+μ0|Ht|2r2 sin θdθdϕdr.
W=34W0n=1 2n+1y2-y*2αnAn*y-Any*+βnAn*y*-Any,
An=[yjn(y)]yjn(y),
W0=23πa3E02M0,
αn=1M+2 ωΓ|y[jn(x)+anhn(x)]|2+M|x[jn(x)+bnhn(x)]|2,
βn=1M+2 ωΓ|x[jn(x)+bnhn(x)]|2+M|y[jn(x)+anhn(x)]|2,
an=-jn(y)[xjn(x)]-jn(x)[yjn(y)]jn(y)[xhn(x)]-hn(x)[yjn(y)],
bn=-Mjn(x)[yjn(y)]-jn(y)[xjn(x)]Mhn(x)[yjn(y)]-jn(y)[xhn(x)].
vE=cfWW0-1+1,

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