Abstract

We use the volume integral equation formulation to consider frequency-domain electromagnetic scattering of a damped inhomogeneous plane wave by a particle immersed in an absorbing medium. We show that if absorption in the host medium is sufficiently weak and the particle size parameter is sufficiently small, then (i) the resulting formalism (including the far-field and radiative-transfer regimes) is largely the same as in the case of a nonabsorbing host medium, and (ii) one can bypass explicit use of sophisticated general solvers of the Maxwell equations applicable to inhomogeneous-wave illumination. These results offer dramatic simplifications for solving the scattering problem in a wide range of practical applications involving absorbing host media.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
  5. M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
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  6. 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(2), 365–369 (1999).
    [Crossref]
  7. I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4–6), 709–714 (2001).
    [Crossref]
  8. Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40(9), 1354–1361 (2001).
    [Crossref]
  9. 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(15), 2740–2759 (2002).
    [Crossref]
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  11. Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100(1–3), 137–142 (2006).
    [Crossref]
  12. J. Yin and L. Pilon, “Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium,” J. Opt. Soc. Am. A 23(11), 2784–2796 (2006).
    [Crossref]
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    [Crossref]
  14. 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(9), 2943–2952 (2007).
    [Crossref]
  15. 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(3), 60 (2007).
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    [Crossref]
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    [Crossref]
  20. 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]
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    [Crossref]
  24. M. I. Mishchenko, Electromagnetic Scattering by Particles and Particle Groups: An Introduction (Cambridge University, 2014).
  25. M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: rigorous derivation and analysis for a set of multi-layered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
    [Crossref]
  26. M. I. Mishchenko and M. A. Yurkin, “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial,” J. Quant. Spectrosc. Radiat. Transfer 214, 158–167 (2018).
    [Crossref]
  27. R. A. Chipman, W.-S. T. Lam, and G. Young, Polarized Light and Optical Systems (CRC Press, 2019).
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    [Crossref]
  29. 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]
  30. G. H. Hale and M. R. Querry, “Optical constants of water in the 200-nm to 200-µm wavelength region,” Appl. Opt. 12(3), 555–563 (1973).
    [Crossref]
  31. S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113(D14), D14220 (2008).
    [Crossref]
  32. G. V. Belokopytov and E. N. Vasil’ev, “Scattering of a plane inhomogeneous wave by a spherical particle,” Radiophys. Quantum Electron. 49(1), 65–73 (2006).
    [Crossref]
  33. J. R. Frisvad, “Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave,” J. Opt. Soc. Am. A 35(4), 669–680 (2018).
    [Crossref]
  34. B. T. Draine and P. J. Flatau, “Discrete dipole approximation for scattering cal­culations,” J. Opt. Soc. Am. A 11(4), 1491–1499 (1994).
    [Crossref]
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    [Crossref]
  36. M. I. Mishchenko and J. M. Dlugach, “Multiple scattering of polarized light by particles in an absorbing medium,” Appl. Opt. 58(18), 4871–4877 (2019).
    [Crossref]
  37. Lord Rayleigh, “On the light from the sky, its polarization and colour,” Phil. Mag. 41(271), 107–120 (1871).
    [Crossref]
  38. L. Rayleigh, “On the scattering of light by small particles,” Phil. Mag. 41(275), 447–454 (1871).
    [Crossref]
  39. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  40. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  41. G. Dassios and R. Kleinman, Low Frequency Scattering (Clarendon, 2000).

2019 (2)

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 and J. M. Dlugach, “Multiple scattering of polarized light by particles in an absorbing medium,” Appl. Opt. 58(18), 4871–4877 (2019).
[Crossref]

2018 (6)

J. R. Frisvad, “Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave,” J. Opt. Soc. Am. A 35(4), 669–680 (2018).
[Crossref]

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: rigorous derivation and analysis for a set of multi-layered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

M. I. Mishchenko and M. A. Yurkin, “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial,” J. Quant. Spectrosc. Radiat. Transfer 214, 158–167 (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 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 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)

2016 (1)

2008 (2)

S. G. Warren and R. E. Brandt, “Optical constants of ice from the ultraviolet to the microwave: a revised compilation,” J. Geophys. Res. 113(D14), D14220 (2008).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109(14), 2386–2390 (2008).
[Crossref]

2007 (4)

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an over­view and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 558–589 (2007).
[Crossref]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 13188–13202 (2007).
[Crossref]

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(9), 2943–2952 (2007).
[Crossref]

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(3), 60 (2007).
[Crossref]

2006 (3)

Q. Fu and W. Sun, “Apparent optical properties of spherical particles in absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 100(1–3), 137–142 (2006).
[Crossref]

J. Yin and L. Pilon, “Efficiency factors and radiation characteristics of spherical scatterers in an absorbing medium,” J. Opt. Soc. Am. A 23(11), 2784–2796 (2006).
[Crossref]

G. V. Belokopytov and E. N. Vasil’ev, “Scattering of a plane inhomogeneous wave by a spherical particle,” Radiophys. Quantum Electron. 49(1), 65–73 (2006).
[Crossref]

2003 (1)

2002 (1)

2001 (2)

I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4–6), 709–714 (2001).
[Crossref]

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40(9), 1354–1361 (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(2), 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(2), 89–96 (1996).
[Crossref]

1994 (1)

1980 (1)

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51(7), 3465–3485 (1980).
[Crossref]

1979 (1)

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

1977 (1)

1974 (1)

1973 (1)

1871 (2)

Lord Rayleigh, “On the light from the sky, its polarization and colour,” Phil. Mag. 41(271), 107–120 (1871).
[Crossref]

L. Rayleigh, “On the scattering of light by small particles,” Phil. Mag. 41(275), 447–454 (1871).
[Crossref]

Adler, R. B.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Baum, B. A.

Belokopytov, G. V.

G. V. Belokopytov and E. N. Vasil’ev, “Scattering of a plane inhomogeneous wave by a spherical particle,” Radiophys. Quantum Electron. 49(1), 65–73 (2006).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72(2), 215–221 (1979).
[Crossref]

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

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(D14), D14220 (2008).
[Crossref]

Calvo-Perez, O.

Chipman, R. A.

R. A. Chipman, W.-S. T. Lam, and G. Young, Polarized Light and Optical Systems (CRC Press, 2019).

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(3), 60 (2007).
[Crossref]

Chu, L. J.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Chylek, P.

I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4–6), 709–714 (2001).
[Crossref]

Chýlek, P.

Dassios, G.

G. Dassios and R. Kleinman, Low Frequency Scattering (Clarendon, 2000).

Dlugach, J. M.

M. I. Mishchenko and J. M. Dlugach, “Multiple scattering of polarized light by particles in an absorbing medium,” Appl. Opt. 58(18), 4871–4877 (2019).
[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]

Draine, B. T.

Durant, S.

Fano, R. M.

R. B. Adler, L. J. Chu, and R. M. Fano, Electromagnetic Energy Transmission and Radiation (Wiley, 1960).

Flatau, P. J.

Frezza, F.

Frisvad, J. R.

J. R. Frisvad, “Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave,” J. Opt. Soc. Am. A 35(4), 669–680 (2018).
[Crossref]

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(3), 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(1–3), 137–142 (2006).
[Crossref]

Q. Fu and W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40(9), 1354–1361 (2001).
[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(2), 215–221 (1979).
[Crossref]

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(2), 365–369 (1999).
[Crossref]

Greffet, J.-J.

Hale, G. H.

Hoekstra, A. G.

M. A. Yurkin and A. G. Hoekstra, “The discrete dipole approximation: an over­view and recent developments,” J. Quant. Spectrosc. Radiat. Transfer 106(1–3), 558–589 (2007).
[Crossref]

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).

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(3), 60 (2007).
[Crossref]

Jones, D. S.

D. S. Jones, The Theory of Electromagnetism (Pergamon, 1964).

Kleinman, R.

G. Dassios and R. Kleinman, Low Frequency Scattering (Clarendon, 2000).

Kong, J. A.

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51(7), 3465–3485 (1980).
[Crossref]

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(2), 365–369 (1999).
[Crossref]

Lam, W.-S. T.

R. A. Chipman, W.-S. T. Lam, and G. Young, Polarized Light and Optical Systems (CRC Press, 2019).

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(2), 365–369 (1999).
[Crossref]

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]

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]

Mangini, F.

Mishchenko, M. I.

M. I. Mishchenko and J. M. Dlugach, “Multiple scattering of polarized light by particles in an absorbing medium,” Appl. Opt. 58(18), 4871–4877 (2019).
[Crossref]

M. A. Yurkin and M. I. Mishchenko, “Volume integral equation for electromagnetic scattering: rigorous derivation and analysis for a set of multi-layered particles with piecewise-smooth boundaries in a passive host medium,” Phys. Rev. A 97(4), 043824 (2018).
[Crossref]

M. I. Mishchenko and M. A. Yurkin, “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial,” J. Quant. Spectrosc. Radiat. Transfer 214, 158–167 (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 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, G. Videen, and P. Yang, “Extinction by a homogeneous spherical particle in an absorbing medium,” Opt. Lett. 42(23), 4873–4876 (2017).
[Crossref]

M. I. Mishchenko, “Multiple scattering by particles embedded in an absorbing medium. 2. Radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109(14), 2386–2390 (2008).
[Crossref]

M. I. Mishchenko, “Electromagnetic scattering by a fixed finite object embedded in an absorbing medium,” Opt. Express 15(20), 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(15), 2740–2759 (2002).
[Crossref]

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

Mundy, W. C.

Park, S. K.

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(2), 89–96 (1996).
[Crossref]

Rayleigh, L.

L. Rayleigh, “On the scattering of light by small particles,” Phil. Mag. 41(275), 447–454 (1871).
[Crossref]

Rayleigh, Lord

Lord Rayleigh, “On the light from the sky, its polarization and colour,” Phil. Mag. 41(271), 107–120 (1871).
[Crossref]

Rostalski, J.

M. Quinten and J. Rostalski, “Lorenz–Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13(2), 89–96 (1996).
[Crossref]

Roux, J. A.

Smith, A. M.

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(2), 365–369 (1999).
[Crossref]

Stratton, J. A.

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

Sudiarta, I. W.

I. W. Sudiarta and P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70(4–6), 709–714 (2001).
[Crossref]

Sun, W.

Tsang, L.

L. Tsang and J. A. Kong, “Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism,” J. Appl. Phys. 51(7), 3465–3485 (1980).
[Crossref]

Tsay, S.-C.

van de Hulst, H. C.

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

Vasil’ev, E. N.

G. V. Belokopytov and E. N. Vasil’ev, “Scattering of a plane inhomogeneous wave by a spherical particle,” Radiophys. Quantum Electron. 49(1), 65–73 (2006).
[Crossref]

Videen, G.

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(D14), D14220 (2008).
[Crossref]

Winker, D. M.

Wiscombe, W. J.

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.

Yin, J.

Young, G.

R. A. Chipman, W.-S. T. Lam, and G. Young, Polarized Light and Optical Systems (CRC Press, 2019).

Yurkin, M. A.

M. I. Mishchenko and M. A. Yurkin, “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial,” J. Quant. Spectrosc. Radiat. Transfer 214, 158–167 (2018).
[Crossref]

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M. I. Mishchenko and M. A. Yurkin, “Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: a tutorial,” J. Quant. Spectrosc. Radiat. Transfer 214, 158–167 (2018).
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Figures (1)

Fig. 1.
Fig. 1. Scattering problem. The real part of the wave vector ${\textbf k^{\prime}}$ is normal to surfaces of constant phase and generally is not parallel to the imaginary part of the wave vector ${\textbf k^{\prime\prime}}.$ In the far zone of the object, the scattered field becomes an outgoing transverse spherical wave.

Equations (34)

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E sca ( r ) = V INT d 3 r G ( r , r ) V INT d 3 r T ( r , r ) E inc ( r ) ,
T ( r , r ) = U ( r ) δ ( r r ) I + U ( r ) V INT d 3 r G ( r , r ) T ( r , r ) .
U ( r ) = Δ { 0 r R 3 V INT , ω 2 ε 2 ( r ) μ 0 k 1 2 ,\  r V INT
k 1 = k 1 + i k 1 = Δ ω ε 1 μ 0
ε 1 = ε 1 + i ε 1 = ε 1 ( 1 + i τ ) ,
E inc ( r ) = E 0 exp(i k r ),
H inc ( r ) = H 0 exp(i k r ),
k = k + i k
k E 0 = k H 0 = 0 ,
H 0 = ( ω μ 0 ) 1 k × E 0 ,
k k = k 1 2 = ω 2 ε 1 μ 0 .
k 2 k 2 = ω 2 ε 1 μ 0 ,
k k = k k cos ζ = 1 2 ω 2 ε 1 μ 0 τ ,
k = ω ε 1 μ 0 { 1 2 [ 1 + ( τ cos ζ ) 2 + 1 ] } 1 / 2 ,
k = ω ε 1 μ 0 { 1 2 [ 1 + ( τ cos ζ ) 2 1 ] } 1 / 2 .
τ / cos ζ 1.
k ω ε 1 μ 0 k 1 ,
k k τ 2 cos ζ , k k .
k E 0 , k H 0 , H 0 = ( ω μ 0 ) 1 k × E 0 .
H inc ( r , t ) E inc ( r , t ) .
S inc ( r ) = 1 2 Re [ E inc ( r ) × H inc ( r ) ] = 1 2 ω μ 0 exp ( 2 k r ) | E 0 | 2 k .
E sca ( r ) = E 1 ( r ^ )exp(i k 1 r ) ,
H sca ( r ) = H 1 ( r ^ )exp(i k 1 r ) ,
r ^ E 1 ( r ^ ) , r ^ H 1 ( r ^ ) , H 1 ( r ^ ) = ( ω μ 0 ) 1 k 1 r ^ × E 1 ,
H sca ( r , t ) E sca ( r , t ) ,
S sca ( r ) = 1 2 Re [ E sca ( r ) × H sca ( r ) ] = 1 2 ω μ 0 exp ( 2 k 1 r ) | E 1 ( r ^ ) | 2 k 1 r ^ .
E sca ( r ) r exp(i k 1 r ) r A ( r ^ , k ^ ) E 0 ,
A ( r ^ , k ^ ) = 1 4 π ( I r ^ r ^ ) V INT d 3 r exp( i k 1 r ^ r ) × V INT d 3 r T ( r , r ) ( I k ^ k ^ ) exp(i k r ) exp ( k r )
E hom sca ( r ) = V INT d 3 r G ( r , r ) V INT d 3 r T ( r , r ) E 0 exp(i k k ^ r )exp( k k ^ r ) .
E sca ( r ) = V INT d 3 r G ( r , r ) V INT d 3 r T ( r , r ) E 0 exp(i k k ^ r )exp( k k ^ r ),
k R 1
( k k 1 ) R = k k + k 1 ( k R ) 1 ,
E sca ( r ) E hom sca ( r )
A ( r ^ , k ^ ) A hom ( r ^ , k ^ ) ,

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