## Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium

Applied Optics, Vol. 41, Issue 27, pp. 5728-5743 (2002)

http://dx.doi.org/10.1364/AO.41.005728

Enhanced HTML Acrobat PDF (371 KB)

### Abstract

The three-dimensional (3-D) finite-difference time-domain (FDTD) technique has been extended to simulate light scattering and absorption by nonspherical particles embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition is used to truncate the computational domain. When computing the single-scattering properties of a particle in an absorbing dielectric medium, we derive the single-scattering properties including scattering phase functions, extinction, and absorption efficiencies using a volume integration of the internal field. A Mie solution for light scattering and absorption by spherical particles in an absorbing medium is used to examine the accuracy of the 3-D UPML FDTD code. It is found that the errors in the extinction and absorption efficiencies from the 3-D UPML FDTD are less than ∼2%. The errors in the scattering phase functions are typically less than ∼5%. The errors in the asymmetry factors are less than ∼0.1%. For light scattering by particles in free space, the accuracy of the 3-D UPML FDTD scheme is similar to a previous model [Appl. Opt. 38, 3141 (1999)].

© 2002 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(010.4450) Atmospheric and oceanic optics : Oceanic optics

(010.7340) Atmospheric and oceanic optics : Water

(280.1310) Remote sensing and sensors : Atmospheric scattering

(290.5850) Scattering : Scattering, particles

(350.4990) Other areas of optics : Particles

**History**

Original Manuscript: January 22, 2002

Revised Manuscript: May 3, 2002

Published: September 20, 2002

**Citation**

Wenbo Sun, Norman G. Loeb, and Qiang Fu, "Finite-difference time-domain solution of light scattering and absorption by particles in an absorbing medium," Appl. Opt. **41**, 5728-5743 (2002)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-41-27-5728

Sort: Year | Journal | Reset

### References

- W. C. Mundy, J. A. Roux, A. M. Smith, “Mie scattering by spheres in an absorbing medium,” J. Opt. Soc. Am. 64, 1593–1597 (1974). [CrossRef]
- P. Chylek, “Light scattering by small particles in an absorbing medium,” J. Opt. Soc. Am. 67, 561–563 (1977). [CrossRef]
- C. F. Bohren, D. P. Gilra, “Extinction by a spherical particle in an absorbing medium,” J. Colloid Interface Sci. 72, 215–221 (1979). [CrossRef]
- M. Quinten, J. Rostalski, “Lorenz-Mie theory for spheres immersed in an absorbing host medium,” Part. Part. Syst. Charact. 13, 89–96 (1996). [CrossRef]
- A. N. Lebedev, M. Gartz, U. Kreibig, O. Stenzel, “Optical extinction by spherical particles in an absorbing medium: application to composite absorbing films,” Eur. Phys. J. D 6, 365–373 (1999).
- Q. Fu, W. Sun, “Mie theory for light scattering by a spherical particle in an absorbing medium,” Appl. Opt. 40, 1354–1361 (2001). [CrossRef]
- I. W. Sudiarta, P. Chylek, “Mie-scattering formalism for spherical particles embedded in an absorbing medium,” J. Opt. Soc. Am. A 18, 1275–1278 (2001). [CrossRef]
- I. W. Sudiarta, P. Chylek, “Mie scattering efficiency of a large spherical particle embedded in an absorbing medium,” J. Quant. Spectrosc. Radiat. Transfer 70, 709–714 (2001). [CrossRef]
- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
- A. Taflove, M. E. Brodwin, “Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell’s equations,” IEEE Trans. Microwave Theory Tech. MTT-23, 623–630 (1975). [CrossRef]
- R. Holland, “Finite-difference time domain (FDTD) analysis of magnetic diffusion,” IEEE Trans. Electromagn. Compat. 36, 32–39 (1994). [CrossRef]
- P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995). [CrossRef]
- P. Yang, K. N. Liou, “Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space,” J. Opt. Soc. Am. A 13, 2072–2085 (1996). [CrossRef]
- W. Sun, Q. Fu, Z. Chen, “Finite-difference time-domain solution of light scattering by dielectric particles with a perfectly matched layer absorbing boundary condition,” Appl. Opt. 38, 3141–3151 (1999). [CrossRef]
- P. Yang, K. N. Liou, M. I. Mishchenko, B. C. Gao, “Efficient finite-difference time-domain scheme for light scattering by dielectric particles: applications to aerosols,” Appl. Opt. 39, 3727–3737 (2000). [CrossRef]
- W. Sun, Q. Fu, “Finite-difference time-domain solution of light scattering by dielectric particles with large complex refractive indices,” Appl. Opt. 39, 5569–5578 (2000). [CrossRef]
- J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
- D. S. Katz, E. T. Thiele, A. Taflove, “Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FD-TD meshes,” IEEE Microwave Guid. Wave Lett. 4, 268–270 (1994). [CrossRef]
- J. P. Berenger, “Three-dimensional perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 127, 363–379 (1996). [CrossRef]
- A. Taflove, S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time Domain Method, 2nd ed. (Artech House, Boston, Mass., 2000).
- Z. S. Sacks, D. M. Kingsland, R. Lee, J. F. Lee, “A perfectly matched anisotropic absorber for use as an absorbing boundary condition,” IEEE Trans. Antennas Propag. 43, 1460–1463 (1995). [CrossRef]
- M. I. Mishchenko, J. W. Hovenier, L. D. Travis, Light Scattering by Nonspherical Particles (Academic, New York, 2000).
- B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves,” Math. Comput. 31, 629–651 (1971).
- A. Bayliss, E. Turkel, “Radiation boundary conditions for wavelike equations,” Commun. Pure Appl. Math. 33, 707–725 (1980). [CrossRef]
- G. Mur, “Absorbing boundary condition for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981). [CrossRef]
- Z. Liao, H. L. Wong, B. Yang, Y. Yuan, “A transmitting boundary for transient wave analyses,” Sci. Sin. 27, 1063–1076 (1984).
- R. L. Higdon, “Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation,” Math. Comput. 47, 437–459 (1986).
- C. E. Reuter, R. M. Joseph, E. T. Thiele, D. S. Katz, T. Taflove, “Ultrawideband absorbing boundary condition for termination of wave guide structures in FD-TD simulations,” IEEE Microwave Guid. Wave Lett. 4, 344–346 (1994). [CrossRef]
- D. M. Sullivan, “A simplified PML for use with the FDTD method,” IEEE Microwave Guid. Wave Lett. 6, 97–99 (1996). [CrossRef]
- D. E. Merewether, R. Fisher, F. W. Smith, “On implementing a numeric Huygen’s source in a finite difference program to illustrate scattering bodies,” IEEE Trans. Nucl. Sci. NS-27, 1829–1833 (1980). [CrossRef]
- K. Umashanker, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EMC-24, 397–405 (1982). [CrossRef]
- A. Taflove, Computational Electrodynamics: the Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).
- S. D. Gedney, “An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices,” IEEE Trans. Antennas Propag. 44, 1630–1639 (1996). [CrossRef]
- C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
- G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2438 (1988). [CrossRef] [PubMed]
- G. Lazzi, O. P. Gandhi, “On the optimal design of the PML absorbing boundary condition for the FDTD code,” IEEE Trans. Antennas Propag. 45, 914–916 (1996). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

### Figures

Fig. 1 |
Fig. 2 |
Fig. 3 |

Fig. 4 |
Fig. 5 |
Fig. 6 |

Fig. 7 |
Fig. 8 |
Fig. 9 |

Fig. 10 |
Fig. 11 |
Fig. 12 |

Fig. 13 |
Fig. 14 |
Fig. 15 |

« Previous Article | Next Article »

OSA is a member of CrossRef.