Abstract

For an assembly of small noninteracting ellipsoidal particles the effect of the shape distribution function on light absorption is considered. Possible determinations of the function parameters from experimental absorption spectra are analyzed. Some features of the problem are discussed that are characteristic of assemblies of dielectric and metal particles.

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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. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960).
  4. G. A. Baker, Jr., and P. Graves-Morris, “Pade approximants,” in Encyclopedia of Mathematics and Its Applications, G. C. Rota, ed. (Addison-Wesley, London, 1981), Vols. 13 and 14.
  5. H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
    [CrossRef]
  6. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379(1972).
    [CrossRef]
  7. P. Appel and A. Ljungbert, “Red shift of surface plasmons in small metal particles,” Solid State Commun. 44, 1367–1369(1982).
    [CrossRef]
  8. I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).
  9. L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
    [CrossRef]
  10. C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
    [CrossRef]
  11. W. A. Curtin and N. W. Ashcroft, “Theory of far-infrared absorption in small-metal-particle–insulator composites,” Phys. Rev. B 31, 3287–3295(1985).
    [CrossRef]
  12. P. M. Hui and D. Stroud, “Complex dielectric response of metal-particle clusters,” Phys. Rev. B 33, 2163–2169(1986).
    [CrossRef]

1986

P. M. Hui and D. Stroud, “Complex dielectric response of metal-particle clusters,” Phys. Rev. B 33, 2163–2169(1986).
[CrossRef]

1985

W. A. Curtin and N. W. Ashcroft, “Theory of far-infrared absorption in small-metal-particle–insulator composites,” Phys. Rev. B 31, 3287–3295(1985).
[CrossRef]

1982

P. Appel and A. Ljungbert, “Red shift of surface plasmons in small metal particles,” Solid State Commun. 44, 1367–1369(1982).
[CrossRef]

1976

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

1975

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379(1972).
[CrossRef]

1969

I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).

1963

H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
[CrossRef]

Appel, P.

P. Appel and A. Ljungbert, “Red shift of surface plasmons in small metal particles,” Solid State Commun. 44, 1367–1369(1982).
[CrossRef]

Ashcroft, N. W.

W. A. Curtin and N. W. Ashcroft, “Theory of far-infrared absorption in small-metal-particle–insulator composites,” Phys. Rev. B 31, 3287–3295(1985).
[CrossRef]

Buhrman, R. A.

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379(1972).
[CrossRef]

Curtin, W. A.

W. A. Curtin and N. W. Ashcroft, “Theory of far-infrared absorption in small-metal-particle–insulator composites,” Phys. Rev. B 31, 3287–3295(1985).
[CrossRef]

Ehrenreich, H.

H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
[CrossRef]

Genzel, L.

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
[CrossRef]

Granqvist, C.

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

Hui, P. M.

P. M. Hui and D. Stroud, “Complex dielectric response of metal-particle clusters,” Phys. Rev. B 33, 2163–2169(1986).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379(1972).
[CrossRef]

Korneeva, T. I.

I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).

Kreibig, U.

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
[CrossRef]

Ljungbert, A.

P. Appel and A. Ljungbert, “Red shift of surface plasmons in small metal particles,” Solid State Commun. 44, 1367–1369(1982).
[CrossRef]

Martin, T. P.

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
[CrossRef]

Philipp, H. R.

H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
[CrossRef]

Segall, B.

H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
[CrossRef]

Shklyarevskii, I. N.

I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).

Sievers, A. J.

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

Stroud, D.

P. M. Hui and D. Stroud, “Complex dielectric response of metal-particle clusters,” Phys. Rev. B 33, 2163–2169(1986).
[CrossRef]

Wyns, J.

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

Zozulya, K. N.

I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).

Opt. Spectrosc.

I. N. Shklyarevskii, T. I. Korneeva, and K. N. Zozulya, “Effective optical constants of thin granular silver films,” Opt. Spectrosc. 27, 174–176(1969).

Phys. Rev.

H. Ehrenreich, H. R. Philipp, and B. Segall, “Optical properties of aluminum,” Phys. Rev. 132, 1918–1928(1963).
[CrossRef]

Phys. Rev. B

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379(1972).
[CrossRef]

W. A. Curtin and N. W. Ashcroft, “Theory of far-infrared absorption in small-metal-particle–insulator composites,” Phys. Rev. B 31, 3287–3295(1985).
[CrossRef]

P. M. Hui and D. Stroud, “Complex dielectric response of metal-particle clusters,” Phys. Rev. B 33, 2163–2169(1986).
[CrossRef]

Phys. Rev. Lett.

C. Granqvist, R. A. Buhrman, J. Wyns, and A. J. Sievers, “Far-infrared absorption in ultrafine Al particles,” Phys. Rev. Lett. 37, 625–629(1976).
[CrossRef]

Solid State Commun.

P. Appel and A. Ljungbert, “Red shift of surface plasmons in small metal particles,” Solid State Commun. 44, 1367–1369(1982).
[CrossRef]

Z. Phys. B

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Phys. B 21, 339–346(1975).
[CrossRef]

Other

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

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

R. V. Churchill, Complex Variables and Applications (McGraw-Hill, New York, 1960).

G. A. Baker, Jr., and P. Graves-Morris, “Pade approximants,” in Encyclopedia of Mathematics and Its Applications, G. C. Rota, ed. (Addison-Wesley, London, 1981), Vols. 13 and 14.

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Figures (4)

Fig. 1
Fig. 1

Domain of integration (striped triangle). The integration parameter Δ changes from zero (δ-type distribution of ellipsoids) to unity (uniform distribution).

Fig. 2
Fig. 2

Imaginary part of the nondimensional effective polarizability Im〈α〉 versus relative frequency ω̃. The parameter Δ of the ellipsoidal-shape distribution is 0, 0.1, 0.2, 0.4, 0.6, and 1.0 (for curves 1, 2, 3, 4, 5, and 6, respectively).

Fig. 3
Fig. 3

Normalized effective absorption cross section F versus Δ for the particles of a typical polar dielectric in the reststrahlen region. The approximations used are the following: relation (11), curves 1, 1; Eq. (12), n=1, curves 2, 2; Eq. (12), n=2, curves 3, 3. The Lorentz oscillator parameters are =10, ωLT=1.1, and Γ˜=0.002 (curves 1–3) and 0.02 (curves 1–3). The numerical integration results are shown by open (Γ˜=0.002) and filled (Γ˜=0.02) circles.

Fig. 4
Fig. 4

Function G=Cabs(ωF)/Cabsmax versus Δ for the aluminum particles. The approximation used is relation (11) (solid curve). The numerical integration results are shown by filled circles.

Equations (15)

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γabs=NCabs=NkVIma,
Cabs(m)=13kV Imi=13 -11+Li(-1),
Cabs=Cabs(m)P(L1,L2)dL1dL2.
P(L1,L2)dL1dL2=1.
P(L1,L2)=PΔ=2Δ-2χ(L1-1/3+1/3Δ)×χ(L2-1/3+1/3Δ)×χ(-L1+1/3+2/3Δ)×χ(-L2+1/3+2/3Δ),
Cabs=kVIm(α)=23Δ2kVIm1/3(1-Δ)1/3(1+2Δ)dL11/3(1-Δ)1-L1dL2×j=12-11+Lj(-1)+-11+(1-L1-L2)(-1).
α=2Δ2(A+1/3+2/3Δ)lnA+1/3+2/3ΔA+1/3-1/3Δ-Δ,
Cabs=2Δ2kVIm(A+1/3+2/3Δ)×lnA+1/3+2/3ΔA+1/3-1/3Δ,
Im(α)=2Δ212A2 ln(z12+z22)+(A1+1/3+2/3Δ)×πχ(-z1)sgn(z2)+arctanz2z1,
Im()=21=Re().
A1Δ-13, or 1(ωmax)=Δ+2Δ-1.
1(ωmax)=Δ+2-1+C1Δ++CnΔn.
F(Δ)=Cabsmax(Δ)Cabsmax(0)=19Cabsmax(Δ)kV2(ωF),
G(Δ)=Cabs(ω=ωF)(Δ)Cabsmax(Δ)
P(L1,L2)=C(σ)exp[σL1(L1-1)]-1×exp[σL2(L2-1)]-1×exp[σ(L1+L2-1)(L1+L2)]-1

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