Abstract

A geometrical optics approximation was used for calculations of inelastic (Raman and fluorescent) scattering on particles with large size parameters. The inelastic part of the radiation was obtained by use of the principle of ray reversibility. The technique presented simplifies the computations and provides a geometric interpretation of how far-field patterns can be calculated by use of the internal field distributions. The numerical results for homogeneous spherical particles are compared with the classic dipole solution.

© 1999 Optical Society of America

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References

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  1. G. Schweiger, “Raman scattering on single aerosol particles and on flowing aerosols: a review,” J. Aerosol Sci. 21, 483–509 (1990).
    [CrossRef]
  2. 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]
  3. 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. 68, 1686–1689 (1978).
    [CrossRef]
  4. M. Kerker, P. J. McNulty, M. Sculley, H. Chew, D. D. Cooke, “Raman and fluorescent scattering by molecules embedded in small particles: numerical results for incoherent optical processes,” J. Opt. Soc. Am. 68, 1676–1686 (1978).
    [CrossRef]
  5. M. Kerker, S. D. Druger, “Raman and fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979).
    [CrossRef] [PubMed]
  6. H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 440–444 (1976).
    [CrossRef]
  7. H. Chew, D. D. Cooke, M. Kerker, “Raman and fluorescent scattering by molecules embedded in dielectric cylinders,” Appl. Opt. 19, 44–52 (1980).
    [CrossRef] [PubMed]
  8. D. S. Wang, M. Kerker, H. Chew, “Raman and fluorescent scattering by molecules embedded in dielectric spheroids,” Appl. Opt. 19, 2315–2328 (1980).
    [CrossRef] [PubMed]
  9. M. Seaver, J. R. Peele, “Noncontact fluorescence thermometry of acoustically levitated water drops,” Appl. Opt. 29, 4956–4961 (1990).
    [CrossRef] [PubMed]
  10. A. S. Kwok, C. F. Wood, R. K. Chang, “Fluorescence imaging of CO2 laser-heated droplets,” Opt. Lett. 15, 664–666 (1990).
    [CrossRef] [PubMed]
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  12. A. Ungut, G. Grehan, G. Gouesbet, “Comparisons between geometrical optics and Lorenz–Mie theory,” Appl. Opt. 20, 2911–2918 (1981).
    [CrossRef] [PubMed]
  13. W. J. Glantschnig, S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
    [CrossRef] [PubMed]
  14. E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
    [CrossRef] [PubMed]
  15. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection,” Appl. Opt. 35, 500–514 (1996).
    [CrossRef] [PubMed]
  16. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects,” Appl. Opt. 35, 515–531 (1996).
    [CrossRef] [PubMed]
  17. K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
    [CrossRef]
  18. J. A. Lock, E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
    [CrossRef]
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    [CrossRef] [PubMed]
  20. M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometrical optics,” Appl. Opt. 28, 4962–4965 (1989).
    [CrossRef] [PubMed]
  21. D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
    [CrossRef] [PubMed]
  22. N. Velesco, T. Kaiser, G. Schweiger, “Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation,” Appl. Opt. 36, 8724–8728 (1997).
    [CrossRef]
  23. G. Roll, T. Kaiser, S. Lange, G. Schweiger, “Ray interpretation of multipole fields in spherical cavities,” J. Opt. Soc. Am. A 15, 2879–2891 (1998).
    [CrossRef]
  24. J. Zhang, D. R. Alexander “Hybrid inelastic-scattering models for particle thermometry: unpolarized emissions,” Appl. Opt. 31, 7132–7139 (1992).
    [CrossRef] [PubMed]
  25. J. Zhang, D. R. Alexander “Hybrid inelastic-scattering models for particle thermometry: polarized emissions,” Appl. Opt. 31, 7140–7146 (1992).
    [CrossRef] [PubMed]
  26. S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
    [CrossRef] [PubMed]
  27. S. C. Hill, G. Videen, J. D. Pendleton, “Reciprocity method for obtaining the far fields generated by a source inside or near a microparticle,” J. Opt. Soc. Am. B 14, 2522–2529 (1997).
    [CrossRef]
  28. W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 20–28 and Chap. 7.
  29. E. Hecht, Optics (Addison-Wesley, New York, 1987).
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    [CrossRef]
  31. J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
    [CrossRef]
  32. I. Hartmann, M. Lankers, J. Popp, M. Trunk, E. Urlaub, W. Kiefer, “Simulation of morphology-dependent resonances in the Raman spectra of optically levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
    [CrossRef]
  33. G. Schweiger, “Observation of input and output structure resonances in the Raman spectrum of a single spheroid dielectric microparticle,” Opt. Lett. 15, 156–158 (1990).
    [CrossRef] [PubMed]

1998 (1)

1997 (4)

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

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

S. C. Hill, G. Videen, J. D. Pendleton, “Reciprocity method for obtaining the far fields generated by a source inside or near a microparticle,” J. Opt. Soc. Am. B 14, 2522–2529 (1997).
[CrossRef]

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

1996 (4)

1992 (3)

1991 (4)

1990 (4)

1989 (1)

1981 (2)

1980 (2)

1979 (1)

1978 (2)

1976 (2)

H. Chew, M. Kerker, P. J. McNulty, “Raman and fluorescent scattering by molecules embedded in concentric spheres,” J. Opt. Soc. Am. 66, 440–444 (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]

Alexander, D. R.

Barber, P. W.

Barnes, M. D.

Chang, R. K.

Chen, S. H.

Chew, H.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 20–28 and Chap. 7.

Chowdhury, D. Q.

Cooke, D. D.

Druger, S. D.

Fast, P.

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Glantschnig, W. J.

Gouesbet, G.

Grehan, G.

Hartmann, I.

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

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

Hecht, E.

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

Hill, S. C.

Hovenac, E. A.

Jarzembski, M. A.

Kaiser, T.

Kerker, M.

Kiefer, W.

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

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

Kwok, A. S.

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 optically levitated microspheres,” J. Raman Spectrosc. 28, 547–550 (1997).
[CrossRef]

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

Lock, J. A.

Lumme, K.

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

McNulty, P. J.

Muinonen, K.

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Nousianen, T.

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Peele, J. R.

Peltoniemi, J. I.

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

Pendleton, J. D.

Popp, J.

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

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

Ramsey, J. M.

Roll, G.

Saleheen, H. I.

Schaschek, K.

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

Schweiger, G.

Sculley, M.

Seaver, M.

Srivastava, V.

Trunk, M.

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

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

Ungut, A.

Urlaub, E.

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

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Velesco, N.

Videen, G.

Wang, D. S.

Whitten, W. B.

Wood, C. F.

Zhang, J.

Appl. Opt. (15)

M. Kerker, S. D. Druger, “Raman and fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength,” Appl. Opt. 18, 1172–1179 (1979).
[CrossRef] [PubMed]

H. Chew, D. D. Cooke, M. Kerker, “Raman and fluorescent scattering by molecules embedded in dielectric cylinders,” Appl. Opt. 19, 44–52 (1980).
[CrossRef] [PubMed]

D. S. Wang, M. Kerker, H. Chew, “Raman and fluorescent scattering by molecules embedded in dielectric spheroids,” Appl. Opt. 19, 2315–2328 (1980).
[CrossRef] [PubMed]

W. J. Glantschnig, S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
[CrossRef] [PubMed]

M. A. Jarzembski, V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometrical optics,” Appl. Opt. 28, 4962–4965 (1989).
[CrossRef] [PubMed]

M. Seaver, J. R. Peele, “Noncontact fluorescence thermometry of acoustically levitated water drops,” Appl. Opt. 29, 4956–4961 (1990).
[CrossRef] [PubMed]

E. A. Hovenac, “Calculation of far-field scattering from nonspherical particles using a geometrical optics approach,” Appl. Opt. 30, 4739–4746 (1991).
[CrossRef] [PubMed]

D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

J. Zhang, D. R. Alexander “Hybrid inelastic-scattering models for particle thermometry: unpolarized emissions,” Appl. Opt. 31, 7132–7139 (1992).
[CrossRef] [PubMed]

J. Zhang, D. R. Alexander “Hybrid inelastic-scattering models for particle thermometry: polarized emissions,” Appl. Opt. 31, 7140–7146 (1992).
[CrossRef] [PubMed]

J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection,” Appl. Opt. 35, 500–514 (1996).
[CrossRef] [PubMed]

S. C. Hill, H. I. Saleheen, M. D. Barnes, W. B. Whitten, J. M. Ramsey, “Modeling fluorescence collection from single molecules in microspheres: effects of position, orientation, and frequency,” Appl. Opt. 35, 6278–6288 (1996).
[CrossRef] [PubMed]

A. Ungut, G. Grehan, G. Gouesbet, “Comparisons between geometrical optics and Lorenz–Mie theory,” Appl. Opt. 20, 2911–2918 (1981).
[CrossRef] [PubMed]

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

J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects,” Appl. Opt. 35, 515–531 (1996).
[CrossRef] [PubMed]

J. Aerosol Sci. (1)

G. Schweiger, “Raman scattering on single aerosol particles and on flowing aerosols: a review,” J. Aerosol Sci. 21, 483–509 (1990).
[CrossRef]

J. Opt. Soc. Am. (3)

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

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

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

K. Muinonen, T. Nousianen, P. Fast, K. Lumme, J. I. Peltoniemi, “Light scattering by Gaussian random particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transfer 55, 577–601 (1996).
[CrossRef]

J. Raman Spectrosc. (2)

J. Popp, M. Trunk, M. Lankers, I. Hartmann, K. Schaschek, W. Kiefer, “Observability of morphology-dependent output resonances in the Raman spectra of optically levitated microdroplets,” J. Raman Spectrosc. 28, 531–536 (1997).
[CrossRef]

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

Opt. Lett. (3)

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 (3)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

W. C. Chew, Waves and Fields in Inhomogeneous Media (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 20–28 and Chap. 7.

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

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Figures (9)

Fig. 1
Fig. 1

Geometric rays leaving the sphere after M = 0, 1, 2 internal reflections at the scattering angle θ = 180° corresponding to the incident rays propagating parallel to the positive z axis. The refractive index is 1.333.

Fig. 2
Fig. 2

Gray-level plots of the polarized scattering functions in the yz plane. The detector is centered on the -z axis (θ = 180°), n = 1.333, α = 1500, M = 0. (a) S XV , ART solution; (b) S XV , reversed ray tracing solution; (c) S YZ , ART solution; (d) S YZ , reversed ray tracing solution.

Fig. 3
Fig. 3

Inelastic scattering function S XV along the z axis. Comparison of analytical and reversed ray tracing for the case with no internal reflections, M = 0. The detector is centered on the -z axis (θ = 180°), n = 1.333, α = 1500.

Fig. 4
Fig. 4

Illustration of differences between the ART and the reversed ray tracing methods. In terms of ART one ray corresponds to a single point source. In the reversed ray tracing method several point sources correspond to a single ray.

Fig. 5
Fig. 5

Gray-level plots of the polarized scattering functions in the yz plane obtained by use of the reversed ray tracing method. n = 1.333, α = 1500, detector centered on the -z axis (θ = 180°). Ten internal reflections are enclosed in the calculations. (a) S XV , (b) S YZ .

Fig. 6
Fig. 6

P XV and P YH as functions of scattering angle θ calculated by use of the classic dipole model and the reversed ray tracing method. Excitation size parameter α1 = 30, emission size parameter α2 = 27. The refractive index is n = 1.333 for excitation and emission. Ten internal reflections are included in the calculations with the reversed ray tracing method.

Fig. 7
Fig. 7

P XV and P YH as functions of scattering angle θ calculated by use of the reversed ray tracing method. Excitation size parameter α1 = 500, emission size parameter α2 = 436. The refractive index is n = 1.333 for excitation and emission. Ten internal reflections are included in the calculations.

Fig. 8
Fig. 8

P XV and P YH as functions of scattering angle θ. Comparison of resonant and nonresonant cases. Excitation size parameters are for the nonresonant case α1 = 500, for the resonance TE508 24 α1 = 499.75819, and for the resonance TM512 23 α1 = 499.61039. The emission size parameter for all cases is α2 = 436. The refractive index is n = 1.333 for excitation and emission.

Fig. 9
Fig. 9

P XV as a function of scattering angle θ for the nonresonant case, the input resonance TE508 24, the output resonance TE443 21 (emission size parameter α2 = 435.79674), and the double resonance (input TE508 24–output TE443 21).

Equations (2)

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Pjiθ=V|JR·CR·ERji|2θdV,
SjiR=JR·eˆji2,

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