OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 44, Iss. 9 — Mar. 21, 2005
  • pp: 1650–1656

Application of the symplectic finite-difference time-domain method to light scattering by small particles

Peng-Wang Zhai, George W. Kattawar, Ping Yang, and Changhui Li  »View Author Affiliations


Applied Optics, Vol. 44, Issue 9, pp. 1650-1656 (2005)
http://dx.doi.org/10.1364/AO.44.001650


View Full Text Article

Enhanced HTML    Acrobat PDF (192 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A three-dimensional fourth-order finite-difference time-domain (FDTD) program with a symplectic integrator scheme has been developed to solve the problem of light scattering by small particles. The symplectic scheme is nondissipative and requires no more storage than the conventional second-order FDTD scheme. The total-field and scattered-field technique is generalized to provide the incident wave source conditions in the symplectic FDTD (SFDTD) scheme. The perfectly matched layer absorbing boundary condition is employed to truncate the computational domain. Numerical examples demonstrate that the fourth-order SFDTD scheme substantially improves the precision of the near-field calculation. The major shortcoming of the fourth-order SFDTD scheme is that it requires more computer CPU time than a conventional second-order FDTD scheme if the same grid size is used. Thus, to make the SFDTD method efficient for practical applications, one needs to parallelize the corresponding computational code.

© 2005 Optical Society of America

History
Original Manuscript: August 31, 2004
Manuscript Accepted: November 3, 2004
Published: March 20, 2005

Citation
Peng-Wang Zhai, George W. Kattawar, Ping Yang, and Changhui Li, "Application of the symplectic finite-difference time-domain method to light scattering by small particles," Appl. Opt. 44, 1650-1656 (2005)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-9-1650


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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).
  2. K. R. Umashankar, A. Taflove, “A novel method to analyze electromagnetic scattering of complex objects,” IEEE Trans. Electromagn. Compat. EC-24, 397–405 (1982). [CrossRef]
  3. A. Taflove, S. C. Hagness, Computational Electromagnetics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).
  4. K. S. Kunz, R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, Boca Raton, Fla., 1993).
  5. 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]
  6. 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]
  7. 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]
  8. P. Yang, K. N. Liou, “Finite-difference time-domain method for light scattering by nonspherical and inhomogeneous 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), pp. 173–221. [CrossRef]
  9. 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]
  10. 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]
  11. K. L. Shlager, J. B. Schneider, “Comparison of the dispersion properties of several low-dispersion finite-difference time-domain algorithms,” IEEE Trans. Antennas Propag. 51, 642–653 (2003). [CrossRef]
  12. J. Fang, “Time domain finite difference computation for Maxwell’s equations,” Ph.D. dissertation (Department of Electrical Engineering, University of California at Berkeley, Berkeley, Calif., 1989).
  13. T. Deveze, L. Beaulieu, W. Tabbara, “A fourth order scheme for the FDTD algorithm applied to Maxwell’s equations,” in Proceedings of the 1992 International IEEE Antennas and Propagation Society Symposium (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1992), pp. 346–349. [CrossRef]
  14. C. W. Manry, S. L. Broschat, J. B. Schneider, “Higher-order FDTD methods for large problems,” Appl. Comput. Electromagn. Soc. J. 10, 17–29 (1995).
  15. J. L. Young, D. Gaitonde, J. S. Shang, “Toward the construction of a fourth-order difference scheme for transient EM wave simulation: staggered grid approach,” IEEE Trans. Antennas Propag. 45, 1573–1580 (1997). [CrossRef]
  16. M. Suzuki, “Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulation,” Phys. Lett. A 146, 319–323 (1990). [CrossRef]
  17. H. Yoshida, “Construction of higher order symplectic integrators,” Phys. Lett. A 150, 262–268 (1990). [CrossRef]
  18. M. Suzuki, “General theory of fractal path integrals with applications to many-body theories and statistical physics,” J. Math. Phys. Lett. 32, 400–407 (1991). [CrossRef]
  19. T. Hirono, W. W. Lui, K. Yokoyama, “Time-domain simulation of electromagnetic field using a symplectic integrator,” IEEE Microwave Guid. Wave Lett. 7, 279–281 (1997). [CrossRef]
  20. I. Saitoh, Y. Suzuki, N. Takahashi, “The symplectic finite difference time domain method,” IEEE Trans. Magn. 37, 3251–3254 (2001). [CrossRef]
  21. T. Hirono, W. Lui, S. Seki, Y. Yoshikuni, “A three-dimensional fourth-order finite-difference time-domain scheme using a symplectic integrator propagator,” IEEE Trans. Microwave Theory Tech. 49, 1640–1648 (2001). [CrossRef]
  22. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic field equations,” IEEE Trans. Electromagn. Compat. EC-23, 377–382 (1981). [CrossRef]
  23. Ref. 3, pp. 175–233.
  24. P.-W. Zhai, Y.-K. Lee, G. W. Kattawar, P. Yang, “Implementing the near- to far-field transformation in the finite-difference time-domain method,” Appl. Opt. 43, 3738–3746 (2004). [CrossRef] [PubMed]
  25. J.-P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
  26. T. Hirono, W. W. Lui, S. Seki, “Successful applications of PML-ABC to the symplectic FDTD scheme with 4th-order accuracy in time and space,” in Vol. 3 of Microwave Symposium Digest, 1999 IEEE MTT-S International (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1999), pp. 1293–1296. [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
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited