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A pseudo-spectral time domain method for light scattering computation

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Light Scattering Reviews 8

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Abstract

Atmospheric particles, for example ice crystals, dust, soot, or various chemical crystals, play a significant role in the atmosphere by scattering and absorbing radiation, principally in two bands: incident solar, with peak at about 0.5 μm, and terrestrial thermal emission, with peak at about 10 μm. Knowledge of aerosol scattering properties is a fundamental but challenging aspect of radiative transfer studies and remote sensing applications. In this chapter we consider only scattering by single homogeneous particles, but in the atmosphere particles occur both individually and as constituents of such aerosols as homogeneous or heterogeneous aggregates with other particles and sometimes coated with liquids. The pseudo-spectral time domain method (PSTD) for calculating scattering properties that we discuss, like a number of other methods currently in use, can be used to investigate scattering properties of a wide variety of aerosols, homogeneous or heterogeneous, singly or in aggregate.

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References

  • Berenger, J.-P., 1994: A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185–200.

    Article  Google Scholar 

  • Bi, L., P. Yang, G. W. Kattawar, and R. Kahn, 2009: Single-scattering properties of triaxial ellipsoidal particles for a size parameter range from the Rayleigh to geometricoptics regimes, Appl. Opt., 48, 114–126.

    Article  Google Scholar 

  • Bi, L., P. Yang, G. W. Kattawar, and R. Kahn, 2010: Modeling optical properties of mineral aerosol particles by using nonsymmetric hexahedra, Appl. Opt., 49, 334–342.

    Article  Google Scholar 

  • Bi, L., P. Yang, G. W. Kattawar, Y. Hu, and B. A. Baum, 2011: Scattering and absorption of light by ice particles: Solution by a new physical-geometric optics hybrid method, J. Quant. Spectrosc. Radiat. Transfer, 112, 1492–1508.

    Article  Google Scholar 

  • Brock, R. S., X.-H. Hu, P. Yang, and J. Lu., 2005: Evaluation of a parallel FDTD code and application to modeling of light scattering by deformed red blood cells, Opt. Express, 13, 5279–5292.

    Google Scholar 

  • Chen, G., 2007: Modeling of the optical properties of nonspherical particles in the atmosphere, Ph.D. dissertation, Texas A&M University.

    Google Scholar 

  • Chen, G., P. Yang, and G. W. Kattawar, 2008: Application of the pseudospectral timedomain method to the scattering of light by nonspherical particles, J. Opt. Soc. Am. A, 25, 785–790.

    Article  Google Scholar 

  • Draine, B. T., and P. J. Flatau, 1994: Discrete-dipole approximation for scattering calculations, J. Opt. Soc. Am. A, 11, 1491–1499.

    Article  Google Scholar 

  • Gedney, S. D., 1996: An anisotropic perfectly matched layer – absorbing medium for the truncation of FDTD lattices, IEEE Trans. Antennas Propag., 44, 1630–1639.

    Article  Google Scholar 

  • Goedecke, G. H., and S. G. O’Brien, 1988: Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm, Appl. Opt., 27, 2431–2438.

    Article  Google Scholar 

  • Gottlieb, D., and C.-W. Shu, 1997: On the Gibbs phenomenon and its resolution, SIAM Rev., 39, 644–668.

    Article  Google Scholar 

  • Jackson, J. D., 1999: Classical Electrodynamics (3rd edn), John Wiley & Sons.

    Google Scholar 

  • Johnson, S. G., 2010: Notes on perfectly matched layers (PML), http://math.mit.edu/∼stevenj/18.369/pml.pdf, online MIT course notes.

  • Jones, D. S., 1957: High-frequency scattering of electromagnetic waves, Proc. R. Soc. Lond. A, 240, 206–213.

    Article  Google Scholar 

  • Kreiss, H.-O., and J. Oliger, 1972: Comparison of accurate methods for the integration of hyperbolic equations, Tellus, 24, 199–215.

    Article  Google Scholar 

  • Liou, K. N., 2002: An Introduction to Atmospheric Radiation, Academic Press.

    Google Scholar 

  • Liu, C., R. L. Panetta, and P. Yang, 2012a: Application of the pseudo-spectral time domain method to compute particle single-scattering properties for size parameters up to 200, J. Quant. Spectrosc. Radiat. Transfer, 113, 1728–1740.

    Article  Google Scholar 

  • Liu, C., L. Bi, R. L. Panetta, P. Yang, and M. A. Yurkin, 2012b: Comparison between the pseudo-spectral time domain method and the discrete dipole approximation for light scattering simulations, Opt. Express, 20, 16763–16776.

    Article  Google Scholar 

  • Liu, C., R. L. Panetta, P. Yang, A. Macke, and A. J. Baran, 2013: Modeling the scattering properties of mineral aerosols using concave fractal polyhedra, Appl. Opt., 52, 640–652.

    Article  Google Scholar 

  • Liu, Q. H., 1994: Transient electromagnetic modeling with the generalized k-space (GKS) method, Microwave Opt. Tech. Lett., 7, 842–848.

    Google Scholar 

  • Liu, Q. H., 1997: The PSTD algorithm: a time-domain method requiring only two cells per wavelength, Microwave Opt. Tech. Lett., 15, 158–165

    Google Scholar 

  • Liu, Q. H., 1998: The pseudospectral time-domain (PSTD) algorithm for acoustic waves in absorptive media, IEEE T. Ultrason Ferr., 45, 1044–1055.

    Article  Google Scholar 

  • Liu, Q. H., 1999: PML and PSTD algorithm for arbitrary lossy anisotropic media, IEEE Microw. Guided. W., 9, 48–50.

    Google Scholar 

  • Macke, A., J. Mueller, and E. Raschke, 1996: Single scattering properties of atmospheric ice crystals, J. Atmos. Sci., 53, 2813–2825.

    Article  Google Scholar 

  • Meng, Z., P. Yang, G. W. Kattawar, L. Bi, K. N. Liou, and I. Laszlo, 2010: Singlescattering properties of tri-axial ellipsoidal mineral dust aerosols: A database for applicationm to radiative transfer calculations, J. Aerosol. Sci., 41, 501–512.

    Article  Google Scholar 

  • Mie, G., 1908: Beitrge zur optik trber medien, speziell kolloidaler metallsungen, Ann. Phys., 25, 377–445.

    Article  Google Scholar 

  • Mishchenko, M. I., L. D. Travis, and D. W. Mackowski, 1996: T-matrix computations of light scattering by nonspherical particles: a review, J. Quant. Spectrosc. Radiat. Transfer, 55, 535–575.

    Article  Google Scholar 

  • Mishchenko, M. I., and L. D. Travis, 1998: Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers, J. Quant. Spectrosc. Radiat. Transfer, 60, 309–324.

    Article  Google Scholar 

  • Morton, K. W., and D. F. Mayers, 2005: Numerical Solution of Partial Differential Equations, Cambridge University Press.

    Google Scholar 

  • Orszag, S. A., 1972: Comparison of pseudospectral and spectral approximation, Studies in Applied Mathematics, 51, 253–259.

    Google Scholar 

  • Purcell, E. M., and C. R. Pennypacker, 1973: Scattering and absorption of light by nonspherical dielectric grains, Astrophys J., 186, 705–714.

    Article  Google Scholar 

  • Sun, W., and Q. Fu, 2000: Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices, Appl. Opt., 39, 5569–5578.

    Article  Google Scholar 

  • Tadmor, E., 1986: The exponential accuracy of Fourier and Chebyshev differencing methods, SIAM J. Numer. Anal., 23, 1–10.

    Article  Google Scholar 

  • Taflove, A., and S. C. Hagness, 2005: Computational Electrodynamics: the Finite-difference Time-domain Method, Artech House.

    Google Scholar 

  • Tian, B., and Q. H. Liu, 2000: Nonuniform fast consine transform and Chebyshev PSTD algorithms, Prog. in Electromagn. Res., 28, 253–273.

    Article  Google Scholar 

  • Trefethen, L. N., 2000: Spectral Methods in Matlab, Society for Industrial and Applied Mathematics.

    Google Scholar 

  • Umashankar, K., and A. Taflove, 1982: A novel method to analyze electromagnetic scattering of complex objects, IEEE Trans. Electromagn. Compat., 24, 397–405.

    Article  Google Scholar 

  • van de Hulst, H. C., 1957: Light Scattering by Small Particles, John Wiley.

    Google Scholar 

  • Warren, S. G., and R. E. Brandt, 2008: Optical constants of ice from the ultraviolet to the microwave: A revised compilation, J. Geophys. Res., 113, doi:10.1029/2007JD009744.

    Google Scholar 

  • Waterman, P. C., 1965: Matrix formulation of electromagnetic scattering, Proc. IEEE, 53, 805–812.

    Article  Google Scholar 

  • Waterman, P. C., 1971: Symmetry, unitarity, and geometry in electromagnetic scattering, Phys. Rev. D, 3, 825–839.

    Article  Google Scholar 

  • Yang, B., D. Gottlieb, and J. S. Hesthaven, 1997: Spectral simulation of electromagnetic wave scattering, J. Comput. Phys., 134, 216–230.

    Article  Google Scholar 

  • Yang, B., and J. S. Hesthaven, 1999: A pseudospectral method for time-domain computation of electromagnetic scattering by bodies of revolution, IEEE Trans. Antennas Propag., 47, 132–141.

    Article  Google Scholar 

  • Yang, B., and J. S. Hesthaven, 2000: Multidomain pseudospectral computation of Maxwell’s equations in 3-D general curvilinear coordinates, Applied Numerical Mathematics, 33, 281–289.

    Article  Google Scholar 

  • Yang, P., and K. N. Liou, 1996a: Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space, J. Opt. Soc. Am. A, 13, 2072–2085.

    Article  Google Scholar 

  • Yang, P., and K. N. Liou, 1996b: Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals, Appl. Opt., 35, 6568–6584.

    Article  Google Scholar 

  • Yang, P., and K. N. Liou, 1997: Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm, J. Opt. Soc. Am. A, 14, 2278–2289.

    Article  Google Scholar 

  • Yang, P., B. A. Baum, A. J. Heymsfield, Y. X. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, 2003: Single-scattering properties of droxtals, J. Quant. Spectrosc. Radiat. Transfer, 79–80, 1159–1169.

    Article  Google Scholar 

  • Yang, P., G. W. Kattawar, K. N. Liou, and J. Q. Lu, 2004: Comparison of cartesian grid configurations for application of the finite-difference time-domain method to electromagnetic scattering by dielectric particles, Appl. Opt., 43, 4611–4624.

    Article  Google Scholar 

  • Yang, P., H.Wei, H.-L. Huang, B. A. Baum, Y. X. Hu, G. W. Kattawar, M. I. Mishchenko, and Q. Fu, 2005: Scattering and absorption property database for nonspherical ice particles in the near- through far- infrared spectral region, Appl. Opt., 44, 5512–5523.

    Article  Google Scholar 

  • Yee, K. S., 1966: Numerical solution of initial boundary value problems involving Maxwell’ïs equations in isotropic media, IEEE Trans. Antennas Propag., 14, 302–307.

    Google Scholar 

  • Yurkin, M. A., A. G. Hoekstra, R. S. Brock, and J. Q. Lu, 2007a: Systematic comparison of the discrete dipole approximation and the finite difference time domain method for large dielectric scatterers, Opt. Express, 15, 17902–17911.

    Article  Google Scholar 

  • Yurkin, M. A., V. P. Maltsev, and A. G. Hoekstra, 2007b: The discrete dipole approximation for simulation of light scattering by particles much larger than the wavelength, J. Quant. Spectrosc. Radiat. Transfer, 106, 546–557.

    Article  Google Scholar 

  • Yurkin, M. A., and A. G. Hoekstra, 2007: The discrete dipole approximation: An overview and recent developments, J. Quant. Spectrosc. Radiat. Transfer, 106, 558–589.

    Article  Google Scholar 

  • Yurkin, M. A., and A. G. Hoekstra, 2011: The discrete-dipole-approximation code ADDA: Capabilities and known limitations, J. Quant. Spectrosc. Radiat. Transfer, 112, 2234–2247.

    Article  Google Scholar 

  • Zhai, P.-W., C. Li, G. W. Kattawar, and P. Yang, 2007: FDTD far-field scattering amplitudes: Comparison of surface and volume integration methods, J. Quant. Spectrosc. Radiat. Transfer, 106, 590–594.

    Article  Google Scholar 

  • Zubko, E. S., M. A. Kreslavskii, and Y. G. Shkuratov, 1999: The role of scatterers comparable to the wavelength in forming negative polarization of light, Solar Sys. Res., 33, 296–301.

    Google Scholar 

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Correspondence to R. Lee Panetta .

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Panetta, R.L., Liu, C., Yang, P. (2013). A pseudo-spectral time domain method for light scattering computation. In: Kokhanovsky, A. (eds) Light Scattering Reviews 8. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32106-1_4

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