F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 117, 59–70 (2013).

[CrossRef]

Y. A. Ilyushin and Y. P. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182(4), 940–945 (2011).

[CrossRef]

J. M. Wang and C. Y. Wu, “Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index,” Int. Commun. Heat Mass Transf. 38(9), 1213–1218 (2011).

[CrossRef]

M. Akamatsu and Z. X. Guo, “Ultrafast radiative heat transfer in three-dimensional highly-scattering media subjected to pulse train irradiation,” Numer. Heat Tranf. Anal. Appl. 59, 653–671 (2011).

S. C. Mishra, R. Muthukumaran, and S. Maruyama, “The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media,” Int. Commun. Heat Mass Transf. 38(3), 291–297 (2011).

[CrossRef]

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53(19-20), 3799–3806 (2010).

[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111(1), 174–186 (2010).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

C. Y. Wu, “Monte Carlo simulation of transient radiative transfer in a medium with a variable refractive index,” Int. J. Heat Mass Transfer 52(19-20), 4151–4159 (2009).

[CrossRef]

E. A. Sergeeva and A. I. Korytin, “Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium,” Radiophys. Quantum Electron. 51(4), 301–314 (2008).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transf. 104(2), 277–287 (2007).

[CrossRef]

M. Sakami and A. Dogariu, “Polarized light-pulse transport through scattering media,” J. Opt. Soc. Am. A 23(3), 664–670 (2006).

[CrossRef]
[PubMed]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed monte carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Rem. Sens. 43(5), 1096–1101 (2005).

[CrossRef]

J. C. Ramella-Roman, S. A. Prahl, and S. L. Jacques, “Three Monte Carlo programs of polarized light transport into scattering media: part I,” Opt. Express 13(12), 4420–4438 (2005).

[CrossRef]
[PubMed]

M. Xu, “Electric field Monte Carlo simulation of polarized light propagation in turbid media,” Opt. Express 12(26), 6530–6539 (2004).

[CrossRef]
[PubMed]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transf. 84(4), 383–394 (2004).

[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, “Three-dimensional transient radiative transfer modeling using the finite-volume method,” J. Quant. Spectrosc. Radiat. Transf. 86(3), 299–313 (2004).

[CrossRef]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer Heat Tranf. B-Fundam. 44(2), 187–208 (2003).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 73(2-5), 169–179 (2002).

[CrossRef]

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transf. 72(4), 467–483 (2002).

[CrossRef]

X. D. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7(3), 279–290 (2002).

[CrossRef]
[PubMed]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40(3), 400–412 (2001).

[CrossRef]
[PubMed]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40(30), 5495–5502 (2001).

[CrossRef]
[PubMed]

P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40(6), 539–549 (2001).

[CrossRef]

S. H. Wu and C. Y. Wu, “Time-resolved spatial distribution of scattered radiative energy in a two-dimensional cylindrical medium with a large mean free path for scattering,” Int. J. Heat Mass Transfer 44(14), 2611–2619 (2001).

[CrossRef]

C. Y. Wu and S. H. Wu, “Integral equation formulation for transient radiative transfer in an anisotropically scattering medium,” Int. J. Heat Mass Transfer 43(11), 2009–2020 (2000).

[CrossRef]

Z. X. Guo, S. Kumar, and K. C. San, “Multidimensional Monte Carlo simulation of short-pulse laser transport in scattering media,” J. Thermophys. Heat Transf. 14, 504–511 (2000).

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 64(3), 227–254 (2000).

[CrossRef]

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).

[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that in include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 41(2), 117–145 (1989).

[CrossRef]

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34(8), 1453–1472 (1989).

[CrossRef]

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Meteorol. Geophys. 37(1), 1–13 (1986).

[CrossRef]

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34(8), 1453–1472 (1989).

[CrossRef]

M. Akamatsu and Z. X. Guo, “Ultrafast radiative heat transfer in three-dimensional highly-scattering media subjected to pulse train irradiation,” Numer. Heat Tranf. Anal. Appl. 59, 653–671 (2011).

Y. A. Ilyushin and Y. P. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182(4), 940–945 (2011).

[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, “Three-dimensional transient radiative transfer modeling using the finite-volume method,” J. Quant. Spectrosc. Radiat. Transf. 86(3), 299–313 (2004).

[CrossRef]

J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer Heat Tranf. B-Fundam. 44(2), 187–208 (2003).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111(1), 174–186 (2010).

[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transf. 104(2), 277–287 (2007).

[CrossRef]

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 117, 59–70 (2013).

[CrossRef]

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed monte carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Rem. Sens. 43(5), 1096–1101 (2005).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed monte carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Rem. Sens. 43(5), 1096–1101 (2005).

[CrossRef]

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).

[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that in include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 41(2), 117–145 (1989).

[CrossRef]

M. Akamatsu and Z. X. Guo, “Ultrafast radiative heat transfer in three-dimensional highly-scattering media subjected to pulse train irradiation,” Numer. Heat Tranf. Anal. Appl. 59, 653–671 (2011).

Z. X. Guo, S. Kumar, and K. C. San, “Multidimensional Monte Carlo simulation of short-pulse laser transport in scattering media,” J. Thermophys. Heat Transf. 14, 504–511 (2000).

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed monte carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Rem. Sens. 43(5), 1096–1101 (2005).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, “Three-dimensional transient radiative transfer modeling using the finite-volume method,” J. Quant. Spectrosc. Radiat. Transf. 86(3), 299–313 (2004).

[CrossRef]

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 73(2-5), 169–179 (2002).

[CrossRef]

P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40(6), 539–549 (2001).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

Y. A. Ilyushin and Y. P. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182(4), 940–945 (2011).

[CrossRef]

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transf. 72(4), 467–483 (2002).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40(3), 400–412 (2001).

[CrossRef]
[PubMed]

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34(8), 1453–1472 (1989).

[CrossRef]

G. W. Kattawar and G. N. Plass, “Radiance and polarization of multiple scattered light from haze and clouds,” Appl. Opt. 7(8), 1519–1527 (1968).

[CrossRef]
[PubMed]

E. A. Sergeeva and A. I. Korytin, “Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium,” Radiophys. Quantum Electron. 51(4), 301–314 (2008).

[CrossRef]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

Z. X. Guo, S. Kumar, and K. C. San, “Multidimensional Monte Carlo simulation of short-pulse laser transport in scattering media,” J. Thermophys. Heat Transf. 14, 504–511 (2000).

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111(1), 174–186 (2010).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, “Three-dimensional transient radiative transfer modeling using the finite-volume method,” J. Quant. Spectrosc. Radiat. Transf. 86(3), 299–313 (2004).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

S. C. Mishra, R. Muthukumaran, and S. Maruyama, “The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media,” Int. Commun. Heat Mass Transf. 38(3), 291–297 (2011).

[CrossRef]

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transf. 72(4), 467–483 (2002).

[CrossRef]

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Meteorol. Geophys. 37(1), 1–13 (1986).

[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transf. 104(2), 277–287 (2007).

[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transf. 84(4), 383–394 (2004).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

S. C. Mishra, R. Muthukumaran, and S. Maruyama, “The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media,” Int. Commun. Heat Mass Transf. 38(3), 291–297 (2011).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 73(2-5), 169–179 (2002).

[CrossRef]

S. C. Mishra, R. Muthukumaran, and S. Maruyama, “The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media,” Int. Commun. Heat Mass Transf. 38(3), 291–297 (2011).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

Z. X. Guo, S. Kumar, and K. C. San, “Multidimensional Monte Carlo simulation of short-pulse laser transport in scattering media,” J. Thermophys. Heat Transf. 14, 504–511 (2000).

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

E. A. Sergeeva and A. I. Korytin, “Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium,” Radiophys. Quantum Electron. 51(4), 301–314 (2008).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 64(3), 227–254 (2000).

[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that in include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 41(2), 117–145 (1989).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).

[CrossRef]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transf. 104(2), 277–287 (2007).

[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111(1), 174–186 (2010).

[CrossRef]

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Meteorol. Geophys. 37(1), 1–13 (1986).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transf. 84(4), 383–394 (2004).

[CrossRef]

J. M. Wang and C. Y. Wu, “Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index,” Int. Commun. Heat Mass Transf. 38(9), 1213–1218 (2011).

[CrossRef]

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53(19-20), 3799–3806 (2010).

[CrossRef]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

X. D. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7(3), 279–290 (2002).

[CrossRef]
[PubMed]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

X. D. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7(3), 279–290 (2002).

[CrossRef]
[PubMed]

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 117, 59–70 (2013).

[CrossRef]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transf. 84(4), 383–394 (2004).

[CrossRef]

J. M. Wang and C. Y. Wu, “Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index,” Int. Commun. Heat Mass Transf. 38(9), 1213–1218 (2011).

[CrossRef]

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53(19-20), 3799–3806 (2010).

[CrossRef]

C. Y. Wu, “Monte Carlo simulation of transient radiative transfer in a medium with a variable refractive index,” Int. J. Heat Mass Transfer 52(19-20), 4151–4159 (2009).

[CrossRef]

S. H. Wu and C. Y. Wu, “Time-resolved spatial distribution of scattered radiative energy in a two-dimensional cylindrical medium with a large mean free path for scattering,” Int. J. Heat Mass Transfer 44(14), 2611–2619 (2001).

[CrossRef]

C. Y. Wu and S. H. Wu, “Integral equation formulation for transient radiative transfer in an anisotropically scattering medium,” Int. J. Heat Mass Transfer 43(11), 2009–2020 (2000).

[CrossRef]

S. H. Wu and C. Y. Wu, “Time-resolved spatial distribution of scattered radiative energy in a two-dimensional cylindrical medium with a large mean free path for scattering,” Int. J. Heat Mass Transfer 44(14), 2611–2619 (2001).

[CrossRef]

C. Y. Wu and S. H. Wu, “Integral equation formulation for transient radiative transfer in an anisotropically scattering medium,” Int. J. Heat Mass Transfer 43(11), 2009–2020 (2000).

[CrossRef]

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 117, 59–70 (2013).

[CrossRef]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40(30), 5495–5502 (2001).

[CrossRef]
[PubMed]

G. W. Kattawar and G. N. Plass, “Radiance and polarization of multiple scattered light from haze and clouds,” Appl. Opt. 7(8), 1519–1527 (1968).

[CrossRef]
[PubMed]

H. H. Tynes, G. W. Kattawar, E. P. Zege, I. L. Katsev, A. S. Prikhach, and L. I. Chaikovskaya, “Monte Carlo and multicomponent approximation methods for vector radiative transfer by use of effective Mueller matrix calculations,” Appl. Opt. 40(3), 400–412 (2001).

[CrossRef]
[PubMed]

Y. A. Ilyushin and Y. P. Budak, “Analysis of the propagation of the femtosecond laser pulse in the scattering medium,” Comput. Phys. Commun. 182(4), 940–945 (2011).

[CrossRef]

C. Davis, C. Emde, and R. Harwood, “A 3-D polarized reversed monte carlo radiative transfer model for millimeter and submillimeter passive remote sensing in cloudy atmospheres,” IEEE Trans. Geosci. Rem. Sens. 43(5), 1096–1101 (2005).

[CrossRef]

J. M. Wang and C. Y. Wu, “Second-order-accurate discrete ordinates solutions of transient radiative transfer in a scattering slab with variable refractive index,” Int. Commun. Heat Mass Transf. 38(9), 1213–1218 (2011).

[CrossRef]

S. C. Mishra, R. Muthukumaran, and S. Maruyama, “The finite volume method approach to the collapsed dimension method in analyzing steady/transient radiative transfer problems in participating media,” Int. Commun. Heat Mass Transf. 38(3), 291–297 (2011).

[CrossRef]

C. Y. Wu and S. H. Wu, “Integral equation formulation for transient radiative transfer in an anisotropically scattering medium,” Int. J. Heat Mass Transfer 43(11), 2009–2020 (2000).

[CrossRef]

S. H. Wu and C. Y. Wu, “Time-resolved spatial distribution of scattered radiative energy in a two-dimensional cylindrical medium with a large mean free path for scattering,” Int. J. Heat Mass Transfer 44(14), 2611–2619 (2001).

[CrossRef]

C. Y. Wu, “Monte Carlo simulation of transient radiative transfer in a medium with a variable refractive index,” Int. J. Heat Mass Transfer 52(19-20), 4151–4159 (2009).

[CrossRef]

J. M. Wang and C. Y. Wu, “Transient radiative transfer in a scattering slab with variable refractive index and diffuse substrate,” Int. J. Heat Mass Transfer 53(19-20), 3799–3806 (2010).

[CrossRef]

S. C. Mishra, P. Chugh, P. Kumar, and K. Mitra, “Development and comparison of the DTM, the DOM and the FVM formulations for the short-pulse laser transport through a participating medium,” Int. J. Heat Mass Transfer 49(11-12), 1820–1832 (2006).

[CrossRef]

P. F. Hsu, “Effects of multiple scattering and reflective boundary on the transient radiative transfer process,” Int. J. Therm. Sci. 40(6), 539–549 (2001).

[CrossRef]

X. D. Wang, L. V. Wang, C. W. Sun, and C. C. Yang, “Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments,” J. Biomed. Opt. 8(4), 608–617 (2003).

[CrossRef]
[PubMed]

X. D. Wang and L. V. Wang, “Propagation of polarized light in birefringent turbid media: A Monte Carlo study,” J. Biomed. Opt. 7(3), 279–290 (2002).

[CrossRef]
[PubMed]

R. Vaillon, B. T. Wong, and M. P. Mengüç, “Polarized radiative transfer in a particle-laden semi-transparent medium via a vector Monte Carlo method,” J. Quant. Spectrosc. Radiat. Transf. 84(4), 383–394 (2004).

[CrossRef]

J. N. Swamy, C. Crofcheck, and M. P. Mengüç, “A Monte Carlo ray tracing study of polarized light propagation in liquid foams,” J. Quant. Spectrosc. Radiat. Transf. 104(2), 277–287 (2007).

[CrossRef]

C. Cornet, L. C. Labonnote, and F. Szczap, “Three-dimensional polarized Monte Carlo atmospheric radiative transfer model (3DMCPOL): 3D effects on polarized visible reflectances of a cirrus cloud,” J. Quant. Spectrosc. Radiat. Transf. 111(1), 174–186 (2010).

[CrossRef]

R. D. M. Garcia and C. E. Siewert, “The FN method for radiative transfer models that in include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 41(2), 117–145 (1989).

[CrossRef]

K. F. Evans and G. L. Stephens, “A new polarized atmospheric radiative transfer model,” J. Quant. Spectrosc. Radiat. Transf. 46(5), 413–423 (1991).

[CrossRef]

C. E. Siewert, “A discrete-ordinates solution for radiative-transfer models that include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 64(3), 227–254 (2000).

[CrossRef]

J. Lenoble, M. Herman, J. L. Deuze, B. Lafrance, R. Santer, and D. Tanre, “A successive order of scattering code for solving the vector equation of transfer in the earth’s atmosphere with aerosols,” J. Quant. Spectrosc. Radiat. Transf. 107(3), 479–507 (2007).

[CrossRef]

F. Xu, R. A. West, and A. B. Davis, “A hybrid method for modeling polarized radiative transfer in a spherical-shell planetary atmosphere,” J. Quant. Spectrosc. Radiat. Transf. 117, 59–70 (2013).

[CrossRef]

H. Ishimoto and K. Masuda, “A Monte Carlo approach for the calculation of polarized light: application to an incident narrow beam,” J. Quant. Spectrosc. Radiat. Transf. 72(4), 467–483 (2002).

[CrossRef]

M. Sakami, K. Mitra, and P. F. Hsu, “Analysis of light pulse transport through two-dimensional scattering and absorbing media,” J. Quant. Spectrosc. Radiat. Transf. 73(2-5), 169–179 (2002).

[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, “Three-dimensional transient radiative transfer modeling using the finite-volume method,” J. Quant. Spectrosc. Radiat. Transf. 86(3), 299–313 (2004).

[CrossRef]

P. W. Zhai, Y. X. Hu, J. Chowdhary, C. R. Trepte, P. L. Lucker, and D. B. Josset, “A vector radiative transfer model for coupled atmosphere and ocean systems with a rough interface,” J. Quant. Spectrosc. Radiat. Transf. 111(7-8), 1025–1040 (2010).

[CrossRef]

E. R. Sommersten, J. K. Lotsberg, K. Stamnes, and J. J. Stamnes, “Discrete ordinate and Monte Carlo simulations for polarized radiative transfer in a coupled system consisting of two medium with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).

[CrossRef]

Z. X. Guo, S. Kumar, and K. C. San, “Multidimensional Monte Carlo simulation of short-pulse laser transport in scattering media,” J. Thermophys. Heat Transf. 14, 504–511 (2000).

G. W. Kattawar and C. N. Adams, “Stokes vector calculations of the submarine light field in an atmosphere–ocean with scattering according to a Rayleigh phase matrix: effect of interface refractive index on radiance and polarization,” Limnol. Oceanogr. 34(8), 1453–1472 (1989).

[CrossRef]

R. Singh, S. C. Mishra, N. K. Roy, N. S. Shekhawat, and K. Mitra, “An insight into the modeling of short-pulse laser transport through a participating medium,” Numer Heat Tranf. B-Fundam. 52(4), 373–385 (2007).

[CrossRef]

J. C. Chai, “One-dimensional transient radiation heat transfer modeling using a finite-volume method,” Numer Heat Tranf. B-Fundam. 44(2), 187–208 (2003).

[CrossRef]

P. Rath, C. S. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Tranf. Anal. Appl. 44, 183–197 (2003).

M. Akamatsu and Z. X. Guo, “Ultrafast radiative heat transfer in three-dimensional highly-scattering media subjected to pulse train irradiation,” Numer. Heat Tranf. Anal. Appl. 59, 653–671 (2011).

K. Masuda and T. Takashima, “Computational accuracy of radiation emerging from the ocean surface in the model atmosphere–ocean system,” Pap. Meteorol. Geophys. 37(1), 1–13 (1986).

[CrossRef]

E. A. Sergeeva and A. I. Korytin, “Theoretical and experimental study of blurring of a femtosecond laser pulse in a turbid medium,” Radiophys. Quantum Electron. 51(4), 301–314 (2008).

[CrossRef]

S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).

H. C. Van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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

R. Green, Spherical Astronomy (Cambridge University, 1985).

B. A. Whitney, “Monte Carlo radiative transfer,” Arxiv preprint arXiv: 1104.4990 (2011).