## Implementing the near- to far-field transformation in the finite-difference time-domain method

Applied Optics, Vol. 43, Issue 18, pp. 3738-3746 (2004)

http://dx.doi.org/10.1364/AO.43.003738

Enhanced HTML Acrobat PDF (357 KB)

### Abstract

When the finite-difference time-domain (FDTD) method is applied to light-scattering computations, the far fields can be obtained by means of integrating the near fields either over the volume bounded by the particle’s surface or on a regular surface encompassing the scatterer. For light scattering by a sphere, the accurate near-field components on the FDTD-staggered meshes can be computed from the rigorous Lorenz-Mie theory. We investigate the errors associated with these near- to far-field transform methods for a canonical scattering problem associated with spheres. For a scatterer with a small refractive index, the surface-integral approach is more accurate than its volume counterpart for computation of the phase functions and extinction efficiencies; however, the volume-integral approach is more accurate for computation of other scattering matrix elements, such as *P*_{12}, *P*_{33}, and *P*_{43}, especially for backscattering. If a large refractive index is involved, the results computed from the volume-integration method become less accurate, whereas the surface method still retains the same order of accuracy as in the situation for the small refractive index.

© 2004 Optical Society of America

**OCIS Codes**

(010.1290) Atmospheric and oceanic optics : Atmospheric optics

(010.1310) Atmospheric and oceanic optics : Atmospheric scattering

(010.3920) Atmospheric and oceanic optics : Meteorology

(280.1310) Remote sensing and sensors : Atmospheric scattering

(290.1090) Scattering : Aerosol and cloud effects

(290.5850) Scattering : Scattering, particles

**History**

Original Manuscript: October 28, 2003

Revised Manuscript: March 25, 2004

Published: June 20, 2004

**Citation**

Peng-Wang Zhai, Yong-Keun Lee, George W. Kattawar, and Ping Yang, "Implementing the near- to far-field transformation in the finite-difference time-domain method," Appl. Opt. **43**, 3738-3746 (2004)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-43-18-3738

Sort: Year | Journal | Reset

### References

- K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. 14, 302–307 (1966). [CrossRef]
- K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. 24, 397–405 (1982). [CrossRef]
- A. Taflove, S. C. Hagness, Computational Electromagnetics, 2nd ed. (Artech House, Boston, Mass., 2000).
- K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).
- S. A. Schelkunoff, Electromagnetic Waves (Van Nostrand, New York, 1943).
- C. L. Britt, “Solution of electromagnetic scattering problems using time domain techniques,” IEEE Trans. Antennas Propag. 37, 1181–1191 (1989). [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 nonspherical particles,” in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, S. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 2000), Chap. 7, pp. 173–221. [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]
- S. C. Hill, G. Videen, W. Sun, Q. Fu, “Scattering and internal fields of a microsphere that contains a saturable absorber: finite-difference time-domain simulations,” Appl. Opt. 40, 5487–5494 (2001). [CrossRef]
- P. J. Flatau, G. L. Stephens, B. T. Draine, “Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the Block-Toeplitz structure,” J. Opt. Soc. Am. A 7, 593–600 (1990). [CrossRef]
- B. T. Draine, P. J. Flatau, “Discrete-dipole approximation for calculation,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
- G. H. Goedecke, S. G. O’Brien, “Scattering by irregular inhomogeneous particles via the digitized Green’s function algorithm,” Appl. Opt. 27, 2431–2437 (1988). [CrossRef] [PubMed]
- T. Wriedt, U. Comberg, “Comparison of computational scattering method,” J. Quant. Spectrosc. Radiat. Transfer 60, 411–423 (1998). [CrossRef]
- M. I. Mishchenko, L. D. Travis, A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, Cambridge, UK, 2002).
- F. M. Kahnert, “Numerical methods in electromagnetic scattering theory,” J. Quant. Spectrosc. Radiat. Transfer 79–80, 775–824 (2003). [CrossRef]
- M. I. Mishchenko, L. D. Travis, “Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation,” Appl. Opt. 33, 7206–7225 (1994). [CrossRef] [PubMed]
- T. Wriedt, “Using the T-matrix method for light scattering computations by nonaxisymmetric particles: superellipsoids and realistically shaped particles,” Part. Part. Syst. Charact. 19, 256–268 (2002). [CrossRef]
- A. J. Baran, P. Yang, S. Havemann, “Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods,” Appl. Opt. 40, 4376–4386 (2001). [CrossRef]
- G. Mie, “Beigrade zur optik truber medien, speziell kolloidaler metallosungen,” Ann. Phys. (Leipzig) 25, 377–455 (1908).
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
- C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
- P. Yang, B.-C. Gao, W. J. Wiscombe, M. I. Mishchenko, S. E. Platnick, H.-L. Huang, B. A. Baum, Y. X. Hu, D. M. Winker, S.-C. Tsay, S. K. Park, “Inherent and apparent scattering properties of coated or uncoated spheres embedded in an absorbing host medium,” Appl. Opt. 41, 2740–2759 (2002). [CrossRef] [PubMed]
- W. J. Wiscombe, “Mie scattering calculation,” NCAR Tech. Note TN-140+STR (National Center for Atmospheric Research, Boulder, Colo., 1979).
- W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). [CrossRef] [PubMed]
- 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]

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.