Abstract

Light propagation in multimode photonic crystal (PC) waveguides and in arrays of single-mode PC waveguides is analyzed. The dispersion relations of the modes traveling along these devices explain the numerically observed formation of single and multiple copies of the input beam. As the analogous devices constructed in a standard planar geometry, the proposed PC devices can be employed as filters and demultiplexers. The use of PC structures, where the light is truly confined by the stopband, adds the valuable benefit of a dramatic reduction of the overall geometrical dimensions.

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  1. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton Univ. Press, 1995).
  2. 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).
  3. 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).
  4. 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).
  5. 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).
  6. 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).
  7. M. Lončar, T. Doll, J. Vučković, A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightw. Technol. 18, 1402-1411 (2000).
  8. 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).
  9. 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).
  10. 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).
  11. 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).
  12. 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).
  13. 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).
  14. 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).
  15. M. Bachmann, P. A. Besse, H. Melchior, "General self-imaging: Properties in $N \times N$ multimode interference couplers including phase relations," Appl. Opt. 33, 3905-3911 (1994).
  16. 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).
  17. 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).
  18. 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).
  19. 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).
  20. A. Martinez, F. Cuesta, J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003).
  21. 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).
  22. A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Diffraction engineering in arrays of photonic crystal waveguides," Opt. Lett. 30, 2894-2896 (2005).
  23. A. Locatelli, M. Conforti, D. Modotto, C. De Angelis, "Discrete negative refraction in photonic crystal waveguide arrays," Opt. Lett. 31, 1343-1345 (2006).
  24. D. Christodoulides, R. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988).
  25. 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).
  26. H. S. Eisenberg, Y. Silberberg, R. Morandotti, J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
  27. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
  28. 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).
  29. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).
  30. P. Ciarlet, J. Zou, "Fully discrete finite element approaches for time-dependent Maxwell's equations," Numer. Math. 82, 193-219 (1999).
  31. J. Lee, R. Lee, A. Cangellaris, "Time-domain finite-element methods," IEEE Trans. Antennas Propag. 45, 430-442 (1997).
  32. J. C. Nedelec, "Mixed finite elements in ${\bf R}^{3}$," Numer. Math. 35, 315-341 (1980).
  33. D. Boffi, M. Conforti, L. Gastaldi, "Modified edge finite elements for photonic crystals," Numer. Math. 105, 249-266 (2006).
  34. 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).
  35. 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).
  36. 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).
  37. 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).
  38. M. Thorhauge, L. H. Frandsen, P. I. Borel, "Efficient photonic crystal directional couplers," Opt. Lett. 28, 1525-1527 (2003).
  39. G. Chen, J. U. Kang, "Waveguide mode converter based on two-dimensional photonic crystals," Opt. Lett. 30, 1656-1658 (2005).
  40. 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).
  41. L. C. Botten, R. A. Hansen, C. M. de Sterke, "Supermodes in multiple coupled photonic crystal waveguides," Opt. Express 14, 387-396 (2006).
  42. M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers ," J. Lightw. Technol. 19, 1970-1975 (2001).
  43. 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).

2006

2005

2004

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).

2003

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).

2002

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).

2001

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

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).

2000

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).

1999

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).

1998

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).

1997

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

1995

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).

1994

1992

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).

1988

1980

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

Appl. Opt.

Appl. Phys. Lett.

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).

IEEE J. Quantum Electron.

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).

IEEE J. Quantum. Electron.

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).

IEEE J. Sel. Topics Quantum Electron.

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).

IEEE Photon. Technol. Lett.

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).

IEEE Trans. Antennas Propag.

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).

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

J. Lightw. Technol.

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).

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).

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

J. Opt. Soc. Amer. B, Opt. Phys.

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).

Numer. Math.

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

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).

Opt. Commun.

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).

Opt. Express

Opt. Lett.

Phys. Rev. B, Condens. Matter

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).

Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top.

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).

Phys. Rev. Lett.

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).

Prog. Quantum Electron.

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).

SIAM J. Numer. Anal.

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).

Other

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

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

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