OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 19, Iss. 10 — Oct. 1, 2002
  • pp: 2005–2017

Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations

Chung-Hsiang Lin, K. Ming Leung, and Theodor Tamir  »View Author Affiliations


JOSA A, Vol. 19, Issue 10, pp. 2005-2017 (2002)
http://dx.doi.org/10.1364/JOSAA.19.002005


View Full Text Article

Acrobat PDF (330 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The scattering of waves by multilayered periodic structures is formulated in three-dimensional space by using Fourier expansions for both the basic lattice and its associated reciprocal lattice. The fields in each layer are then expressed in terms of characteristic modes, and the complete solution is found rigorously by using a transmission-line representation to address the pertinent boundary-value problems. Such an approach can treat periodic arbitrary lattices containing arbitrarily shaped dielectric components, which may generally be absorbing and have biaxial properties along directions that are parallel or perpendicular to the layers. We illustrate the present approach by comparing our numerical results with data reported in the past for simple structures. In addition, we provide new results for more complex configurations, which include multiple periodic regions that contain absorbing uniaxial components with several possible canonic shapes and high dielectric constants.

© 2002 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(230.1950) Optical devices : Diffraction gratings
(230.5160) Optical devices : Photodetectors

Citation
Chung-Hsiang Lin, K. Ming Leung, and Theodor Tamir, "Modal transmission-line theory of three-dimensional periodic structures with arbitrary lattice configurations," J. Opt. Soc. Am. A 19, 2005-2017 (2002)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-10-2005


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. P. Vincent, “A finite-difference method for dielectric and conducting crossed gratings,” Opt. Commun. 26, 293–296 (1978).
  2. D. Maystre and M. Nevière, “Electromagnetic theory of crossed gratings,” J. Opt. (Paris) 9, 301–306 (1978).
  3. G. H. Derrick, R. C. McPhedran, D. Maystre, and M. Nevière, “Crossed gratings: a theory and its applications,” Appl. Phys. 18, 39–52 (1979).
  4. R. C. McPhedran, G. H. Derrick, and L. C. Botten, “Theory of crossed gratings,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, New York, 1980), pp. 227–276.
  5. M. G. Moharam, “Coupled-wave analysis of two-dimensional dielectric gratings,” in Holographic Optics: Design and Applications, I. Cindrich, ed., Proc. SPIE 883, 8–11 (1988).
  6. S. T. Han, Y.-L. Tsao, R. M. Wasler, and M. F. Becker, “Electromagnetic scattering of two-dimensional surface-relief dielectric gratings,” Appl. Opt. 31, 2343–2352 (1992).
  7. P. Bräuer and O. Bryngdahl, “Electromagnetic diffraction analysis of two-dimensional gratings,” Opt. Commun. 100, 1–5 (1993).
  8. E. Noponen and J. Turunen, “Eigenmode method for electromagnetic three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994).
  9. E. B. Grann, M. G. Moharam, and D. A. Pommet, “Artificial uniaxial and biaxial dielectrics with use of two-dimensional subwavelength binary gratings,” J. Opt. Soc. Am. A 11, 2695–2703 (1994).
  10. E. B. Grann and M. G. Moharam, “Comparison between continuous and discrete subwave-length grating structures for antireflection surfaces,” J. Opt. Soc. Am. A 13, 988–992 (1996).
  11. S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13, 993–1005 (1996).
  12. J. B. Harris, T. W. Preist, J. R. Sambles, R. N. Thorpe and R. A. Watts, “Optical response of bigratings,” J. Opt. Soc. Am. A 13, 2041–2049 (1996).
  13. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997).
  14. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
  15. M. Bagieu and D. Maystre, “Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings,” J. Opt. Soc. Am. A 16, 284–292 (1999).
  16. V. Bagnoud and S. Mainguy, “Diffraction of electromagnetic waves by dielectric cross gratings: a three-dimensional Rayleigh–Fourier solution,” J. Opt. Soc. Am. A 16, 1277–1285 (1999).
  17. E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886–2894 (2001).
  18. E. Popov and M. Nevière, “Arbitrary shaped periodic anisotropic media: new presentation of Maxwell’s equations in the truncated Fourier space,” in Physics, Theory, and Applications of Periodic Structures in Optics, P. Lalanne, ed., Proc. SPIE 4438, 19–30 (2001).
  19. G. Granet and J. P. Plumey, “Rigorous electromagnetic analysis of 2D resonant subwavelength metallic gratings by parametric Fourier-modal analysis,” in Physics, Theory, and Applications of Periodic Structures in Optics, P. Lalanne, ed., Proc. SPIE 4438, 124–131 (2001).
  20. L. Li, “Fourier modal method for crossed anisotropic gratings,” in Physics, Theory, and Applications of Periodic Structures in Optics, P. Lalanne, ed., Proc. SPIE 4438, 132–142 (2001).
  21. K. M. Leung and C.-H. Lin, “Modal transmission-line theory of photonic band-gap structures,” in Proceedings of the 8th Asia–Pacific Physics Conference (World Scientific, Singapore, 2001), pp. 397–402.
  22. C.-H. Lin, “Modal transmission-line theory of photonic band-gap structures,” Ph.D. dissertation (Polytechnic University, Brooklyn, N.Y., 2001).
  23. C.-H. Lin, K. M. Leung, M. Jiang, and T. Tamir, “Modal transmission-line theory of composite periodic structures: II. Three-dimensional configurations,” in Proceedings of the 2001 URSI International Symposium on Electromagnetic Theory (Union Radio-Scientifique Internationale, Ghent, Belgium, 2001), pp. 335–337.
  24. L. Yan, M. Jiang, T. Tamir, and K. K. Choi, “Electromagnetic modeling of quantum-well photodetectors containing diffractive elements,” IEEE J. Quantum Electron. 35, 1870–1877 (1999).
  25. M. Jiang, T. Tamir, and S. Zhang, “Modal theory of diffraction by multilayered gratings containing dielectric and metallic components,” J. Opt. Soc. Am. A 18, 807–820 (2001).
  26. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, Pa., 1976).
  27. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
  28. T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
  29. K. K. Choi, The Physics of Quantum Well Infrared Photodetectors (World Scientific, Singapore, 1997).
  30. J. Mao, A. Majumdar, K. K. Choi, D. C. Tsui, K. M. Leung, C. H. Lin, T. Tamir, and G. A. Vawter, “Light coupling mechanism of quantum grid infrared photodetectors,” Appl. Phys. Lett. 80, 868–870 (2002).

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