Fourier factorization with complex polarization bases in the plane-wave expansion method applied to two-dimensional photonic crystals

Optics Express

Volumn 18, Issue 26, 2010, Pages 27511-27524

  Antos, Roman ^a   Veis, Martin ^a  

^a CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

FACTORIZATION; HOLMIUM; LASER OPTICS; PHOTONIC DEVICES; POLARIZATION; TWO DIMENSIONAL;

ARBITRARY CROSS SECTION; COMPLETE CONTINUITY; CONVERGENCE PROPERTIES; ELLIPTIC POLARIZATION; FOURIER FACTORIZATION; NORMAL VECTOR; PERIODIC ELEMENTS; PHOTONIC CRYSTAL WAVEGUIDE; PLANE WAVE EXPANSION METHOD; POLARIZATION TRANSFORMS; TWO-DIMENSIONAL PHOTONIC CRYSTALS;

PHOTONIC CRYSTALS;

ARTICLE; CRYSTALLIZATION; FOURIER ANALYSIS; LIGHT; METHODOLOGY; PHOTON; RADIATION SCATTERING; REFRACTOMETRY; SURFACE PLASMON RESONANCE;

CRYSTALLIZATION; FOURIER ANALYSIS; LIGHT; PHOTONS; REFRACTOMETRY; SCATTERING, RADIATION; SURFACE PLASMON RESONANCE;

EID: 78650539697     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.18.027511     Document Type: Article

References (41)

1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ., 1995).
2. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
3. K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
4. J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, "Photonic crystals: Putting a new twist on light," Nature 386, 143-149 (1997).
5. S.-Y. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, "Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal," Science 282, 274-276 (1998).
6. S. Noda, "Recent progresses and future prospects of two- and three-dimensional photonic crystals," J. Lightwave Technol. 24, 4554-4567 (2006).
7. J. P. Hugonin, P. Lalanne, T. P. White, and T. F. Krauss, "Coupling into slow-mode photonic crystal waveguides," Opt. Lett. 32, 2638-2640 (2007).
8. S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, "Effective dielectric constant of periodic composite structures," Phys. Rev. B 48, 14936-14943 (1993).
9. F. Genereux, S.W. Leonard, H. M. van Driel, A. Birner, and U. Gosele, "Large birefringence in two-dimensional silicon photonic crystals," Phys. Rev. B 63, 161101 (2001).
10. A. A. Krokhin, P. Halevi, and J. Arriaga, "Long-wavelength limit (homogenization) for two-dimensional photonic crystals," Phys. Rev. B 65, 115208 (2002).
11. E. Reyes, A. A. Krokhin, and J. Roberts, "Effective dielectric constants of photonic crystal of aligned anisotropic cylinders and the optical response of a periodic array of carbon nanotubes," Phys. Rev. B 72, 155118 (2005).
12. N. Skivesen, A. Tetu, M. Kristensen, J. Kjems, L. H. Frandsen, and P. I. Borel, "Photonic-crystal waveguide biosensor," Opt. Express 15, 3169-3176 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-6- 3169.
13. I. D. Block, N. Ganesh, M. Lu, and B. T. Cunningham, "Sensitivity model for predicting photonic crystal biosensor performance," IEEE Sens. J. 8, 274-280 (2008).
14. 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).
15. A. A. Krokhin and E. Reyes, "Homogenization of magnetodielectric photonic crystals," Phys. Rev. Lett. 93, 023904 (2004).
16. H. Benisty, "Dark modes, slow modes, and coupling in multimode systems," J. Opt. Soc. Am. B 26, 718-724 (2009).
17. P. Vukusic and J. R. Sambles, "Photonic structures in biology," Nature 424, 852-855 (2003).
18. S. Kinoshita and S. Yoshioka, "Structural colors in nature: The role of regularity and irregularity in the structure," ChemPhysChem 6, 1442-1459 (2005).
19. R. Petit (ed.), Electromagnetic Theory of Gratings (Springer, Berlin, 1980).
20. M. Neviere and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, New York, 2003).
21. D. Maystre, "Rigorous vector theories of diffraction gratings," Prog. Opt. 21, 1-67 (1984).
22. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
23. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
24. E. Popov and M. Neviere, "Grating theory: new equations in Fourier space leading to fast converging results for TM polarization," J. Opt. Soc. Am. A 17, 1773-1784 (2000).
25. L. Li, "Reformulation of the Fourier modal method for surface-relief gratings made with anisotropic materials," J. Mod. Opt. 45, 1313-1334 (1998).
26. B. Chernov, M. Neviere, and E. Popov, "Fast Fourier factorization method applied to modal analysis of slanted lamellar diffraction gratings in conical mountings," Opt. Commun. 194, 289-297 (2001).
27. K. Watanabe, R. Petit, and M. Neviere, "Differential theory of gratings made of anisotropic materials," J. Opt. Soc. Am. A 19, 325-334 (2002).
28. K. Watanabe, "Numerical integration schemes used on the differential theory for anisotropic gratings," J. Opt. Soc. Am. A 19, 2245-2252 (2002).
29. L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A 5, 345-355 (2003).
30. P. Boyer, E. Popov, M. Neviere, and G. Tayeb, "Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section," J. Opt. Soc. Am. A 21, 2146-2153 (2004).
31. N. Bonod, E. Popov, and M. Neviere, "Light transmission through a subwavelength microstructured aperture: electromagnetic theory and applications," Opt. Commun. 245, 355-361 (2005).
32. N. Bonod, E. Popov, and M. Neviere, "Fourier factorization of nonlinear Maxwell equations in periodic media: application to the optical Kerr effect," Opt. Commun. 244, 389-398 (2005).
33. A. David, H. Benisty, and C. Weisbuch, "Fast factorization rule and plane-wave expansion method for twodimensional photonic crystals with arbitrary hole-shape," Phys. Rev. B 73, 075107 (2006).
34. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, andW. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Am. A 24, 2880-2890 (2007).
35. P. Gotz, T. Schuster, K. Frenner, S. Rafler, and W. Osten, "Normal vector method for the RCWA with automated vector field generation," Opt. Express 16, 17295-17301 (2008), http://www.opticsinfobase.org/oe/abstract.cfm? URI=oe-16-22-17295.
36. R. Antos, "Fourier factorization with complex polarization bases in modeling optics of discontinuous bi-periodic structures," Opt. Express 17, 7269-7274 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9- 7269.
37. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North Holland, Amsterdam, 1997).
38. S. Mahmoodian, C. G. Poulton, K. B. Dossou, R. C. McPhedran, L. C. Botten, and C. M. de Sterke, "Modes of shallow photonic crystal waveguides: semi-analytic treatment," Opt. Express 17, 19629-19643 (2009), http: //www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-22-19629.
39. S. Mahmoodian, R. C. McPhedran, C. M. de Sterke, K. B. Dossou, C. G. Poulton, and L. C. Botten, "Single and coupled degenerate defect modes in two-dimensional photonic crystal band gaps," Phys. Rev. A 79, 013814 (2009).
40. K. B. Dossou, C. G. Poulton, L. C. Botten, S. Mahmoodian, R. C. McPhedran, and C. M. de Sterke, "Modes of symmetric composite defects in two-dimensional photonic crystals," Phys. Rev. A 80, 013826 (2009).
41. S. Visnovsky and K. Yasumoto, "Multilayer anisotropic bi-periodic diffraction gratings," Czech. J. Phys. 51, 229-247 (2001).