Abstract

Transient/time-dependent radiative transfer in a two-dimensional scattering medium is numerically solved by the discontinuous finite element method (DFEM). The time-dependent term of the transient vector radiative transfer equation is discretized by the second-order central difference scheme and the space domain is discretized into non-overlapping quadrilateral elements by using the discontinuous finite element approach. The accuracy of the transient DFEM model for the radiative transfer equation considering the polarization effect is verified by comparing the time-resolved Stokes vector component distributions against the steady solutions for a polarized radiative transfer problem in a two-dimensional rectangular enclosure filled with a scattering medium. The transient polarized radiative transfer problems in a scattering medium exposed to an external beam and in an irregular emitting medium are solved. The distributions of the time-resolved Stokes vector components are presented and discussed.

© 2017 Optical Society of America

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2017 (3)

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

C. H. Wang, H. L. Yi, and H.-P. Tan, “Discontinuous finite element method for vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 189, 383–397 (2017).
[Crossref]

C. H. Wang, H. L. Yi, and H. P. Tan, “Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method,” Opt. Express 25(7), 7418–7442 (2017).
[Crossref] [PubMed]

2016 (1)

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

2015 (4)

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
[Crossref]

J. M. Zhao, J. Y. Tan, and L. H. Liu, “Monte Carlo method for polarized radiative transfer in gradient-index media,” J. Quant. Spectrosc. Radiat. Transf. 152, 114–126 (2015).
[Crossref]

2014 (2)

2013 (3)

Y. Zhang, H. Yi, and H. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21(21), 24532–24549 (2013).
[Crossref] [PubMed]

Z. C. Wang, Q. Cheng, and H. C. Zhou, “The DRESOR method for transient radiation transfer in 1-D graded index medium with pulse irradiation,” Int. J. Therm. Sci. 68, 127–135 (2013).
[Crossref]

J. M. Zhao, J. Y. Tan, and L. H. Liu, “A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media,” J. Comput. Phys. 232(1), 431–455 (2013).
[Crossref]

2012 (1)

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

2011 (1)

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

2010 (3)

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (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 media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[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), 3799–3806 (2010).
[Crossref]

2009 (1)

K. E. Sheetz and J. Squier, “Ultrafast optics: Imaging and manipulating biological systems,” J. Appl. Phys. 105(5), 051101 (2009).
[Crossref]

2008 (1)

Q. Cheng, H. C. Zhou, Z. F. Huang, Y. L. Yu, and D. X. Huang, “The solution of transient radiative transfer with collimated incident serial pulse in a plane-parallel medium by the DRESOR method,” ASME J. Heat Transfer 130(10), 102701 (2008).
[Crossref]

2006 (2)

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), 1820–1832 (2006).
[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]

2005 (2)

S. C. Mishra and A. Lankadasu, “Transient conduction-radiation heat transfer in participating media using the lattice Boltzmann method and the discrete transfer method,” Numer. Heat Transf. A 47(9), 935–954 (2005).
[Crossref]

S. C. Mishra, A. Lankadasu, and K. N. Beronov, “Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem,” Int. J. Heat Mass Transfer 48(17), 3648–3659 (2005).
[Crossref]

2004 (2)

J. C. Chai, “Transient radiative transfer in irregular two-dimensional geometries,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 281–294 (2004).
[Crossref]

R. Vaillona, 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]

2003 (4)

X. 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 Transf. B 44(2), 187–208 (2003).
[Crossref]

Z. Guo and K. Kim, “Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method,” Appl. Opt. 42(16), 2897–2905 (2003).
[Crossref] [PubMed]

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
[Crossref]

2002 (5)

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), 169–179 (2002).
[Crossref]

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 73(2), 159–168 (2002).
[Crossref]

C. Y. Wu and N. R. Ou, “Differential approximation for transient radiative transfer through a participating medium exposed to collimated irradiation,” J. Quant. Spectrosc. Radiat. Transf. 73(1), 111–120 (2002).
[Crossref]

M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. 27(5), 336–338 (2002).
[Crossref] [PubMed]

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), 169–179 (2002).
[Crossref]

2001 (4)

2000 (4)

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]

Z. Guo and S. Kumar, “Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media,” Appl. Opt. 39(24), 4411–4417 (2000).
[Crossref] [PubMed]

C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transf. 64(5), 537–548 (2000).
[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]

1999 (2)

K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38(1), 188–196 (1999).
[Crossref] [PubMed]

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transf. 33, 187–294 (1999).
[Crossref]

1997 (1)

K. Mitra, M. S. Lai, and S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” AIAA J. Thermophys. Heat Transfer 11(3), 409–414 (1997).
[Crossref]

1991 (1)

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]

1989 (1)

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

1973 (1)

1947 (1)

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Math. Proc. Camb. Philos. Soc. 43(1), 50–67 (1947).
[Crossref]

Aber, J.

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 73(2), 159–168 (2002).
[Crossref]

Ai, Q.

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

Barlakas, V.

C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
[Crossref]

Beronov, K. N.

S. C. Mishra, A. Lankadasu, and K. N. Beronov, “Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem,” Int. J. Heat Mass Transfer 48(17), 3648–3659 (2005).
[Crossref]

Brown, A. J.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

A. J. Brown, “Spectral bluing induced by small particles under the Mie and Rayleigh regimes,” Icarus 239, 85–95 (2014).
[Crossref]

A. J. Brown, “Equivalence relations and symmetries for laboratory, LIDAR, and planetary Müeller matrix scattering geometries,” J. Opt. Soc. Am. A 31(12), 2789–2794 (2014).
[Crossref] [PubMed]

Budak, V. P.

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

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

Byrne, S.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Catchings, F. E.

Cerussi, A. E.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

Chai, J. C.

J. C. Chai, “Transient radiative transfer in irregular two-dimensional geometries,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 281–294 (2004).
[Crossref]

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A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
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Guo, Z.

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J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Math. Proc. Camb. Philos. Soc. 43(1), 50–67 (1947).
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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), 169–179 (2002).
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Q. Cheng, H. C. Zhou, Z. F. Huang, Y. L. Yu, and D. X. Huang, “The solution of transient radiative transfer with collimated incident serial pulse in a plane-parallel medium by the DRESOR method,” ASME J. Heat Transfer 130(10), 102701 (2008).
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A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
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Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 73(2), 159–168 (2002).
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J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
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C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
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C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
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P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
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Mayer, B.

C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
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R. Vaillona, 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).
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A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Min, Q.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

Mishra, S. C.

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), 1820–1832 (2006).
[Crossref]

S. C. Mishra and A. Lankadasu, “Transient conduction-radiation heat transfer in participating media using the lattice Boltzmann method and the discrete transfer method,” Numer. Heat Transf. A 47(9), 935–954 (2005).
[Crossref]

S. C. Mishra, A. Lankadasu, and K. N. Beronov, “Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem,” Int. J. Heat Mass Transfer 48(17), 3648–3659 (2005).
[Crossref]

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
[Crossref]

Mitra, K.

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), 1820–1832 (2006).
[Crossref]

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
[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), 169–179 (2002).
[Crossref]

M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. 27(5), 336–338 (2002).
[Crossref] [PubMed]

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), 169–179 (2002).
[Crossref]

K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38(1), 188–196 (1999).
[Crossref] [PubMed]

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transf. 33, 187–294 (1999).
[Crossref]

K. Mitra, M. S. Lai, and S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” AIAA J. Thermophys. Heat Transfer 11(3), 409–414 (1997).
[Crossref]

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A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
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J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Math. Proc. Camb. Philos. Soc. 43(1), 50–67 (1947).
[Crossref]

O’Sullivan, T. D.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

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C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
[Crossref]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
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Plass, G. N.

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[Crossref]

Rath, P.

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
[Crossref]

Rozanov, V. V.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

Saha, U. K.

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
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Sakami, M.

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

M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. 27(5), 336–338 (2002).
[Crossref] [PubMed]

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), 169–179 (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), 169–179 (2002).
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Shum, H. C.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
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Siewert, C. E.

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 include polarization effects,” J. Quant. Spectrosc. Radiat. Transf. 41(2), 117–145 (1989).
[Crossref]

Sommersten, E. R.

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 media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Squier, J.

K. E. Sheetz and J. Squier, “Ultrafast optics: Imaging and manipulating biological systems,” J. Appl. Phys. 105(5), 051101 (2009).
[Crossref]

Stamnes, J. J.

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 media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Stamnes, K.

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 media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Stephens, G. L.

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]

Sun, C. W.

X. 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]

Sun, W.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Tan, H.

Tan, H. P.

C. H. Wang, H. L. Yi, and H. P. Tan, “Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method,” Opt. Express 25(7), 7418–7442 (2017).
[Crossref] [PubMed]

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

Tan, H.-P.

C. H. Wang, H. L. Yi, and H.-P. Tan, “Discontinuous finite element method for vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 189, 383–397 (2017).
[Crossref]

Tan, J. Y.

J. M. Zhao, J. Y. Tan, and L. H. Liu, “Monte Carlo method for polarized radiative transfer in gradient-index media,” J. Quant. Spectrosc. Radiat. Transf. 152, 114–126 (2015).
[Crossref]

J. M. Zhao, J. Y. Tan, and L. H. Liu, “A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media,” J. Comput. Phys. 232(1), 431–455 (2013).
[Crossref]

Tan, Z. M.

Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” ASME J. Heat Transfer 123(3), 466–475 (2001).
[Crossref]

Tang, A. H.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Titus, T. N.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Tromberg, B. J.

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

Tsia, K. K.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Vaillona, R.

R. Vaillona, 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]

Videen, G.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Vo-Dinh, T.

Wang, C. H.

C. H. Wang, H. L. Yi, and H.-P. Tan, “Discontinuous finite element method for vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 189, 383–397 (2017).
[Crossref]

C. H. Wang, H. L. Yi, and H. P. Tan, “Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method,” Opt. Express 25(7), 7418–7442 (2017).
[Crossref] [PubMed]

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

Wang, J. M.

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), 3799–3806 (2010).
[Crossref]

Wang, L. V.

X. 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]

Wang, X.

X. 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]

Wang, Z. C.

Z. C. Wang, Q. Cheng, and H. C. Zhou, “The DRESOR method for transient radiation transfer in 1-D graded index medium with pulse irradiation,” Int. J. Therm. Sci. 68, 127–135 (2013).
[Crossref]

Wei, X.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Wendisch, M.

C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
[Crossref]

Wolff, M. J.

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

Wong, B. T.

R. Vaillona, 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]

Wong, K. K.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Wu, C. Y.

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), 3799–3806 (2010).
[Crossref]

C. Y. Wu and N. R. Ou, “Differential approximation for transient radiative transfer through a participating medium exposed to collimated irradiation,” J. Quant. Spectrosc. Radiat. Transf. 73(1), 111–120 (2002).
[Crossref]

C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transf. 64(5), 537–548 (2000).
[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]

Wu, J.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Wu, S. H.

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]

Xu, J.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Xu, Y.

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Yang, C. C.

X. 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]

Yi, H.

Yi, H. L.

C. H. Wang, H. L. Yi, and H.-P. Tan, “Discontinuous finite element method for vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 189, 383–397 (2017).
[Crossref]

C. H. Wang, H. L. Yi, and H. P. Tan, “Transient polarized radiative transfer analysis in a scattering medium by a discontinuous finite element method,” Opt. Express 25(7), 7418–7442 (2017).
[Crossref] [PubMed]

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

Yokota, T.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

Yu, Y. L.

Q. Cheng, H. C. Zhou, Z. F. Huang, Y. L. Yu, and D. X. Huang, “The solution of transient radiative transfer with collimated incident serial pulse in a plane-parallel medium by the DRESOR method,” ASME J. Heat Transfer 130(10), 102701 (2008).
[Crossref]

Zege, E. P.

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

Zhang, Y.

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

Y. Zhang, H. Yi, and H. Tan, “One-dimensional transient radiative transfer by lattice Boltzmann method,” Opt. Express 21(21), 24532–24549 (2013).
[Crossref] [PubMed]

Zhao, J. M.

J. M. Zhao, J. Y. Tan, and L. H. Liu, “Monte Carlo method for polarized radiative transfer in gradient-index media,” J. Quant. Spectrosc. Radiat. Transf. 152, 114–126 (2015).
[Crossref]

J. M. Zhao, J. Y. Tan, and L. H. Liu, “A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media,” J. Comput. Phys. 232(1), 431–455 (2013).
[Crossref]

Zhou, H. C.

Z. C. Wang, Q. Cheng, and H. C. Zhou, “The DRESOR method for transient radiation transfer in 1-D graded index medium with pulse irradiation,” Int. J. Therm. Sci. 68, 127–135 (2013).
[Crossref]

Q. Cheng, H. C. Zhou, Z. F. Huang, Y. L. Yu, and D. X. Huang, “The solution of transient radiative transfer with collimated incident serial pulse in a plane-parallel medium by the DRESOR method,” ASME J. Heat Transfer 130(10), 102701 (2008).
[Crossref]

Adv. Heat Transf. (1)

S. Kumar and K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transf. 33, 187–294 (1999).
[Crossref]

AIAA J. Thermophys. Heat Transfer (1)

K. Mitra, M. S. Lai, and S. Kumar, “Transient radiation transport in participating media within a rectangular enclosure,” AIAA J. Thermophys. Heat Transfer 11(3), 409–414 (1997).
[Crossref]

Appl. Opt. (7)

ASME J. Heat Transfer (2)

Q. Cheng, H. C. Zhou, Z. F. Huang, Y. L. Yu, and D. X. Huang, “The solution of transient radiative transfer with collimated incident serial pulse in a plane-parallel medium by the DRESOR method,” ASME J. Heat Transfer 130(10), 102701 (2008).
[Crossref]

Z. M. Tan and P. F. Hsu, “An integral formulation of transient radiative transfer,” ASME J. Heat Transfer 123(3), 466–475 (2001).
[Crossref]

Comput. Phys. Commun. (1)

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

Icarus (1)

A. J. Brown, “Spectral bluing induced by small particles under the Mie and Rayleigh regimes,” Icarus 239, 85–95 (2014).
[Crossref]

Int. J. Heat Mass Transfer (4)

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]

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), 3799–3806 (2010).
[Crossref]

S. C. Mishra, A. Lankadasu, and K. N. Beronov, “Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction–radiation problem,” Int. J. Heat Mass Transfer 48(17), 3648–3659 (2005).
[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), 1820–1832 (2006).
[Crossref]

Int. J. Therm. Sci. (1)

Z. C. Wang, Q. Cheng, and H. C. Zhou, “The DRESOR method for transient radiation transfer in 1-D graded index medium with pulse irradiation,” Int. J. Therm. Sci. 68, 127–135 (2013).
[Crossref]

J. Appl. Phys. (1)

K. E. Sheetz and J. Squier, “Ultrafast optics: Imaging and manipulating biological systems,” J. Appl. Phys. 105(5), 051101 (2009).
[Crossref]

J. Biomed. Opt. (2)

T. D. O’Sullivan, A. E. Cerussi, D. J. Cuccia, and B. J. Tromberg, “Diffuse optical imaging using spatially and temporally modulated light,” J. Biomed. Opt. 17(7), 071311 (2012).
[PubMed]

X. 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. Comput. Phys. (1)

J. M. Zhao, J. Y. Tan, and L. H. Liu, “A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media,” J. Comput. Phys. 232(1), 431–455 (2013).
[Crossref]

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

J. Quant. Spectrosc. Radiat. Transf. (16)

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

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]

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 media with different refractive indices,” J. Quant. Spectrosc. Radiat. Transf. 111(4), 616–633 (2010).
[Crossref]

Z. Guo, J. Aber, B. A. Garetz, and S. Kumar, “Monte Carlo simulation and experiments of pulsed radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 73(2), 159–168 (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), 169–179 (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), 169–179 (2002).
[Crossref]

J. C. Chai, “Transient radiative transfer in irregular two-dimensional geometries,” J. Quant. Spectrosc. Radiat. Transf. 84(3), 281–294 (2004).
[Crossref]

C. Y. Wu, “Propagation of scattered radiation in a participating planar medium with pulse irradiation,” J. Quant. Spectrosc. Radiat. Transf. 64(5), 537–548 (2000).
[Crossref]

C. Y. Wu and N. R. Ou, “Differential approximation for transient radiative transfer through a participating medium exposed to collimated irradiation,” J. Quant. Spectrosc. Radiat. Transf. 73(1), 111–120 (2002).
[Crossref]

A. J. Brown, T. I. Michaels, S. Byrne, W. Sun, T. N. Titus, A. Colaprete, M. J. Wolff, G. Videen, and C. J. Grund, “The case for a modern multi-wavelength, polarization-sensitive LIDAR in orbit around Mars,” J. Quant. Spectrosc. Radiat. Transf. 153, 131–143 (2015).
[Crossref]

C. H. Wang, H. L. Yi, and H.-P. Tan, “Discontinuous finite element method for vector radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 189, 383–397 (2017).
[Crossref]

R. Vaillona, 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]

A. A. Kokhanovsky, V. P. Budak, C. Cornet, M. Z. Duan, C. Emde, I. L. Katsev, D. A. Klyukov, S. V. Korkin, L. C-Labonnote, B. Mayer, Q. Min, T. Nakajima, Y. Ota, A. S. Prikhach, V. V. Rozanov, T. Yokota, and E. P. Zege, “Benchmark results in vector atmospheric radiative transfer,” J. Quant. Spectrosc. Radiat. Transf. 111(12), 1931–1946 (2010).
[Crossref]

C. Emde, V. Barlakas, C. Cornet, F. Evans, S. Korkin, Y. Ota, L. C. Labonnote, A. Lyapustin, A. Macke, B. Mayer, and M. Wendisch, “IPRT polarized radiative transfer model intercomparison project – Phase A,” J. Quant. Spectrosc. Radiat. Transf. 164, 8–36 (2015).
[Crossref]

J. M. Zhao, J. Y. Tan, and L. H. Liu, “Monte Carlo method for polarized radiative transfer in gradient-index media,” J. Quant. Spectrosc. Radiat. Transf. 152, 114–126 (2015).
[Crossref]

Light Sci. Appl. (1)

J. Wu, Y. Xu, J. Xu, X. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, E. Y. Lam, K. K. Wong, and K. K. Tsia, “Ultrafast laser-scanning time-stretch imaging at visible wavelengths,” Light Sci. Appl. 6(1), e16196 (2017).
[Crossref]

Math. Proc. Camb. Philos. Soc. (1)

J. Crank, P. Nicolson, and D. R. Hartree, “A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type,” Math. Proc. Camb. Philos. Soc. 43(1), 50–67 (1947).
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Numer. Heat Transf. A (4)

C. H. Wang, Y. Zhang, H. L. Yi, and H. P. Tan, “Transient radiative transfer in two-dimensional graded index medium by Monte Carlo method combined with the time shift and superposition principle,” Numer. Heat Transf. A 69(6), 574–588 (2016).
[Crossref]

S. C. Mishra and A. Lankadasu, “Transient conduction-radiation heat transfer in participating media using the lattice Boltzmann method and the discrete transfer method,” Numer. Heat Transf. A 47(9), 935–954 (2005).
[Crossref]

P. Rath, S. C. Mishra, P. Mahanta, U. K. Saha, and K. Mitra, “Discrete transfer method applied to transient radiative transfer problems in participating medium,” Numer. Heat Transf. A 44(2), 183–197 (2003).
[Crossref]

C. H. Wang, Q. Ai, H. L. Yi, and H. P. Tan, “Transient radiative transfer in a graded index medium with specularly reflecting surfaces,” Numer. Heat Transf. A 67(11), 1232–1252 (2015).
[Crossref]

Numer. Heat Transf. B (1)

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

Opt. Lett. (1)

Other (2)

S. Chandrasekhar, Radiative transfer (Dover, 1960).

D. H. Goldstein, Polarized light (Dekker, 2003).

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Figures (9)

Fig. 1
Fig. 1 Sketch of elements, element boundaries and the radiation values on the boundaries for the two-dimensional discrete elements.
Fig. 2
Fig. 2 Physical model of the two-dimensional scattering medium exposed to an external collimated beam illumination.
Fig. 3
Fig. 3 Comparisons of the time-resolved Stokes vector radiative fluxes along the top boundary against the steady solution.
Fig. 4
Fig. 4 Time-resolved Stokes vector radiative flux along the top boundary.
Fig. 5
Fig. 5 Time-resolved Stokes vector radiative flux along the right boundary.
Fig. 6
Fig. 6 Distributions of the false temperature within the rectangular atmosphere at different times.
Fig. 7
Fig. 7 (a): The geometric coordinate in meters and the grid discretization, and (b): time-resolved radiative heat flux along the bottom boundary of the irregular emitting medium.
Fig. 8
Fig. 8 Polarized radiative flux distributions of Stokes vector component (a): I and (b): Q on the bottom boundary of the irregular medium at different times.
Fig. 9
Fig. 9 False temperature distributions within the emitting irregular medium at different times.

Tables (1)

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Table 1 Nomenclature.

Equations (13)

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1 c 0 I(r,Ω,t) t +ΩI(r,Ω,t)+βI(r,Ω,t)=S(r,Ω,t) ,
S(z,Ω,t)= κ a I b + κ s 4π 4π Z( Ω ,Ω)I(r, Ω ,t) d Ω ,
I( r w ,Ω,t)= R s I( r w , Ω ,t)+ 1 π n w Ω n >0 R d I( r w , Ω ,t)| n w Ω |d Ω ,
[ I n ]= Ω n I ¯ n +| Ω n | I n n K ,
I ¯ n = 1 2 ( I n + I + n ), I n = 1 2 ( I n I + n ) .
K k n I k n = H k n ,
K k,ji n = e ϕ i Ω n ϕ j dA + 1 2 e ( Ω n n e +| Ω n | ϕ i ϕ j )ds + e β ˜ ϕ i ϕ j dA ,
H k,j n = e S ˜ k n ϕ j dA 1 2 e ( Ω n n e | Ω n |) I k,+ n ϕ j ds ,
β ˜ =( 2 Δ t * +1)β ,
S ˜ k n (r,Ω)= S k (r,Ω)+ S k1 (r,Ω)Ω I k1 (r,Ω)(1 2 Δ t * )β I k1 (r,Ω) ,
I= I c + I d ,
I c (r, Ω 0 , t * )= I 0 exp(βx) .
S(r,Ω, t * )= κ s 4π [ Z(r, Ω 0 ,Ω) I c (r, Ω 0 , t * )+ 4π Z(r, Ω Ω) I d (r, Ω , t * )d Ω ] ,

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