OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 46, Iss. 7 — Mar. 1, 2007
  • pp: 1150–1156

Modeling light scattered from and transmitted through dielectric periodic structures on a substrate

Wenbo Sun, Gorden Videen, Bing Lin, and Yongxiang Hu  »View Author Affiliations

Applied Optics, Vol. 46, Issue 7, pp. 1150-1156 (2007)

View Full Text Article

Enhanced HTML    Acrobat PDF (438 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Light scattering and transmission by rough surfaces are of considerable interest in a variety of applications including remote sensing and characterization of surfaces. In this work, the finite-difference time-domain technique is applied to calculate the scattered and transmitted electromagnetic fields of an infinite periodic rough surface. The elements of the Mueller matrix for scattered light are calculated by an integral of the near fields over a significant number of periods of the surface. The normalized Mueller matrix elements of the scattered light and the spatial distribution of the transmitted flux for a monolayer of micrometer-sized dielectric spheres on a silicon substrate are presented. The numerical results show that the nonzero Mueller matrix elements for scattering from a surface consisting of a monolayer of dielectric spheres on a silicon substrate have specific maxima at some scattering angles. These maxima may be used in the characterization of features of the surface. For light transmitted through the monolayer of spheres, our results show that the transmitted energy focuses around the ray passing through centers of the spheres. At other locations, the transmitted flux is very small. Therefore, micrometer-sized dielectric spheres might be placed on a semiconductor surface to burn nanometer-sized holes in a layer using laser pulses. The method may also be useful in the assembly of periodic microstructures on surfaces.

© 2007 Optical Society of America

OCIS Codes
(220.4000) Optical design and fabrication : Microstructure fabrication
(240.5770) Optics at surfaces : Roughness
(290.5880) Scattering : Scattering, rough surfaces

Original Manuscript: July 5, 2006
Revised Manuscript: October 19, 2006
Manuscript Accepted: October 19, 2006
Published: February 12, 2007

Wenbo Sun, Gorden Videen, Bing Lin, and Yongxiang Hu, "Modeling light scattered from and transmitted through dielectric periodic structures on a substrate," Appl. Opt. 46, 1150-1156 (2007)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. L. Schuler, J.-S. Lee, D. Kasilingam, and G. Nesti, "Surface roughness and slope measurements using polarimetric SAR data," IEEE Trans. Geosci. Remote Sens. 40, 687-698 (2002). [CrossRef]
  2. S. Gomez, K. Hale, J. Burrows, and B. Griffiths, "Measurements of surface defects on optical components," Meas. Sci. Technol. 9, 607-616 (1998). [CrossRef]
  3. H. Lin and J. Zhu, "Characterization of nanocrystalline silicon films," Proc. SPIE 4700, 354-356 (2002).
  4. H. Budiarto and J. Takada, The Electromagnetic Wave Scattering from Building Surfaces for the Mobile Propagation Modeling, ITE Technical Report 25 (ITE, 2001), pp. 7-11.
  5. Lord Rayleigh, The Theory of Sound (MacMillan, 1896).
  6. U. Fano, "The theory of anomalous diffraction gratings and of quasi-stationary waves on metallic surfaces (Sommerfeld's waves)," J. Opt. Soc. Am. 31, 213-222 (1941). [CrossRef]
  7. S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351-378 (1951). [CrossRef]
  8. S. O. Rice, Reflection of EM from Slightly Rough Surfaces (Interscience, 1963).
  9. C. Eckart, "The scattering of sound from the sea surface," J. Acoust. Soc. Am. 25, 66-570 (1953). [CrossRef]
  10. H. Davies, "The reflection of electromagnetical waves from rough surfaces," Proc. Inst. Electr. Eng. 101, 209-214 (1954).
  11. P. Beckmann and A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  12. A. K. Fung and G. W. Pan, "An integral equation method for rough surface scattering," in Proceedings of the International Symposium on Multiple Scattering of Waves in Random Media and Random Surfaces (1986), pp. 701-714.
  13. A. K. Fung, Z. Li, and K. S. Chen, "Backscattering from a randomly rough dielectric surface," IEEE Trans. Geosci. Remote Sens. 30, 356-369 (1992). [CrossRef]
  14. A. K. Fung, Microwave Scattering and Emission Models and Their Applications (Artech House, 1994).
  15. L. Tsang, J. A. Kong, K. H. Ding, and C. O. Ao, Scattering of Electromagnetic Waves: Numerical Simulations (Wiley, 2001). [CrossRef]
  16. M. Saillard and A. Sentenac, "Rigorous solutions for electromagnetic scattering from rough surfaces," Waves Random Media 11, 103-137 (2001). [CrossRef]
  17. P. P. Silvester and R. L. Ferrari, Finite Elements for Electrical Engineers (Cambridge U. Press, 1990).
  18. J. M. Jin, The Finite Element Method in Electromagnetics (Wiley, 1993).
  19. 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).
  20. K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics (CRC Press, 1993).
  21. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
  22. C. Y. Hsieh, A. K. Fung, G. Nesti, A. J. Siber, and P. Coppo, "A further study of the IEM surface scattering model," IEEE Trans. Geosci. Remote Sens. 35, 901-909 (1997). [CrossRef]
  23. A. K. Fung, Z. Li, and K. S. Chen, "An improved IEM model for bistatic scattering from rough surfaces," J. Electromagn. Waves Appl. 16, 689-702 (2002). [CrossRef]
  24. K. S. Chen, T. D. Wu, and A. K. Fung, "A study of backscattering from multiscale rough surface," J. Electromagn. Waves Appl. 12, 961-979 (1998). [CrossRef]
  25. F. Mattia, "Backscattering properties of multi-scale rough surfaces," J. Electromagn. Waves Appl. 13, 493-527 (1999). [CrossRef]
  26. C. H. Chan, S. H. Lou, L. Tsang, and J. A. Kong, "Electromagnetic scattering of waves by rough surfaces: a finite-difference time-domain approach," Microwave Opt. Technol. Lett. 4, 355-359 (1991). [CrossRef]
  27. A. K. Fung, M. R. Shah, and S. Tjuatja, "Numerical simulation of scattering from three-dimensional randomly rough surfaces," IEEE Trans. Geosci. Remote Sens. 32, 986-994 (1994). [CrossRef]
  28. F. D. Hastings, J. B. Schneider, and S. L. Broschat, "A Monte-Carlo FDTD technique for rough surface scattering," IEEE Trans. Antennas Propag. 43, 1183-1191 (1995).
  29. R. J. Luebbers and C. Penney, "Scattering from apertures in infinite ground planes using FDTD," IEEE Trans. Antennas Propag. 42, 731-736 (1994). [CrossRef]
  30. K. Demarest, R. Plumb, and Z. Huang, "FDTD modeling of scatterers in stratified media," IEEE Trans. Antennas Propag. 43, 1164-1168 (1995). [CrossRef]
  31. P. B. Wong, G. L. Tyler, J. E. Baron, E. M. Gurrola, and R. A. Simpson, "A three-wave FDTD approach to surface scattering with applications to remote sensing of geophysical surfaces," IEEE Trans. Antennas Propag. 44, 504-513 (1996). [CrossRef]
  32. F. Moreno, F. Gonzalez, J. M. Saiz, P. J. Valle, and D. L. Jordan, "Experimental study of copolarized light scattering by spherical metallic particles on conducting flat substrates," J. Opt. Soc. Am. A 10, 141-149 (1993). [CrossRef]
  33. J. Mullins, "The stuff of beams," New Sci. 190, 44-47 (2006).
  34. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field," J. Opt. Soc. Am. A 23, 2324-2330 (2006). [CrossRef]
  35. T. M. Grzegorczyk, B. A. Kemp, and J. A. Kong, "Stable optical trapping based on optical binding forces," Phys. Rev. Lett. 96, 113903 (2006). [CrossRef] [PubMed]
  36. Z. S. Sacks, D. M. Kingsland, R. Lee, and J.-F. Lee, "A perfectly matched anisotropic absorber for use as an absorbing boundary condition," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995). [CrossRef]
  37. S. D. Gedney, "An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices," IEEE Trans. Antennas Propag. 44, 1630-1639 (1996). [CrossRef]
  38. D. E. Merewether, R. Fisher, and 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]
  39. K. Umashanker and A. Taflove, "A novel method to analyze electromagnetic scattering of complex objects," IEEE Trans. Electromagn. Compat. EMC-24, 397-405 (1982). [CrossRef]
  40. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  41. P. Yang and 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]
  42. W. Sun, N. G. Loeb, and Q. Fu, "Finite-difference time domain solution of light scattering and absorption by particles in an absorbing medium," Appl. Opt. 41, 5728-5743 (2002). [CrossRef] [PubMed]

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.

CrossCheck Deposited