D. Boffi, M. Conforti, L. Gastaldi, "Modified edge finite elements for photonic crystals," Numer. Math. 105, 249-266 (2006).

L. C. Botten, R. A. Hansen, C. M. de Sterke, "Supermodes in multiple coupled photonic crystal waveguides," Opt. Express 14, 387-396 (2006).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Discrete negative refraction in photonic crystal waveguide arrays," Opt. Lett. 31, 1343-1345 (2006).

C. C. Chen, C. Y. Chen, W. K. Wang, F. H. Huang, C. K. Lin, W. Y. Chiu, Y. J. Chan, "Photonic crystal directional couplers formed by InAlGaAs nano-rods," Opt. Express 13, 38-43 (2005).

G. Chen, J. U. Kang, "Waveguide mode converter based on two-dimensional photonic crystals," Opt. Lett. 30, 1656-1658 (2005).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Diffraction engineering in arrays of photonic crystal waveguides," Opt. Lett. 30, 2894-2896 (2005).

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal
couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

F. S. S. Chien, Y. J. Hsu, W. F. Hsieh, S. C. Cheng, "Dual wavelength demultiplexing by coupling and decoupling of photonic crystal waveguides
," Opt. Express 12, 1119-1125 (2004).

C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, R. C. McPhedran, "Modes of coupled photonic crystal waveguides," Opt. Lett. 29, 1384-1386 (2004).

I. Park, H. S. Lee, H. J. Kim, K. M. Moon, S. G. Lee, B. H. O, S. G. Park, E. H. Lee, "Photonic crystal power-splitter based on directional coupling," Opt. Express 12, 3599-3604 (2004).

H. J. Kim, I. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, "Self-imaging phenomena in multi-mode photonic crystal line-defect waveguides: Application to
wavelength de-multiplexing," Opt. Express 12, 5625-5633 (2004).

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, M. Mansuripur, "Multimode interference-based photonic crystal waveguide power splitter," J. Lightw. Technol. 22, 2842-2846 (2004).

M. Tokushima, H. Yamada, Y. Arakawa, "1.5-μm-wavelength light guiding in waveguides in
square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, H. I. Smith, "Guiding 1.5 μm in photonic crystals based on
dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).

A. Martinez, J. Garcia, G. Sanchez, J. Marti, "Planar photonic crystal structure with inherently single-mode waveguides," J. Opt. Soc. Amer. B, Opt. Phys. 20, 2131-2136 (2003).

A. Martinez, F. Cuesta, J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003).

M. Thorhauge, L. H. Frandsen, P. I. Borel, "Efficient photonic crystal directional couplers," Opt. Lett. 28, 1525-1527 (2003).

V. V. Poborchii, T. Tada, T. Kanayama, "Si pillar photonic crystal slab with linear defects: Transmittance and waveguide properties
," Opt. Commun. 210, 285-290 (2002).

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides
," IEEE J. Quantum Electron. 38, 47-53 (2002).

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic
crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 66, 066608 (2002).

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, R. Baets, "Fabrication of photonic crystals in silicon-on-insulator using 248-nm deep UV lithography
," IEEE J. Sel. Topics Quantum Electron. 8, 928-934 (2002).

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, D. Nedeljkovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum. Electron. 38, 1349-1352 (2002).

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).

M. Lončar, T. Doll, J. Vučković, A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightw. Technol. 18, 1402-1411 (2000).

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the
substrate," Appl. Phys. Lett. 76, 532-534 (2000).

S. G. Johnson, P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B, Condens. Matter 62, 8212-8222 (2000).

H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, S. Forrest, "Fabrication of ultracompact 3-dB 2 × 2 MMI power
splitters," IEEE Photon. Technol. Lett. 11, 1009-1011 (1999).

T. F. Krauss, R. M. De La Rue, "Photonic crystals in the optical regime-past, present and future," Prog. Quantum Electron. 23, 51-96 (1999).

P. Ciarlet, J. Zou, "Fully discrete finite element approaches for time-dependent Maxwell's equations," Numer. Math. 82, 193-219 (1999).

D. Boffi, P. Fernandes, L. Gastaldi, I. Perugia, "Computational models of electromagnetic resonators: Analysis of edge element approximation
," SIAM J. Numer. Anal. 36, 1264-1290 (1999).

K. S. Komisarek, N. N. Wang, A. K. Dominek, R. Hann, "An investigation of new FETD/ABC methods of computation of scattering from three-dimensional
material objects," IEEE Trans. Antennas Propag. 47, 1579-1585 (1999).

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).

J. Lee, R. Lee, A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propag. 45, 430-442 (1997).

L. B. Soldano, E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications
," J. Lightw. Technol. 13, 615-627 (1995).

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightw. Technol. 10, 1843-1850 (1992).

J. C. Nedelec, "Mixed finite elements in ${\bf R}^{3}$," Numer. Math. 35, 315-341 (1980).

M. Tokushima, H. Yamada, Y. Arakawa, "1.5-μm-wavelength light guiding in waveguides in
square-lattice-of-rod photonic crystal slab," Appl. Phys. Lett. 84, 4298-4300 (2004).

S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, H. I. Smith, "Guiding 1.5 μm in photonic crystals based on
dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: Positive role of the
substrate," Appl. Phys. Lett. 76, 532-534 (2000).

S. Boscolo, M. Midrio, C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides
," IEEE J. Quantum Electron. 38, 47-53 (2002).

T. Kamalakis, T. Sphicopoulos, "Numerical study of the implications of size nonuniformities in the performance of photonic crystal
couplers using coupled mode theory," IEEE J. Quantum Electron. 41, 863-871 (2005).

S. Kuchinsky, V. Y. Golyatin, A. Y. Kutikov, T. P. Pearsall, D. Nedeljkovic, "Coupling between photonic crystal waveguides," IEEE J. Quantum. Electron. 38, 1349-1352 (2002).

W. Bogaerts, V. Wiaux, D. Taillaert, S. Beckx, B. Luyssaert, P. Bienstman, R. Baets, "Fabrication of photonic crystals in silicon-on-insulator using 248-nm deep UV lithography
," IEEE J. Sel. Topics Quantum Electron. 8, 928-934 (2002).

A. Martinez, F. Cuesta, J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003).

D. S. Levy, K. H. Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, S. Forrest, "Fabrication of ultracompact 3-dB 2 × 2 MMI power
splitters," IEEE Photon. Technol. Lett. 11, 1009-1011 (1999).

J. Lee, R. Lee, A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propag. 45, 430-442 (1997).

K. S. Komisarek, N. N. Wang, A. K. Dominek, R. Hann, "An investigation of new FETD/ABC methods of computation of scattering from three-dimensional
material objects," IEEE Trans. Antennas Propag. 47, 1579-1585 (1999).

T. Liu, A. R. Zakharian, M. Fallahi, J. V. Moloney, M. Mansuripur, "Multimode interference-based photonic crystal waveguide power splitter," J. Lightw. Technol. 22, 2842-2846 (2004).

M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers
," J. Lightw. Technol. 19, 1970-1975 (2001).

M. Lončar, T. Doll, J. Vučković, A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightw. Technol. 18, 1402-1411 (2000).

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightw. Technol. 10, 1843-1850 (1992).

L. B. Soldano, E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: Principles and applications
," J. Lightw. Technol. 13, 615-627 (1995).

A. Martinez, J. Garcia, G. Sanchez, J. Marti, "Planar photonic crystal structure with inherently single-mode waveguides," J. Opt. Soc. Amer. B, Opt. Phys. 20, 2131-2136 (2003).

J. C. Nedelec, "Mixed finite elements in ${\bf R}^{3}$," Numer. Math. 35, 315-341 (1980).

D. Boffi, M. Conforti, L. Gastaldi, "Modified edge finite elements for photonic crystals," Numer. Math. 105, 249-266 (2006).

P. Ciarlet, J. Zou, "Fully discrete finite element approaches for time-dependent Maxwell's equations," Numer. Math. 82, 193-219 (1999).

V. V. Poborchii, T. Tada, T. Kanayama, "Si pillar photonic crystal slab with linear defects: Transmittance and waveguide properties
," Opt. Commun. 210, 285-290 (2002).

H. J. Kim, I. Park, B. H. O, S. G. Park, E. H. Lee, S. G. Lee, "Self-imaging phenomena in multi-mode photonic crystal line-defect waveguides: Application to
wavelength de-multiplexing," Opt. Express 12, 5625-5633 (2004).

I. Park, H. S. Lee, H. J. Kim, K. M. Moon, S. G. Lee, B. H. O, S. G. Park, E. H. Lee, "Photonic crystal power-splitter based on directional coupling," Opt. Express 12, 3599-3604 (2004).

C. C. Chen, C. Y. Chen, W. K. Wang, F. H. Huang, C. K. Lin, W. Y. Chiu, Y. J. Chan, "Photonic crystal directional couplers formed by InAlGaAs nano-rods," Opt. Express 13, 38-43 (2005).

S. G. Johnson, J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis
," Opt. Express 8, 173-190 (2001).

F. S. S. Chien, Y. J. Hsu, W. F. Hsieh, S. C. Cheng, "Dual wavelength demultiplexing by coupling and decoupling of photonic crystal waveguides
," Opt. Express 12, 1119-1125 (2004).

L. C. Botten, R. A. Hansen, C. M. de Sterke, "Supermodes in multiple coupled photonic crystal waveguides," Opt. Express 14, 387-396 (2006).

M. Thorhauge, L. H. Frandsen, P. I. Borel, "Efficient photonic crystal directional couplers," Opt. Lett. 28, 1525-1527 (2003).

G. Chen, J. U. Kang, "Waveguide mode converter based on two-dimensional photonic crystals," Opt. Lett. 30, 1656-1658 (2005).

C. M. de Sterke, L. C. Botten, A. A. Asatryan, T. P. White, R. C. McPhedran, "Modes of coupled photonic crystal waveguides," Opt. Lett. 29, 1384-1386 (2004).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Diffraction engineering in arrays of photonic crystal waveguides," Opt. Lett. 30, 2894-2896 (2005).

A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Discrete negative refraction in photonic crystal waveguide arrays," Opt. Lett. 31, 1343-1345 (2006).

D. Christodoulides, R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).

S. G. Johnson, P. R. Villeneuve, S. Fan, J. D. Joannopoulos, "Linear waveguides in photonic-crystal slabs," Phys. Rev. B, Condens. Matter 62, 8212-8222 (2000).

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic
crystals," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top. 66, 066608 (2002).

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).

H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).

T. F. Krauss, R. M. De La Rue, "Photonic crystals in the optical regime-past, present and future," Prog. Quantum Electron. 23, 51-96 (1999).

D. Boffi, P. Fernandes, L. Gastaldi, I. Perugia, "Computational models of electromagnetic resonators: Analysis of edge element approximation
," SIAM J. Numer. Anal. 36, 1264-1290 (1999).

A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton Univ. Press, 1995).