## Comparative study of the modeling of three-dimensional photonic bandgap structures

JOSA A, Vol. 20, Issue 4, pp. 644-654 (2003)

http://dx.doi.org/10.1364/JOSAA.20.000644

Acrobat PDF (591 KB)

### Abstract

A comparative study of theoretical models of different three-dimensional photonic bandgap (3D-PBG) structures has been performed, taking into account instability and convergence problems. Some rules for solving these problems and for reducing the computational time by finding symmetries in the structures are also explained. Finally, some applications produced by defects in 3D structures are shown by studying the creation of a complete bandgap in one of them and the variation of partial bandgaps in several 3D-PBG structures when several parameters of the defects, such as the number of layers stacked at each side of the defect, its thickness, and the real and imaginary parts of its index of refraction, are changed.

© 2003 Optical Society of America

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(050.1950) Diffraction and gratings : Diffraction gratings

(050.1960) Diffraction and gratings : Diffraction theory

(050.2770) Diffraction and gratings : Gratings

(080.2730) Geometric optics : Matrix methods in paraxial optics

(260.2110) Physical optics : Electromagnetic optics

**Citation**

Ignacio R. Matias, Ignacio Del Villar, Francisco J. Arregui, and Richard O. Claus, "Comparative study of the modeling of three-dimensional photonic bandgap structures," J. Opt. Soc. Am. A **20**, 644-654 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-4-644

Sort: Year | Journal | Reset

### References

- J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, Princeton, N.J., 1995).
- 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).
- J. Tervo, M. Kuittinen, P. Vahimaa, J. Turunen, T. Aalto, P. Heimala, and M. Leppilhalme, “Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffers’s star product,” Opt. Commun. 198, 265–272 (2001).
- P. R. Villeneuve, D. S. Abrams, S. Fan, and J. D. Jonannopoulos, “Single-mode waveguide microcavity for fast optical switching,” Opt. Lett. 21, 2017–2019 (1996).
- P. Tran, “Optical switching with a nonlinear photonic crystal: a numerical study,” Opt. Lett. 21, 1138–1140 (1996).
- J. Broeng, D. Mogilevstev, S. E. Barkou, and A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
- R. W. Ziolkowski and T. Liang, “Design and characterization of a grating-assisted coupler enhanced by a photonic-band-gap structure for effective wavelength-division demultiplexing,” Opt. Lett. 22, 1033–1035 (1997).
- J. T. Daly, A. C. Greenwald, E. A. Johnson, W. A. Stevenson, J. A. Wollam, T. George, and E. W. Jones, “Nanostructured surfaces for tuned infrared emission for spectroscopic applications,” in Micro- and Nano-photonic Materials and Devices, J. W. Perry and A. Scherer, eds., Proc. SPIE 3937, 80–91 (2000).
- J. B. Pendry and A. MacKinnon, “Calculation of photon dispersion relation,” Phys. Rev. Lett. 69, 2772–2775 (1992).
- N. P. K. Cotter, T. W. Preist, and J. R. Sambles, “Scattering-matrix approach to multilayer diffraction,” J. Opt. Soc. Am. A 12, 1097–1103 (1995).
- W. C. Tan, T. W. Preist, J. R. Sambles, M. B. Sobnack, and N. P. Wanstall, “Calculation of photonic band structures of periodic multilayer grating systems by use of curvilinear coordinate transformation,” J. Opt. Soc. Am. A 15, 2365–2372 (1998).
- 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).
- L. Li and J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” J. Opt. Soc. Am. A 13, 2247–2255 (1996).
- H. Y. D. Yang, “Finite difference analysis of 2-D photonic crystals,” IEEE Trans. Microwave Theory Tech. 44, 2688–2695 (1996).
- L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184–1189 (1993).
- V. Bagnoud and S. Mainguy, “Diffraction of electromagnetic waves by dielectric crossed gratings: a three-dimensional Rayleigh–Fourier solution,” J. Opt. Soc. Am. A 16, 1277–1285 (1999).
- M. Bagieu and D. Maystre, “Waterman and Rayleigh methods for diffraction grating problems: extension of the convergence domain,” J. Opt. Soc. Am. A 15, 1566–1576 (1998).
- M. Bagieu and D. Maystre, “Regularized Waterman and Rayleigh methods: extension to two-dimensional gratings,” J. Opt. Soc. Am. A 16, 284–292 (1999).
- M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
- E. Noponen and J. Turunen, “Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles,” J. Opt. Soc. Am. A 11, 2494–2502 (1994).
- P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A 14, 1592–1598 (1997).
- L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997).
- N. Chateau and J. P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321–1331 (1994).
- M. G. Moharam, D. A. Pommet, and E. B. Grann, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
- F. Montiel, M. Nevière, and P. Peyrot, “Waveguide confinement of Cerenkov second-harmonic generation through a graded-index grating coupler: electromagnetic optimization,” J. Mod. Opt. 45, 2169–2186 (1998).
- L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
- F. Montiel and M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity though the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 11, 3241–3250 (1994).
- P. Lalanne, “Convergence performance of the coupled wave and the differential methods for thin gratings,” J. Opt. Soc. Am. A 14, 1583–1591 (1997).
- P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
- M. M. Sigalas, R. Biswas, C. T. Chan, and K. M. Ho, “Electromagnetic-wave propagation through dispersive and absorptive photonic-band-gap materials,” Phys. Rev. B 49, 11080–11087 (1994).
- L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
- 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).
- P. Lalanne and D. Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43, 2063–2085 (1996).
- P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed-binary subwavelength gratings with efficiencies larger than those of conventional échelette gratings,” Opt. Lett. 23, 1081–1083 (1998).
- P. Lalanne and D. Lalanne, “Depth dependence of the effective properties of subwavelength gratings,” J. Opt. Soc. Am. A 14, 450–458 (1997).
- E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993).

## 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.