Abstract

The radiative properties of aerosol–soot mixtures, both internal and external, are determined in the visible and near-infrared bands by use of exact indirect mode-matching solutions to electromagnetic-wave scattering from a sphere with an eccentric spherical inclusion and from a cluster of spheres. Spherical sulfate droplets are assumed to represent aerosol particles. Soot particles are represented by volume-equivalent carbon spheres, the size distribution of which is obtained from the number distribution of the primary carbon particles that aggregate into soot grains. The mean gram-specific absorption cross section and the mean albedo of aerosol–soot mixtures are obtained by integration of the corresponding characteristics of composite sulfate–carbon particles over the size range of carbon spheres. Enhanced absorption of light by soot in aerosol–soot mixtures, a result of lensing by sulfate droplets, is highlighted by maps of the electromagnetic field in a sulfate–carbon particle.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Horvath, “Atmospheric light absorption—a review,” Atmos. Environ. Part A 27, 293–317 (1993).
    [CrossRef]
  2. R. A. Dobbins, C. M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991).
    [CrossRef] [PubMed]
  3. D. W. Mackowski, “Electrostatics analysis of radiative absorption by sphere clusters in the Rayleigh limit: application to soot particles,” Appl. Opt. 34, 3535–3545 (1995).
    [CrossRef] [PubMed]
  4. C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
    [CrossRef] [PubMed]
  5. C. W. Bruce, T. F. Stromberg, K. P. Gurton, J. B. Mozer, “Trans-spectral absorption and scattering of electromagnetic radiation by diesel soot,” Appl. Opt. 30, 1537–1546 (1991).
    [CrossRef] [PubMed]
  6. G. S. Kent, G. K. Yue, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 laser wavelengths. 1. Aerosol properties, modeling techniques, and associated problems,” Appl. Opt. 22, 1655–1665 (1983).
    [CrossRef]
  7. G. S. Kent, G. K. Yue, “The modeling of CO2 lidar backscatter from stratospheric aerosols,” J. Geophys. Res. 96, 5279–5292 (1991).
    [CrossRef]
  8. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A. 12, 881–892 (1995).
    [CrossRef]
  9. T. P. Ackerman, O. B. Toon, “Absorption of visible radiation in atmosphere containing mixtures of absorbing and nonabsorbing particles,” Appl. Opt. 20, 3661–3668 (1981).
    [CrossRef] [PubMed]
  10. G. L. Stephens, S. C. Tsay, “On the cloud absorption anomaly,” Q. J. R. Meteorol. Soc. 116, 671–704 (1990).
    [CrossRef]
  11. P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
    [CrossRef]
  12. N. C. Skaropoulos, M. P. Ioannidou, D. P. Chrissoulidis, “Indirect mode-matching solution to scattering from a dielectric sphere with an eccentric inclusion,” J. Opt. Soc. Am. A 11, 1859–1866 (1994).
    [CrossRef]
  13. M. P. Ioannidou, N. C. Skaropoulos, D. P. Chrissoulidis, “Study of interactive scattering by clusters of spheres,” J. Opt. Soc. Am. A 12, 1782–1789 (1995).
    [CrossRef]
  14. M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972).
  15. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE Press, New York, 1987).
    [CrossRef]
  16. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980).
  17. P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).
  18. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
  19. S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).
  20. O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).
  21. J. D. Kanellopoulos, J. G. Fikioris, “Resonant frequencies in an electromagnetic eccentric spherical cavity,” Q. Appl. Math. 37, 51–66 (1979).
  22. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  23. K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995).
    [CrossRef]
  24. G. K. Yue, G. S. Kent, U. O. Farrukh, A. Deepak, “Modeling atmospheric aerosol backscatter at CO2 laser wavelengths. 3. Effects of changes in wavelength and ambient conditions,” Appl. Opt. 22, 1671–1678 (1983).
    [CrossRef]

1995

1994

1993

H. Horvath, “Atmospheric light absorption—a review,” Atmos. Environ. Part A 27, 293–317 (1993).
[CrossRef]

1992

1991

1990

G. L. Stephens, S. C. Tsay, “On the cloud absorption anomaly,” Q. J. R. Meteorol. Soc. 116, 671–704 (1990).
[CrossRef]

1984

P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
[CrossRef]

1983

1981

1979

J. D. Kanellopoulos, J. G. Fikioris, “Resonant frequencies in an electromagnetic eccentric spherical cavity,” Q. Appl. Math. 37, 51–66 (1979).

1962

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

1961

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Ackerman, T. P.

Bruce, C. W.

Cai, J.

Cheng, R. J.

P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
[CrossRef]

Chrissoulidis, D. P.

Chylek, P.

P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
[CrossRef]

Cruzan, O. R.

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE Press, New York, 1987).
[CrossRef]

Deepak, A.

Dobbins, R. A.

Farrukh, U. O.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).

Fikioris, J. G.

J. D. Kanellopoulos, J. G. Fikioris, “Resonant frequencies in an electromagnetic eccentric spherical cavity,” Q. Appl. Math. 37, 51–66 (1979).

Fuller, K. A.

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. III. Spheres containing arbitrarily located spherical inhomogeneities,” J. Opt. Soc. Am. A 12, 893–904 (1995).
[CrossRef]

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A. 12, 881–892 (1995).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980).

Gurton, K. P.

Horvath, H.

H. Horvath, “Atmospheric light absorption—a review,” Atmos. Environ. Part A 27, 293–317 (1993).
[CrossRef]

Ioannidou, M. P.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Kanellopoulos, J. D.

J. D. Kanellopoulos, J. G. Fikioris, “Resonant frequencies in an electromagnetic eccentric spherical cavity,” Q. Appl. Math. 37, 51–66 (1979).

Kent, G. S.

Lu, N.

Mackowski, D. W.

Megaridis, C. M.

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).

Mozer, J. B.

Ramaswamy, V.

P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
[CrossRef]

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE Press, New York, 1987).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980).

Skaropoulos, N. C.

Sorensen, C. M.

Stein, S.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

Stephens, G. L.

G. L. Stephens, S. C. Tsay, “On the cloud absorption anomaly,” Q. J. R. Meteorol. Soc. 116, 671–704 (1990).
[CrossRef]

Stratton, J. A.

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

Stromberg, T. F.

Toon, O. B.

Tsay, S. C.

G. L. Stephens, S. C. Tsay, “On the cloud absorption anomaly,” Q. J. R. Meteorol. Soc. 116, 671–704 (1990).
[CrossRef]

Yue, G. K.

Appl. Opt.

Atmos. Environ. Part A

H. Horvath, “Atmospheric light absorption—a review,” Atmos. Environ. Part A 27, 293–317 (1993).
[CrossRef]

J. Atmos. Sci.

P. Chylek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
[CrossRef]

J. Geophys. Res.

G. S. Kent, G. K. Yue, “The modeling of CO2 lidar backscatter from stratospheric aerosols,” J. Geophys. Res. 96, 5279–5292 (1991).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. A.

K. A. Fuller, “Scattering and absorption cross sections of compounded spheres. II. Calculations for external aggregation,” J. Opt. Soc. Am. A. 12, 881–892 (1995).
[CrossRef]

Q. Appl. Math.

S. Stein, “Addition theorems for spherical wave functions,” Q. Appl. Math. 19, 15–24 (1961).

O. R. Cruzan, “Translational addition theorems for spherical vector wave functions,” Q. Appl. Math. 20, 33–40 (1962).

J. D. Kanellopoulos, J. G. Fikioris, “Resonant frequencies in an electromagnetic eccentric spherical cavity,” Q. Appl. Math. 37, 51–66 (1979).

Q. J. R. Meteorol. Soc.

G. L. Stephens, S. C. Tsay, “On the cloud absorption anomaly,” Q. J. R. Meteorol. Soc. 116, 671–704 (1990).
[CrossRef]

Other

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972).

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (IEEE Press, New York, 1987).
[CrossRef]

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, San Diego, Calif., 1980).

P. M. Morse, H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953).

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Composite sulfate–carbon particle: (a) internal and (b) external mixtures.

Fig. 2
Fig. 2

Internal aerosol–soot mixture: mean gram-specific absorption cross section 〈A a 〉 [m2/gr] against the wavelength λ [µm] of incident light (ϑinc = 0°, 90°, 180°).

Fig. 3
Fig. 3

Internal aerosol-soot mixture: mean gram-specific absorption cross section 〈A a 〉 [m2/gr] against (a) the angle of incidence θinc [°] and (b) the normalized eccentricity k 0 d (λ = 0.55 µm; ϑinc = 0°, 90°, 180°).

Fig. 4
Fig. 4

External aerosol–soot mixture: mean gram-specific absorption cross section 〈A a 〉 [m2/gr] against (a) the angle of incidence θinc [°] and (b) the normalized center-to-center separation k 0 d (λ = 0.55 µm; ϑinc = 0°, 90°, 180°).

Fig. 5
Fig. 5

(a) Internal and (b) external mixtures: mean albedo 〈W 0〉 against the wavelength λ [µm] of incident light (ϑinc = 0°, 90°, 180°).

Fig. 6
Fig. 6

Maps of normalized electric-field intensity |E/E inc| [dB] in the H plane of a composite sulfate–carbon particle. Incidence is from below the particle (λ = 0.55 µm; α1 = 0.25 µm; α2 = 〈αes〉 = 51.556 nm).

Tables (1)

Tables Icon

Table 1 Parameters of Log-Normal Number Density Distribution n(N)

Equations (31)

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

nN=1S0N13σg2πexp-12lnN/Ng3σg2.
1S0πx0xexp-x2dx=1,
S0=12erflnN/Ng32σgN=N0N=N,
nαes=nNdαes/dNN=αes/αp3.
nαes=1S0αes1σg2πexp- 12lnαes/αpNg1/3σg2,
αes=αes,0αes, αesnαesdαes=N0N αpN1/3nNdN.
αes=αpS013σg2πexp- 12ln Ng3σg2×x0xexp- x2-6σg2+2 ln Ngx18σg2dx,
αes=αp2S0exp12 σg2+13ln Ng×erf1213σglnN/Ng-σgN=N0N=N.
Eincr1=n=1m=-nn ξmnλmnιMmn1r1, k0-jμmnιNmn1r1, k0,
Escar1=n=1m=-nnamnιMmn3r1, k0+bmnιNmn3r1, k0,
Ecr2=n=1m=-nncmnιMmn1r2, k2+dmnιNmn1r2, k2,
Es r2=n=1m=-nnemnιMmn1r2, k1+fmnιMmn3r2, k1+gmnιNmn1r2, k1+hmnιNmn3r2, k1.
nξ-knλ-knιAkn,1klUn1,ik0, k1, α1-jξ-knμ-knιBkn,1klVn1,ik0, k1, α1+a-knιAkn,1klUn3,ik0, k1, α1+b-knιBkn,1klVn3,ik0, k1, α1=α2/α12c-klιUl1,ik2, k1, α2,
nξ-knλ-knιBkn,1klUn1,ik0, k1, α1-jξ-knμ-knιAkn,1klVn1,ik0, k1, α1+a-knιBkn,1klUn3,ik0, k1, α1+b-knιAkn,1klVn3,ik0, k1, α1=α2/α12d-klιVl1,ik2, k1, α2.
emnι=Un1,3k2, k1, α2Un1,3k1, k1, α2 cmnι,
fmnι=Un1,1k2, k1, α2Un3,1k1, k1, α2 cmnι,
gmnι=Vn1,3k2, k1, α2Vn1,3k1, k1, α2 dmnι,
hmnι=Vn1,1k2, k1, α2Vn3,1k1, k1, α2 dmnι.
Eincr1=n=1m=-nn ξmnλmn1ιMmn1r1, k0-jμmn1ιNmn1r1, k0,
Esca=n=1m=-nnamn1ιMmn3r1, k0+bmn1ιNmn3r1, k0+amn2ιMmn3r2, k0+bmn2ιNmn3r2, k0,
Esr1=n=1m=-nncmn1ιMmn1r1, k1+dmn1ιNmn1r1, k1,
Ecr2=n=1m=-nncmn2ιMmn1r2, k2+dmn2ιNmn1r2, k2.
Ul3,1k0, k1, α1Ul1,1k0, k1, α1 a-kl1ι+ξ-klλ-kl1ι=- n=1A-kl,3-kna-kn2ι+B-kl,3-knb-kn2ι,
Vl3,1k0, k1, α1Vl1,1k0, k1, α1 b-kl1ι-jξ-klμ-kl1ι=- n=1B-kl,3-kna-kn2ι+A-kl,3-knb-kn2ι,
Ul3,1k0, k2, α2Ul1,1k0, k2, α2 a-kl2ι+ξ-klλ-kl2ι=--1ln=1-1nA-kl,3-kna-kn1ι-B-kl,3-knb-kn1ι,
Vl3,1k0, k2, α2Vl1,1k0, k2, α2 b-kl2ι-jξ-klμ-kl2ι=-1ln=1-1nB-kl,3-kna-kn1ι-A-kl,3-knb-kn1ι.
cmnqι=Un1,3k0, k0, αqUn1,1k0, kq, αq amnqι,
dmnqι=Vn1,3k0, k0, αqVn1,1k0, kq, αq bmnqι,
fιiˆ, sˆ=1k0n=1m=-nn j-nmamnιPnmcos θsin θ+bmnιdPnmcos θdθθˆ+jmbmnιPnmcos θsin θ+amnιdPnmcos θdθϕˆexpjmϕ.
Aa=αes,0αes, Aaαesnαesdαes,
W0=αes,0αes, W0αesnαesdαes.

Metrics