Abstract

The investigation of particles with inclusions is of high interest in many parts of scientific research. Raman scattering is very good at yielding information on the internal composition of the particle. We use a geometrical-optics-based technique to determine the angle dependence of the inelastic scattering on particles with several spherical inclusions.

© 2005 Optical Society of America

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References

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  1. P. Chýlek, V. Ramaswamy, R. J. Cheng, “Effect of graphitic carbon on the albedo of clouds,” J. Atmos. Sci. 41, 3076–3084 (1984).
    [CrossRef]
  2. P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
    [CrossRef]
  3. A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
    [CrossRef]
  4. P. M.A. Sloot, C. G. Figdor, “Elastic light scattering from nucleated blood cells: rapid numerical analysis,” Appl. Opt. 25, 3559–3565 (1986).
    [CrossRef] [PubMed]
  5. S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. Pan, J. Bottiger, B. V. Bronk, S. Holler, R. K. Chang, “Flourescence from airborne microparticles: dependence on size, concentration of flourophores, and illumination intensity,” Appl. Opt. 40, 3005–3013 (2001)
    [CrossRef]
  6. H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
    [CrossRef]
  7. H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
    [CrossRef]
  8. H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
    [CrossRef]
  9. J. Schulte, G. Schweiger, “Inelastic scattering on spherical microparticles with inclusions,” J. Opt. Soc. Am. A 18, 117–123 (2001).
    [CrossRef]
  10. I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
  15. N. Velesco, G. Schweiger, “Geometrical optics calculation of inelastic scattering on large particles,” Appl. Opt. 38, 1046–1052 (1999).
    [CrossRef]
  16. T. Weigel, J. Schulte, G. Schweiger, “Inelastic scattering on nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 89, 365–369 (2004).
    [CrossRef]
  17. E. Hecht, Optics (Addison-Wesley, New York, 1987).
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    [CrossRef]
  19. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975)

2004 (1)

T. Weigel, J. Schulte, G. Schweiger, “Inelastic scattering on nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 89, 365–369 (2004).
[CrossRef]

2001 (2)

2000 (1)

1999 (1)

1997 (2)

N. Velesco, T. Kaiser, G. Schweiger, “Computation of the internal field of a large spherical particle by using geometrical optics approximation,” Appl. Opt. 36, 8724–8728 (1997).
[CrossRef]

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

1996 (2)

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
[CrossRef]

1994 (1)

1992 (2)

1986 (1)

1984 (1)

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

1976 (3)

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
[CrossRef]

H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

Alexander, D.

Barton, J. B.

Bottiger, J.

Bronk, B. V.

Cairns, B.

A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
[CrossRef]

Chang, R. K.

Cheng, R. J.

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

Chew, H.

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
[CrossRef]

H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

Chýlek, P.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

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

Cooke, D. D.

Fell, N. F.

Figdor, C. G.

Hartmann, I.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, New York, 1987).

Hill, S. C.

Holler, S.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975)

Kaiser, T.

Kerker, M.

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

Kiefer, W.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Klett, J. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Lange, S.

Lankers, M.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Lesins, G. B.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Macke, A.

A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
[CrossRef]

McNulty, P. J.

H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
[CrossRef]

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Mishchenko, M. I.

A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
[CrossRef]

Ngo, D.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Niles, S.

Pan, Y.

Pinnick, R. G.

S. C. Hill, R. G. Pinnick, S. Niles, N. F. Fell, Y. Pan, J. Bottiger, B. V. Bronk, S. Holler, R. K. Chang, “Flourescence from airborne microparticles: dependence on size, concentration of flourophores, and illumination intensity,” Appl. Opt. 40, 3005–3013 (2001)
[CrossRef]

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Popp, J.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Ramaswamy, V.

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

Schulte, J.

T. Weigel, J. Schulte, G. Schweiger, “Inelastic scattering on nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 89, 365–369 (2004).
[CrossRef]

J. Schulte, G. Schweiger, “Inelastic scattering on spherical microparticles with inclusions,” J. Opt. Soc. Am. A 18, 117–123 (2001).
[CrossRef]

Schweiger, G.

Sculley, M.

Sloot, P. M.A.

Trunk, M.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Urlaub, E.

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Velesco, N.

Videen, G.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Weigel, T.

T. Weigel, J. Schulte, G. Schweiger, “Inelastic scattering on nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 89, 365–369 (2004).
[CrossRef]

Wong, J. G.D.

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

Zhang, J.

Appl. Opt. (6)

J. Atmos. Sci. (1)

P. Chýlek, 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. (2)

P. Chýlek, G. B. Lesins, G. Videen, J. G.D. Wong, R. G. Pinnick, D. Ngo, J. D. Klett, “Black carbon and absorption of solar radiation by clouds,” J. Geophys. Res. 101, 23,365–23,317 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, B. Cairns, “The influence of inclusions on light scattering by large ice particles,” J. Geophys. Res. 101, 23,311–23,316 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 1676–1686 (1976).
[CrossRef]

H. Chew, M. Sculley, M. Kerker, P. J. McNulty, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: results for coherent optical processes,” J. Opt. Soc. Am. 66, 440–444 (1976).
[CrossRef]

J. Opt. Soc. Am. A (2)

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

J. Quant. Spectrosc. Radiat. Transf. (1)

T. Weigel, J. Schulte, G. Schweiger, “Inelastic scattering on nonspherical particles,” J. Quant. Spectrosc. Radiat. Transf. 89, 365–369 (2004).
[CrossRef]

J. Raman Spectrosc. (1)

I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optical levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

Phys. Rev. A (1)

H. Chew, P. J. McNulty, M. Kerker, “Model for Raman and fluorescent scattering by molecules embedded in small particles,” Phys. Rev. A 13, 396–404 (1976).
[CrossRef]

Other (2)

E. Hecht, Optics (Addison-Wesley, New York, 1987).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975)

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Figures (7)

Fig. 1
Fig. 1

Path of rays for a particle ( n P = 1.5 ) with one inclusion ( n inc = 1.9 ) .

Fig. 2
Fig. 2

Weighting of the RRT field; see Eq. (4).

Fig. 3
Fig. 3

Particle ( x P = 100 , n P = 1.333 ) with one spherical inclusion x inc = 30 , n inc = 1.5 . Distance from the center of the host particle is 0.6 × r P (logarithmic scaling). (a) Inclusion in the front, (b) inclusion in the back.

Fig. 4
Fig. 4

Particle ( n P = 1.333 , x P = 500 ) with seven spherical inclusions ( r inc = 0.1 × r P , n inc = 1.5 ) . (a) Inclusions along the z axis, (b) inclusions perpendicular to the z axis.

Fig. 5
Fig. 5

Inelastic scattering of a particle with one inclusion, rotated about the y axis (perpendicular to the plane of detection). x P = 1000 , x P , inel = 948.55 , n P = 1.333 , r inc = 0.3 × r P . Distance between inclusion and center of the particle is 0.6 × r P , n inc = 1.5 . (For the explanation of the white arrows, please read text).

Fig. 6
Fig. 6

Inelastic scattering on a particle ( n P = 1.333 , x P = 500 , x P , inel = 422.825 ) with seven inclusions ( r inc = 0.1 × r P , n inc = 1.5 ) arranged along the z axis.

Fig. 7
Fig. 7

Inelastic scattering on a particle ( n P = 1.333 , x P = 500 , x P , inel = 422.825 ) with seven inclusions ( r inc = 0.1 × r P ) arranged along the x axis.

Equations (5)

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

p = α E inc .
P l m ( σ ) = V Part [ I ( σ , r ) C ( r ) E ( r ) 2 ] σ d V ,
P inel ( σ ) k inel 4 rays , i dipoles , j E i RRT ( r j , σ ) w i j 2 ,
w i j = e RRT , i p j = p j cos ( E i RRT , p j )
e RRT , i = E i RRT E i RRT

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