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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 40–49

Analysis of semi-infinite periodic structures using a domain reduction technique

Arya Fallahi and Christian Hafner  »View Author Affiliations


JOSA A, Vol. 27, Issue 1, pp. 40-49 (2010)
http://dx.doi.org/10.1364/JOSAA.27.000040


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Abstract

A new boundary condition is introduced to calculate the effective impedance matrix of semi-infinite periodic structures such as photonic crystals and metamaterials, which leads to a reduction of the solution space. The obtained effective impedance matrix allows one to relate a matrix to a PC, which includes all of its properties in terms of reflection from its interface. For one-dimensional photonic crystals or multilayer films, it is shown that a closed-form equation can be found for the effective impedance. For two-dimensional photonic crystals the impedance is obtained using the scattering matrices by solving a unilateral quadratic matrix equation. Several examples are outlined to validate the developed scheme. In the examples, the goal is mainly the computation of the reflection from a semi-infinite periodic structure when a plane wave illuminates its boundary.

© 2009 Optical Society of America

OCIS Codes
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(160.3918) Materials : Metamaterials
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Diffraction and Gratings

History
Original Manuscript: August 27, 2009
Revised Manuscript: October 28, 2009
Manuscript Accepted: November 5, 2009
Published: December 7, 2009

Citation
Arya Fallahi and Christian Hafner, "Analysis of semi-infinite periodic structures using a domain reduction technique," J. Opt. Soc. Am. A 27, 40-49 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-1-40


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References

  1. C. Caloz and T. Itoh, Electromagnetic Metamaterials Transmission Line Theory and Microwave Applications (Wiley, 2006).
  2. N. Engheta and R. W. Ziolkowski, Metamaterials Physics and Engineering Explorations (Wiley2006).
  3. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals Molding the Flow of Light, 2nd ed. (Princeton Univ. Press, 2008).
  4. K.Busch, S.Lölkes, R.B.Wehrspohn, and H.Föll, eds., Photonic Crystals Advances in Design Fabrication and Characterization (Wiley-VCH, 2004).
  5. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef]
  6. S. John, “Strong localization of photons in certain disordered dieletric superlattices,” Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef]
  7. E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagnetic waves: negative refraction by photonic crystals,” Nature 423, 604-605 (2003). [CrossRef]
  8. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002). [CrossRef]
  9. Y. A. Vlasov, M. O'Boyle, H. F. Hamann, and S. J. McNab, “Active control of slow light on a chip with PC waveguides,” Nature 438, 65-69 (2005). [CrossRef]
  10. S. G. Johnson, P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Linear waveguides in photonic-crystal slabs,” Phys. Rev. B 62, 8212-8222 (2000). [CrossRef]
  11. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Design of PC microcavities for cavity qed,” Phys. Rev. B 65, 016608 (2001).
  12. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998). [CrossRef]
  13. K. B. Chung and S. W. Hong, “Wavelength demultiplexers based on the superprism phenomena in photonic crystals,” Appl. Phys. Lett. 81, 1549-1551 (2002). [CrossRef]
  14. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003). [CrossRef]
  15. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779-6782 (1998). [CrossRef]
  16. F.-R. Yang, K.-P. Ma, Y. Qian, and T. Itoh, “A uniplanar compact photonic-bandgap (UC-PBG) structure and its applications for microwave circuit,” IEEE Trans. Microwave Theory Tech. 47, 1509-1514 (1999). [CrossRef]
  17. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702-2712 (2002). [CrossRef]
  18. T.K.Wu, ed., Frequency Selective Surface and Grid Array (Wiley, 1995).
  19. B. A. Munk, Frequency Selective Surfaces Theory and Design (Wiley, 2000).
  20. D. L. Jaggard, A. R. Mickelson, and C. H. Papas, “On electromagnetic waves in chiral media,” Appl. Phys. A 18, 211-216 (1979).
  21. C. Hafner, “Mmp computation of periodic structures,” J. Opt. Soc. Am. A 12, 1057-1067 (1995). [CrossRef]
  22. D. D. Karkashadze, F. G. Bogdanov, R. S. Zaridze, A. Y. Bijamov, C. Hafner, and D. Erni, “Simulation of Finite Photonic Crystals Made of Biisotropic or Chiral Material,” in Advances in Electromagnetics of Complex Media and Metamaterials NATO Science Series. II. Mathematics, Physics and Chemistry (2003), Vol. 89, pp. 175-193.
  23. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581-2591 (1993). [CrossRef]
  24. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
  25. A. Fallahi, K. Z. Aghaie, A. Enayati, and M. Shahabadi, “Diffraction analysis of periodic structures using a transmission-line formulation: principles and applications,” J. Comput. Theor. Nanosci. 4, 649-666 (2007).
  26. A. Fallahi, M. Mishrikey, C. Hafner, and R. Vahldieck, “Analysis of multilayer frequency selective surfaces on periodic and anisotropic substrates,” Metamaterials 3, 63-74 (2009). [CrossRef]
  27. K.Yasumoto, ed., Electromagnetic Theory and Applications for Photonic Crystals (Taylor & Francis, Fukuoka, Japan, 2006).
  28. P. Dansas and N. Paraire, “Fast modeling of photonic bandgap structures by use of a diffraction-grating approach,” J. Opt. Soc. Am. A 15, 1586-1598 (1998). [CrossRef]
  29. L. C. Botten, N. A. Nicorovici, R. C. McPhedran, C. M. de Sterke, and A. A. Asatryan, “Photonic band structure calculations using scattering matrices,” Phys. Rev. E 64, 046603 (2001). [CrossRef]
  30. Y.-C. Hsue and T.-J. Yang, “Applying a modified plane-wave expansion method to the calculations of transmittivity and reflectivity of a semi-infinite PC,” Phys. Rev. E 70, 016706 (2004). [CrossRef]
  31. B. Momeni, A. A. Eftekhar, and A. Adibi, “Effective impedance model for analysis of reflection at the interfaces of photonic crystals,” Opt. Lett. 32, 778-780 (2007). [CrossRef]
  32. B. Momeni, M. Badieirostami, and A. Adibi, “Accurate and efficient techniques for the analysis of reflection at the interfaces of three-dimensional photonic crystals,” J. Opt. Soc. Am. B 24, 2957-2963 (2007). [CrossRef]
  33. Z.-Y. Li and K.-M. Ho, “Light propagation in semi-infinite photonic crystals and related waveguide structures,” Phys. Rev. B 68, 155101 (2003). [CrossRef]
  34. W. Jiang, R. T. Chen, and X. Lu, “Theory of light refraction at the surface of a PC,” Phys. Rev. B 71, 245115 (2005). [CrossRef]
  35. F. Montiel and M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the r-matrix propagation algorithm,” J. Opt. Soc. Am. A 11, 3241-3250 (1994). [CrossRef]
  36. E. Popov and M. Nevière, “Grating theory: new equations in fourier space leading to fast converging results for tm polarization,” J. Opt. Soc. Am. A 17, 1773-1784 (2000). [CrossRef]
  37. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024-1035 (1996). [CrossRef]

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