Abstract

We study multiple scattering of light by particles embedded in an absorbing host medium using a recently developed single-scattering and vector radiative-transfer methodology directly based on the Maxwell equations. The first-principles results are compared with those rendered by the conventional heuristic approach according to which the single-scattering properties of particles can be computed by assuming that the host medium is nonabsorbing. Our analysis shows that the conventional approach yields very accurate results in the case of aerosol and cloud particles suspended in an absorbing gaseous atmosphere. In the case of air bubbles in water, the traditional approach can cause large relative errors in reflectance, but only when strong absorption in the host medium makes the resulting reflectance very small. The corresponding polarization errors are substantially smaller.

© 2019 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  2. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).
  3. J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
    [Crossref]
  4. V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, 1975).
  5. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  6. H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, 1980), Vols. 1 and 2.
  7. R. G. Newton, Scattering Theory of Waves and Particles (Springer, 1982).
  8. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  9. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).
  10. R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis (Oxford, 1989).
  11. E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).
  12. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).
  13. K. N. Liou, An Introduction to Atmospheric Radiation (Academic, 2002).
  14. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  15. J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres– Basic Concepts and Practical Methods (Springer, 2004).
  16. A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).
  17. P. A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Cambridge University, 2006).
  18. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).
  19. F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles. Theory and Applications to Environmental Physics (Springer, 2007).
  20. M. Wendisch and P. Yang, Theory of Atmospheric Radiative Transfer (Wiley-VCH, 2012).
  21. M. I. Mishchenko, Electromagnetic Scattering by Particles and Particle Groups: An Introduction (Cambridge University, 2014).
  22. G. Kristensson, Scattering of Electromagnetic Waves by Obstacles (Scitech Publishing, 2016).
  23. K.-N. Liou and P. Yang, Light Scattering by Ice Crystals: Fundamentals and Applications (Cambridge, 2016).
  24. G. Gouesbet and G. Gréhan, Generalized Lorenz—Mie Theories (Springer, 2017).
  25. M. Loewen, “Inside whitecaps,” Nature 418, 830 (2002).
    [Crossref]
  26. G. H. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-μm wavelength region,” Appl. Opt. 12, 555–563 (1973).
    [Crossref]
  27. S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
    [Crossref]
  28. J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).
  29. W. C. Mundy, J. A. Roux, and A. M. Smith, “Mie scattering by spheres in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
    [Crossref]
  30. P. Chýlek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977).
    [Crossref]
  31. C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
    [Crossref]
  32. P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
    [Crossref]
  33. M. Quinten and J. Rostalski, “Lorenz—Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
    [Crossref]
  34. A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
    [Crossref]
  35. W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
    [Crossref]
  36. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
    [Crossref]
  37. P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
    [Crossref]
  38. G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42, 6724–6727(2003).
    [Crossref]
  39. W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
    [Crossref]
  40. Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
    [Crossref]
  41. J. Randrianalisoa, D. Baillis, and L. Pilon, “Modeling radiation characteristics of semitransparent media containing bubbles or particles,” J. Opt. Soc. Am. A 23, 1645–1656 (2006).
    [Crossref]
  42. J. Yin and L. Pilon, “Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium,” J. Opt. Soc. Am. A 23, 2784–2796 (2006).
    [Crossref]
  43. J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz—Mie theory,” ACM Trans. Graph. 26, 60 (2007).
    [Crossref]
  44. S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, “Light scattering by a random distribution of particles embedded in absorbing media: diagrammatic expansion of the extinction coefficient,” J. Opt. Soc. Am. A 24, 2943–2952 (2007).
    [Crossref]
  45. S. Durant, O. Calvo-Perez, N. Vukadinovic, and J.-J. Greffet, “Light scattering by a random distribution of particles embedded in absorbing media: full-wave Monte Carlo solutions of the extinction coefficient,” J. Opt. Soc. Am. A 24, 2953–2962 (2007).
    [Crossref]
  46. L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell House, 2010).
  47. R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.
  48. B. Aernouts, R. Watté, R. van Beers, F. Delport, M. Merchiers, J. de Block, J. Lammertyn, and W. Saeys, “Flexible tool for simulating the bulk optical properties of polydisperse spherical particles in an absorbing host: experimental validation,” Opt. Express 22, 20223–20238 (2014).
    [Crossref]
  49. L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
    [Crossref]
  50. M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15, 13188–13202 (2007).
    [Crossref]
  51. M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16, 2288–2301 (2008).
    [Crossref]
  52. M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2386–2390 (2008).
    [Crossref]
  53. M. I. Mishchenko and P. Yang, “Far-field Lorenz—Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
    [Crossref]
  54. M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
    [Crossref]
  55. M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42, 4873–4876 (2017).
    [Crossref]
  56. M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
    [Crossref]
  57. M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
    [Crossref]
  58. J. Lenoble, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (A. Deepak Publishing, 1985).
  59. K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
    [Crossref]
  60. M. I. Mishchenko, D. Goldstein, J. Chowdhary, and A. Lompado, “Radiative transfer theory verified by controlled laboratory experiments,” Opt. Lett. 38, 3522–3525 (2013).
    [Crossref]

2019 (1)

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

2018 (3)

M. I. Mishchenko and P. Yang, “Far-field Lorenz—Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

2017 (1)

2015 (1)

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

2014 (1)

2013 (1)

2012 (1)

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

2008 (3)

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16, 2288–2301 (2008).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2386–2390 (2008).
[Crossref]

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

2007 (4)

2006 (3)

2004 (1)

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[Crossref]

2003 (1)

2002 (2)

2001 (2)

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[Crossref]

1999 (1)

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

1996 (1)

M. Quinten and J. Rostalski, “Lorenz—Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[Crossref]

1993 (1)

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
[Crossref]

1979 (1)

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[Crossref]

1977 (1)

1974 (2)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

W. C. Mundy, J. A. Roux, and A. M. Smith, “Mie scattering by spheres in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974).
[Crossref]

1973 (1)

Aernouts, B.

Baillis, D.

Baum, B. A.

Berg, M. J.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.

Biscans, B.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.

Bohren, C. F.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[Crossref]

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

Borghese, F.

F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles. Theory and Applications to Environmental Physics (Springer, 2007).

Brandt, R. E.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
[Crossref]

Calvo-Perez, O.

Ceolato, R.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.

Chowdhary, J.

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

M. I. Mishchenko, D. Goldstein, J. Chowdhary, and A. Lompado, “Radiative transfer theory verified by controlled laboratory experiments,” Opt. Lett. 38, 3522–3525 (2013).
[Crossref]

Christensen, N. J.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz—Mie theory,” ACM Trans. Graph. 26, 60 (2007).
[Crossref]

Chylek, P.

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
[Crossref]

Chýlek, P.

de Block, J.

Delport, F.

Denti, P.

F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles. Theory and Applications to Environmental Physics (Springer, 2007).

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

Doicu, A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Dombrovsky, L. A.

L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell House, 2010).

Domke, H.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres– Basic Concepts and Practical Methods (Springer, 2004).

Durant, S.

Eremin, Y. A.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Frisvad, J. R.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz—Mie theory,” ACM Trans. Graph. 26, 60 (2007).
[Crossref]

Fu, Q.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[Crossref]

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[Crossref]

Gao, B.-C.

Gilra, D. P.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[Crossref]

Goldstein, D.

Goody, R. M.

R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis (Oxford, 1989).

Gouesbet, G.

G. Gouesbet and G. Gréhan, Generalized Lorenz—Mie Theories (Springer, 2017).

Gratz, M.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

Greffet, J.-J.

Gréhan, G.

G. Gouesbet and G. Gréhan, Generalized Lorenz—Mie Theories (Springer, 2017).

Hale, G. H.

Hansen, J. E.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Hovenier, J. W.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres– Basic Concepts and Practical Methods (Springer, 2004).

Hu, Y. X.

Huang, H.-L.

Huffman, D. R.

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

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Ismaelli, A.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
[Crossref]

Jensen, H. W.

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz—Mie theory,” ACM Trans. Graph. 26, 60 (2007).
[Crossref]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

Kong, J. A.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Kreibig, U.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

Kristensson, G.

G. Kristensson, Scattering of Electromagnetic Waves by Obstacles (Scitech Publishing, 2016).

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

Lammertyn, J.

Lebedev, A. N.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

Lenoble, J.

J. Lenoble, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (A. Deepak Publishing, 1985).

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, 2002).

Liou, K.-N.

K.-N. Liou and P. Yang, Light Scattering by Ice Crystals: Fundamentals and Applications (Cambridge, 2016).

Liu, L. H.

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

Lock, J. A.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

Loeb, N. G.

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[Crossref]

Loewen, M.

M. Loewen, “Inside whitecaps,” Nature 418, 830 (2002).
[Crossref]

Lompado, A.

Ma, L. X.

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

Martin, P. A.

P. A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Cambridge University, 2006).

Merchiers, M.

Mishchenko, M. I.

M. I. Mishchenko and P. Yang, “Far-field Lorenz—Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42, 4873–4876 (2017).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

M. I. Mishchenko, D. Goldstein, J. Chowdhary, and A. Lompado, “Radiative transfer theory verified by controlled laboratory experiments,” Opt. Lett. 38, 3522–3525 (2013).
[Crossref]

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2386–2390 (2008).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 1. Foldy-Lax equations, order-of-scattering expansion, and coherent field,” Opt. Express 16, 2288–2301 (2008).
[Crossref]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15, 13188–13202 (2007).
[Crossref]

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[Crossref]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, Electromagnetic Scattering by Particles and Particle Groups: An Introduction (Cambridge University, 2014).

Muinonen, K.

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

Mundy, W. C.

Newton, R. G.

R. G. Newton, Scattering Theory of Waves and Particles (Springer, 1982).

Park, S. K.

Penttilä, A.

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

Pilon, L.

Platnick, S. E.

Querry, M. R.

Quinten, M.

M. Quinten and J. Rostalski, “Lorenz—Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[Crossref]

Randrianalisoa, J.

Riviere, N.

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.

Rostalski, J.

M. Quinten and J. Rostalski, “Lorenz—Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[Crossref]

Roux, J. A.

Saeys, W.

Saija, R.

F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles. Theory and Applications to Environmental Physics (Springer, 2007).

Shin, R. T.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Smith, A. M.

Sobolev, V. V.

V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, 1975).

Stenzel, O.

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

Stratton, J. A.

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

Sudiarta, W.

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[Crossref]

W. Sudiarta and P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001).
[Crossref]

Sun, W.

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[Crossref]

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[Crossref]

G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42, 6724–6727(2003).
[Crossref]

Travis, L. D.

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

Tsang, L.

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

Tsay, S.-C.

van Beers, R.

van de Hulst, H. C.

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

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, 1980), Vols. 1 and 2.

van der Mee, C.

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres– Basic Concepts and Practical Methods (Springer, 2004).

Videen, G.

M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42, 4873–4876 (2017).
[Crossref]

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

G. Videen and W. Sun, “Yet another look at light scattering from particles in absorbing media,” Appl. Opt. 42, 6724–6727(2003).
[Crossref]

Vukadinovic, N.

Wang, C. C.

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

Warren, S. G.

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

Watté, R.

Wendisch, M.

M. Wendisch and P. Yang, Theory of Atmospheric Radiative Transfer (Wiley-VCH, 2012).

Winker, D. M.

Wiscombe, W. J.

Wriedt, T.

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

Xie, B. W.

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

Yang, P.

M. I. Mishchenko and P. Yang, “Far-field Lorenz—Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42, 4873–4876 (2017).
[Crossref]

P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, and S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002).
[Crossref]

M. Wendisch and P. Yang, Theory of Atmospheric Radiative Transfer (Wiley-VCH, 2012).

K.-N. Liou and P. Yang, Light Scattering by Ice Crystals: Fundamentals and Applications (Cambridge, 2016).

Yanovitskij, E. G.

E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).

Yin, J.

Yung, Y. L.

R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis (Oxford, 1989).

Yurkin, M. A.

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

Zaccanti, G.

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
[Crossref]

Zakharova, N. T.

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

Zubko, E.

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

ACM Trans. Graph. (1)

J. R. Frisvad, N. J. Christensen, and H. W. Jensen, “Computing the scattering properties of participating media using Lorenz—Mie theory,” ACM Trans. Graph. 26, 60 (2007).
[Crossref]

Appl. Opt. (3)

Astrophys. J. (1)

K. Muinonen, M. I. Mishchenko, J. M. Dlugach, E. Zubko, A. Penttilä, and G. Videen, “Coherent backscattering verified numerically for a finite volume of spherical particles,” Astrophys. J. 760, 118 (2012).
[Crossref]

Eur. Phys. J. D (1)

A. N. Lebedev, M. Gratz, U. Kreibig, and O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–369(1999).
[Crossref]

J. Colloid Interface Sci. (1)

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979).
[Crossref]

J. Geophys. Res. (1)

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113, D14220 (2008).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Quant. Spectrosc. Radiat. Transfer (9)

W. Sun, N. G. Loeb, and Q. Fu, “Light scattering by a coated sphere immersed in absorbing medium: a comparison between the FDTD and analytic solutions,” J. Quant. Spectrosc. Radiat. Transfer 83, 483–492 (2004).
[Crossref]

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100, 137–142 (2006).
[Crossref]

W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001).
[Crossref]

L. X. Ma, B. W. Xie, C. C. Wang, and L. H. Liu, “Radiative transfer in dispersed media: considering the effect of host medium absorption on particle scattering,” J. Quant. Spectrosc. Radiat. Transfer 230, 24–35 (2019).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2386–2390 (2008).
[Crossref]

M. I. Mishchenko and P. Yang, “Far-field Lorenz—Mie scattering in an absorbing host medium: theoretical formalism and FORTRAN program,” J. Quant. Spectrosc. Radiat. Transfer 205, 241–252 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. A. Lock, and M. A. Yurkin, “Far-field Lorenz—Mie scattering in an absorbing host medium. II: Improved stability of the numerical algorithm,” J. Quant. Spectrosc. Radiat. Transfer 217, 274–277 (2018).
[Crossref]

M. I. Mishchenko and J. M. Dlugach, “Scattering and extinction by spherical particles immersed in an absorbing host medium,” J. Quant. Spectrosc. Radiat. Transfer 211, 179–187 (2018).
[Crossref]

M. I. Mishchenko, J. M. Dlugach, J. Chowdhary, and N. T. Zakharova, “Polarized bidirectional reflectance of optically thick sparse particulate layers: an efficient numerically exact radiative-transfer solution,” J. Quant. Spectrosc. Radiat. Transfer 156, 97–108 (2015).
[Crossref]

Nature (1)

M. Loewen, “Inside whitecaps,” Nature 418, 830 (2002).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Part. Part. Syst. Charact. (1)

M. Quinten and J. Rostalski, “Lorenz—Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996).
[Crossref]

Space Sci. Rev. (1)

J. E. Hansen and L. D. Travis, “Light scattering in planetary atmospheres,” Space Sci. Rev. 16, 527–610 (1974).
[Crossref]

Waves Random Media (1)

P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, “A note on the definition of scattering cross sections and phase functions for spheres immersed in an absorbing medium,” Waves Random Media 3, 147–156 (1993).
[Crossref]

Other (27)

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

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

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969).

J. Lenoble, Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures (A. Deepak Publishing, 1985).

V. V. Sobolev, Light Scattering in Planetary Atmospheres (Pergamon, 1975).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, 1980), Vols. 1 and 2.

R. G. Newton, Scattering Theory of Waves and Particles (Springer, 1982).

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

L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).

R. M. Goody and Y. L. Yung, Atmospheric Radiation: Theoretical Basis (Oxford, 1989).

E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds., Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications (Academic, 2000).

K. N. Liou, An Introduction to Atmospheric Radiation (Academic, 2002).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

J. W. Hovenier, C. van der Mee, and H. Domke, Transfer of Polarized Light in Planetary Atmospheres– Basic Concepts and Practical Methods (Springer, 2004).

A. Doicu, T. Wriedt, and Y. A. Eremin, Light Scattering by Systems of Particles (Springer, 2006).

P. A. Martin, Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (Cambridge University, 2006).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University, 2006).

F. Borghese, P. Denti, and R. Saija, Scattering from Model Nonspherical Particles. Theory and Applications to Environmental Physics (Springer, 2007).

M. Wendisch and P. Yang, Theory of Atmospheric Radiative Transfer (Wiley-VCH, 2012).

M. I. Mishchenko, Electromagnetic Scattering by Particles and Particle Groups: An Introduction (Cambridge University, 2014).

G. Kristensson, Scattering of Electromagnetic Waves by Obstacles (Scitech Publishing, 2016).

K.-N. Liou and P. Yang, Light Scattering by Ice Crystals: Fundamentals and Applications (Cambridge, 2016).

G. Gouesbet and G. Gréhan, Generalized Lorenz—Mie Theories (Springer, 2017).

L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (Begell House, 2010).

R. Ceolato, N. Riviere, M. J. Berg, and B. Biscans, “Electromagnetic scattering from aggregates embedded in absorbing media,” in Progress In Electromagnetics Research Symposium Proceedings, Taipei (2013), pp. 717–721.

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Figures (4)

Fig. 1.
Fig. 1. Scattering geometry. A laterally infinite particulate layer is confined to the space between the two imaginary horizontal planes. The layer is illuminated from above by a plane electromagnetic wave.
Fig. 2.
Fig. 2. Single-scattering phase function (upper panels) and the degree of linear polarization (lower panels) computed for model 3 using schemes A (red curves) and B (blue curves). At the three shorter wavelengths listed in Table 5, the scheme A and B results (not shown) are virtually indistinguishable.
Fig. 3.
Fig. 3. Reflection coefficient for model 3 computed using schemes A and B. The results are shown for six wavelengths and two values of the particle volume fraction. The scheme A and B results in the upper three panels are virtually indistinguishable.
Fig. 4.
Fig. 4. Degree of linear polarization P ( μ ) (%) for model 3 computed using schemes A and B. The results are shown for six wavelengths and two values of the particle volume fraction. Scheme B results are shown only for λ = 3.3 μm , since at other wavelengths, they are hardly distinguishable from the respective scheme A results.

Tables (6)

Tables Icon

Table 1. Optical Properties of Model 1 According to Scheme A

Tables Icon

Table 2. Optical Properties of Model 1 According to Scheme B

Tables Icon

Table 3. Optical Properties of Model 2 According to Scheme A

Tables Icon

Table 4. Optical Properties of Model 2 According to Scheme B

Tables Icon

Table 5. Optical Properties of Model 3

Tables Icon

Table 6. Effective Single-Scattering Albedo of Model 3

Equations (15)

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

k 1 = k 1 + i k 1
k 2 = k 2 + i k 2 ,
m 1 = m 1 + i m 1
m 2 = m 2 + i m 2 .
k 1 = 2 π m 1 λ = 2 π m 1 λ + i 2 π m 1 λ
k 2 = 2 π m 2 λ = 2 π m 2 λ + i 2 π m 2 λ .
T host = 2 Z k 1 = 4 π Z m 1 λ .
k 1 = T host 2 Z
m 1 = T host λ 4 π Z .
T = T host + T particles ,
T particles = Z n 0 C ext
ϖ eff = C sca eff 2 n 0 1 k 1 + C ext ,
I ˜ = 1 π μ 0 R ( μ , μ 0 , ϕ , ϕ 0 ) I ,
F ( Θ ) = [ F 11 ( Θ ) F 21 ( Θ ) 0 0 F 21 ( Θ ) F 11 ( Θ ) 0 0 0 0 F 33 ( Θ ) F 34 ( Θ ) 0 0 F 34 ( Θ ) F 33 ( Θ ) ] ,
P ( μ ) = R 21 ( μ , μ 0 = 1 , ϕ = 0 , ϕ 0 = 0 ) R 11 ( μ , μ 0 = 1 , ϕ = 0 , ϕ 0 = 0 ) .

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