Abstract

The model of two-dimensional (2-D) guided-wave photonic band-gap structures based on the Bloch-Floquet theory is proposed for the first time for both infinite and finite length devices. The efficient computation of dispersion curves and field distribution is carried out in very short computer time. Both guided and radiated modes can be easily identified to give a physical insight, even in defective structures. The accuracy of the model has been tested through the design of a very compact narrow-band 2-D guided-wave photonic band-gap filter at 1.55 µm. The filter has a channel isolation of 22 dB, a large number of channel (>80) with a channel spacing of 50 GHz, and a very short length (24 µm).

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  2. M. Loncar, T. Yoshie, A. Scherer, P. Gogna and Y. Qiu, "Low-threshold photonic crystal laser", Appl. Phys. Lett., vol. 81, no. 15, pp. 2680-2682, 2002.
  3. T. D. Happ, A. Markard, M. Kamp, A. Forchel, S. Anand, J.-L. Gentner and N. Bouadma, "Nanofabrication of two-dimensional photonic crystal mirrors for 1.5 µ m short cavity lasers", J. Vacuum Sci. Technol. B, vol. 19, no. 6, pp. 2775-2778, 2001.
  4. A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs", Phys. Rev. B, vol. 62, no. 7, pp. 4488 -4492, 2000.
  5. D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue and R. Baets, "A compact two-dimensional grating coupler used as a polarization splitter", Photon. Technol. Lett., vol. 15, no. 9, pp. 1249-1251, Sep. 2003.
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  30. E. Popov and M. Nevière, "Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: New theoretical approaches", J. Opt. Soc. Amer. B, vol. 11, no. 9, pp. 1555-1564, 1994.
  31. S. T. Peng, T. Tamir and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., vol. MTT-23, no. 1, pp. 123-133, Jan. 1975.
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  33. V. M. N. Passaro, R. Diana and M. N. Armenise, "Optical fiber Bragg gratings. Part I: Modeling of infinitely long gratings", J. Opt. Soc. Amer. A, vol. 19, no. 9, pp. 1844-1854, 2002.
  34. A. Giorgio, A. G. Perri and M. N. Armenise, "Modeling of fully etched waveguiding photonic bandgap structures", J. Quant. Electron., vol. 38, no. 6, pp. 630-639, Jun. 2002.
  35. K. Sakoda, "Transmittance and Bragg reflectivity of two-dimensional photonic lattices", Phys. Rev. B, vol. 52, no. 12, pp. 8992-9002, 1995.
  36. W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs", Photon. Technol. Lett., vol. 13, no. 6, pp. 565-567, Jun. 2001.
  37. M. G. Moharam, E. B. Grann and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings", J. Opt. Soc. Amer. A, vol. 12, no. 5, pp. 1068-1076, 1995.
  38. 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. Amer. A, vol. 12, no. 5, pp. 1077-1085, 1995.
  39. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings", J. Opt. Soc. Amer. A, vol. 13, no. 5, pp. 1024-1035, 1996.
  40. S. F. Mahmoud and J. C. Real, "Scattering of surface waves at dielectric discontinuity on a planar waveguide", Trans. Microwave Theory Tech., vol. MTT-23, no. 2, pp. 193-198, Feb. 1975.
  41. M. Zelsmann, E. Picard, T. Charvolin, E. Hadji, B. Dal'zotto, M. E. Nier, C. Seassal, P. Rojo-Romeo and X. Letartre, "Transmission spectroscopy of photonic crystals in a silicon-on-insulator waveguide structure", Appl. Phys. Lett. , vol. 81, no. 13, pp. 2340-2342, 2002.
  42. C. Ciminelli, F. Peluso, V. M. N. Passaro and M. N. Armenise, "Angular response of narrow band 2D-PBG guided wave filters", Microresonators as Building Blocks for VLSI Photonics, vol. 709, pp. 439-440, 2004.
  43. D. J. Ripin, K. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen and L. A. Kolodziejski, "One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides", J. Lightwave Technol., vol. 17, no. 11, pp. 2152-2160, Nov. 1999.
  44. W. Bogaerts, P. Bienstman and R. Baets, "Scattering at sidewall roughness in photonic crystal slabs", Opt. Lett., vol. 28, no. 9, 2003.
  45. T. Suzuki and P. K. L. Yu, "Tunneling in photonic band structures", J. Opt. Soc. Amer. B, vol. 12, no. 5, pp. 804-820, 1995.
  46. D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdrè, U. Oesterle, D. Cassagne and C. Jouanin, "Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths", Phys. Rev. Lett., vol. 79, no. 21, pp. 4147-4150, 1997.
  47. D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdrè, U. Oesterle and V. Bardinal, "Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices", J. Quant. Electron., vol. 35, no. 7, Jul. 1999.
  48. M. Rattier, H. Benisty, C. J. M. Smith, A. Beraud, D. Cassagne, C. Jouanin, T. F. Krauss and C. Weisbuch, "Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry-Pérot resonators", J. Quant. Electron., vol. 37, no. 2, Feb. 2001.
  49. D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, V. Bardinal and U. Oesterle, "Demonstration of cavity mode between two-dimensional photonic-crystal mirrors", Electron. Lett., vol. 33, no. 23, pp. 1978-1980, 1997.
  50. C. J. M. Smith, R. M. De La Rue, H. Benisty, U. Oesterle, T. F. Krauss, D. Labilloy, C. Weisbuch and R. Houdrè, "In-plane microcavity resonators with two-dimensional photonic bandgap mirrors", Proc. Optoelectron. , vol. 145, no. 6, pp. 373-378, 1998.
  51. R. Ferrini, D. Leuenberger, M. Mulot, M. Qiu, J. Moosburger, M. Kamp, A. Forchel, S. Anand and R. Houdrè, "Optical study of two-dimensional InP-based photonic crystals by internal light source technique", J. Quant. Electron., vol. 38, no. 7, pp. 786-799, Jul. 2002.

Other (51)

M. Rattier, T. F. Krauss, J.-F. Carlin, R. Stanley, U. Oesterle, R. Houdrè, C. J. M. Smith, R. M. De La Rue, H. Benisty and C. Weisbuch, "High extraction efficiency, laterally injected, light emitting diodes combining microcavities and photonic crystals", Opt. Quantum Electron., vol. 34, pp. 79-89, 2002.

M. Loncar, T. Yoshie, A. Scherer, P. Gogna and Y. Qiu, "Low-threshold photonic crystal laser", Appl. Phys. Lett., vol. 81, no. 15, pp. 2680-2682, 2002.

T. D. Happ, A. Markard, M. Kamp, A. Forchel, S. Anand, J.-L. Gentner and N. Bouadma, "Nanofabrication of two-dimensional photonic crystal mirrors for 1.5 µ m short cavity lasers", J. Vacuum Sci. Technol. B, vol. 19, no. 6, pp. 2775-2778, 2001.

A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs", Phys. Rev. B, vol. 62, no. 7, pp. 4488 -4492, 2000.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue and R. Baets, "A compact two-dimensional grating coupler used as a polarization splitter", Photon. Technol. Lett., vol. 15, no. 9, pp. 1249-1251, Sep. 2003.

K. Agi, M. Mojahedi, B. Minhas, E. Schamiloglu and K. J. Malloy, "The effects of an electromagnetic crystal substrate on a microstrip patch antenna", Trans. Antennas Propagat., vol. 50, no. 4, pp. 451-456, Apr. 2002.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs", Phys. Rev. B, vol. 60, no. 8, pp. 5751-5758, 1999.

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals", Appl. Phys. Lett., vol. 81, no. 7, pp. 1163-1165, 2002.

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Norwood, MA: Artech House, 1995.

B. D'Urso, O. Painter, J. O'Brien, T. Tombrello, A. Yariv and A. Scherer, "Modal reflectivity in finite-depth two-dimensional photonic-crystal microcavities", J. Opt. Soc. Amer. B, vol. 15, no. 3, pp. 1155-1159, 1998.

M. Boroditsky, R. Coccioli and E. Yablonovitch, "Analysis of photonic crystals for light emitting diodes using the finite differences time domain technique", in Proc. SPIE, vol. 3283, 1998, pp. 184- 190.

A. J. Ward and J. B. Pendry, "A program for calculating photonic band structures, Green's functions and transmission/reflection coefficients using a nonorthogonal FDTD method", Comp. Phys. Commun., vol. 128, pp. 590-621, 2000.

D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt, Eds. Finite Elements-Theory and Application, New York: Springer-Verlag, 1986.

J.-K. Hwang, S.-B. Hyum, H.-Y. Ryu and Y.-H. Lee, "Resonant modes of two-dimensional photonic bandgap cavities determined by the finite-element method and by use of the anisotropic perfectly matched layer boundary conditions", J. Opt. Soc. Amer. B, vol. 15, no. 8, pp. 2316-2324, 1998.

J. B. Pendry, "Photonic band structures", J. Modern Opt., vol. 41, no. 2, pp. 209-229, 1994.

B. Gralak, S. Enoch and G. Tayeb, "Anomalous refractive properties of photonic crystals", J. Opt. Soc. Amer. A, vol. 17, no. 6, pp. 1012-1020, 2000.

J. Yonekura, M. Ikeda and T. Baba, "Analysis of finite 2-D photonic crystals of columns and lightwave devices using the scattering matrix method", J. Lightwave Technol., vol. 17, no. 8, pp. 1500-1508, Aug. 1999.

E. Centeno and D. Felbacq, "Rigorous vector diffraction of electromagnetic waves by bidimensional photonic crystals", J. Opt. Soc. Amer. A, vol. 17, no. 2, pp. 1-8, 2000.

G. Sztefka and H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps", Photon. Technol. Lett. , vol. 5, no. 5, pp. 554-557, 1993.

J. Ctyroky, S. Helfert and R. Pregla, "Analysis of a deep waveguide Bragg grating", Opt. Quant. Electron., vol. 30, no. 5/6, pp. 343-358, 1998.

S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis", Opt. Express, vol. 8, no. 3, pp. 173-190, 2001.

M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice", Phys. Rev. B, vol. 44, no. 16, pp. 8565-8571, 1991.

F. Ramos-Mendieta and P. Halevi, "Electromagnetic surface modes of a dielectric superlattice: The supercell method", J. Opt. Soc. Amer. B, vol. 14, no. 2, pp. 370-381, 1997.

S. Kuchinsky, D. C. Allan, N. F. Borrelli and J. C. Cotteverte, "3D localization in a channel waveguide in a photonic crystal with 2D periodicity", Opt. Commun., vol. 175, pp. 147-152, 2000.

M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction", J. Opt. Soc. Amer. , vol. 71, no. 7, pp. 811-818, 1981.

S. Peng and G. M. Morris, "Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings", J. Opt. Soc. Amer. A, vol. 12, no. 5, pp. 1087-1096, 1995.

D. M. Whittaker and I. S. Culshaw, "Scattering-matrix treatment of patterned multilayer photonic structures", Phys. Rev. B, vol. 60, no. 4, pp. 2610-2618, 1999.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs", Phys. Rev. B, vol. 66, p. 45102, 2002.

E. Silberstein, P. Lalanne, J.-P. Hugonin and Q. Cao, "Use of grating theories in integrated optics", J. Opt. Soc. Amer. A, vol. 18, no. 11, pp. 2865-2875, 2001.

E. Popov and M. Nevière, "Surface-enhanced second-harmonic generation in nonlinear corrugated dielectrics: New theoretical approaches", J. Opt. Soc. Amer. B, vol. 11, no. 9, pp. 1555-1564, 1994.

S. T. Peng, T. Tamir and H. L. Bertoni, "Theory of periodic dielectric waveguides", Trans. Microwave Theory Tech., vol. MTT-23, no. 1, pp. 123-133, Jan. 1975.

V. M. N. Passaro and M. N. Armenise, "Analysis of radiation loss in grating-assisted codirectional couplers", J. Quant. Electron., vol. 31, no. 9, pp. 1691-1697, Sep. 1995.

V. M. N. Passaro, R. Diana and M. N. Armenise, "Optical fiber Bragg gratings. Part I: Modeling of infinitely long gratings", J. Opt. Soc. Amer. A, vol. 19, no. 9, pp. 1844-1854, 2002.

A. Giorgio, A. G. Perri and M. N. Armenise, "Modeling of fully etched waveguiding photonic bandgap structures", J. Quant. Electron., vol. 38, no. 6, pp. 630-639, Jun. 2002.

K. Sakoda, "Transmittance and Bragg reflectivity of two-dimensional photonic lattices", Phys. Rev. B, vol. 52, no. 12, pp. 8992-9002, 1995.

W. Bogaerts, P. Bienstman, D. Taillaert, R. Baets and D. De Zutter, "Out-of-plane scattering in photonic crystal slabs", Photon. Technol. Lett., vol. 13, no. 6, pp. 565-567, Jun. 2001.

M. G. Moharam, E. B. Grann and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings", J. Opt. Soc. Amer. A, vol. 12, no. 5, pp. 1068-1076, 1995.

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. Amer. A, vol. 12, no. 5, pp. 1077-1085, 1995.

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings", J. Opt. Soc. Amer. A, vol. 13, no. 5, pp. 1024-1035, 1996.

S. F. Mahmoud and J. C. Real, "Scattering of surface waves at dielectric discontinuity on a planar waveguide", Trans. Microwave Theory Tech., vol. MTT-23, no. 2, pp. 193-198, Feb. 1975.

M. Zelsmann, E. Picard, T. Charvolin, E. Hadji, B. Dal'zotto, M. E. Nier, C. Seassal, P. Rojo-Romeo and X. Letartre, "Transmission spectroscopy of photonic crystals in a silicon-on-insulator waveguide structure", Appl. Phys. Lett. , vol. 81, no. 13, pp. 2340-2342, 2002.

C. Ciminelli, F. Peluso, V. M. N. Passaro and M. N. Armenise, "Angular response of narrow band 2D-PBG guided wave filters", Microresonators as Building Blocks for VLSI Photonics, vol. 709, pp. 439-440, 2004.

D. J. Ripin, K. Lim, G. S. Petrich, P. R. Villeneuve, S. Fan, E. R. Thoen, J. D. Joannopoulos, E. P. Ippen and L. A. Kolodziejski, "One-dimensional photonic bandgap microcavities for strong optical confinement in GaAs and GaAs/AlxOy semiconductor waveguides", J. Lightwave Technol., vol. 17, no. 11, pp. 2152-2160, Nov. 1999.

W. Bogaerts, P. Bienstman and R. Baets, "Scattering at sidewall roughness in photonic crystal slabs", Opt. Lett., vol. 28, no. 9, 2003.

T. Suzuki and P. K. L. Yu, "Tunneling in photonic band structures", J. Opt. Soc. Amer. B, vol. 12, no. 5, pp. 804-820, 1995.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdrè, U. Oesterle, D. Cassagne and C. Jouanin, "Quantitative measurement of transmission, reflection and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths", Phys. Rev. Lett., vol. 79, no. 21, pp. 4147-4150, 1997.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, D. Cassagne, C. Jouanin, R. Houdrè, U. Oesterle and V. Bardinal, "Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices", J. Quant. Electron., vol. 35, no. 7, Jul. 1999.

M. Rattier, H. Benisty, C. J. M. Smith, A. Beraud, D. Cassagne, C. Jouanin, T. F. Krauss and C. Weisbuch, "Performance of waveguide-based two-dimensional photonic-crystal mirrors studied with Fabry-Pérot resonators", J. Quant. Electron., vol. 37, no. 2, Feb. 2001.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, V. Bardinal and U. Oesterle, "Demonstration of cavity mode between two-dimensional photonic-crystal mirrors", Electron. Lett., vol. 33, no. 23, pp. 1978-1980, 1997.

C. J. M. Smith, R. M. De La Rue, H. Benisty, U. Oesterle, T. F. Krauss, D. Labilloy, C. Weisbuch and R. Houdrè, "In-plane microcavity resonators with two-dimensional photonic bandgap mirrors", Proc. Optoelectron. , vol. 145, no. 6, pp. 373-378, 1998.

R. Ferrini, D. Leuenberger, M. Mulot, M. Qiu, J. Moosburger, M. Kamp, A. Forchel, S. Anand and R. Houdrè, "Optical study of two-dimensional InP-based photonic crystals by internal light source technique", J. Quant. Electron., vol. 38, no. 7, pp. 786-799, Jul. 2002.

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