Abstract

Using finite-difference time-domain calculations, we investigate out-of-plane coupling between a square-lattice planar photonic crystal and a conventional waveguide located above the photonic crystal. We couple a waveguide oriented in the ΓX direction to a photonic crystal mode in the second band and show that anticrossing takes place. In this way, a self-collimated beam is launched in the planar photonic crystal, with full power transfer. Furthermore, we investigate the coupling between a waveguide oriented in the ΓM direction and a photonic crystal and show that single photonic crystal modes can be selectively excited.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
  2. T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
    [CrossRef]
  3. S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  4. D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
    [CrossRef]
  5. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  6. M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
    [CrossRef]
  7. C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. Y. Xu, R. K. Lee, A. Yariv, “Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,” Opt. Lett. 25, 755–757 (2000).
    [CrossRef]
  14. A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
    [CrossRef]
  15. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
    [CrossRef]
  16. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
    [CrossRef]
  17. J. Witzens, M. Lončar, A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
    [CrossRef]
  18. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  19. K. Okamoto, Fundamentals of Optical Waveguides (Academic, NTT Photonics Laboratories, Japan, 2000).
  20. C. M. de Sterke, D. Salinas, J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
    [CrossRef]

2002

J. Witzens, M. Lončar, A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
[CrossRef]

2001

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

2000

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268–270 (2000).
[CrossRef]

Y. Xu, R. K. Lee, A. Yariv, “Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,” Opt. Lett. 25, 755–757 (2000).
[CrossRef]

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

1999

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
[CrossRef]

M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

1998

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

1997

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

1996

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

C. M. de Sterke, D. Salinas, J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Astratov, V. N.

Bardinal, V.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Benisty, H.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Bhat, R.

Boroditsky, M.

Brand, S.

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Cassagne, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Coccioli, R.

Culshaw, I. S.

Dapkus, P. D.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

De La Rue, R. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

de Sterke, C. M.

C. M. de Sterke, D. Salinas, J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

Doll, T.

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Fan, S. H.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Houdré, R.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

A. Mekis, J. D. Joannopoulos, “Tapered couplers for efficient interfacing between dielectric and photonic crystal waveguides,” J. Lightwave Technol. 19, 861–865 (2001).
[CrossRef]

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Johnson, S. G.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Jouanin, C.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268–270 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268–270 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Kim, I.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Kolodziejski, L. A.

S. G. Johnson, S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268–270 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Krauss, T. F.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

M. Boroditsky, R. Vrijen, T. F. Krauss, R. Coccioli, R. Bhat, E. Yablonovitch, “Spontaneous emission extraction and Purcell enhancement from thin-film 2-D photonic crystals,” J. Lightwave Technol. 17, 2096–2112 (1999).
[CrossRef]

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Lightwave Technol. 17, 2050–2057 (1999).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

T. F. Krauss, R. M. De La Rue, S. Brand, “Two-dimensional photonic-bandgap structures operating at near infrared wavelengths,” Nature 383, 699–702 (1996).
[CrossRef]

Labilloy, D.

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Lee, R. K.

Y. Xu, R. K. Lee, A. Yariv, “Adiabatic coupling between conventional dielectric waveguides and waveguides with discrete translational symmetry,” Opt. Lett. 25, 755–757 (2000).
[CrossRef]

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Loncar, M.

J. Witzens, M. Lončar, A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
[CrossRef]

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Mekis, A.

Nedeljkovic, D.

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Noda, S.

S. Noda, A. Chutinan, M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

O’Brian, J. D.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Oesterle, U.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

D. Labilloy, H. Benisty, C. Weisbuch, T. F. Krauss, R. M. De La Rue, V. Bardinal, R. Houdré, U. Oesterle, D. Cassagne, C. Jouanin, “Quantitative measurement of transmission, reflection, and diffraction of two-dimensional photonic band gap structures at near-infrared wavelengths,” Phys. Rev. Lett. 79, 4147–4150 (1997).
[CrossRef]

Okamoto, K.

K. Okamoto, Fundamentals of Optical Waveguides (Academic, NTT Photonics Laboratories, Japan, 2000).

Olivier, S.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Painter, O.

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Pearsall, T. P.

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

Rattier, M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Salinas, D.

C. M. de Sterke, D. Salinas, J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, S. Kawakami, “Photonic-crystal spot-size converter,” Appl. Phys. Lett. 76, 268–270 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74, 1212–1214 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–R10099 (1998).
[CrossRef]

Scherer, A.

J. Witzens, M. Lončar, A. Scherer, “Self-collimation in planar photonic crystals,” IEEE J. Sel. Top. Quantum Electron. 8, 1246–1257 (2002).
[CrossRef]

M. Lončar, D. Nedeljković, T. Doll, J. Vučković, A. Scherer, T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000).
[CrossRef]

O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brian, P. D. Dapkus, I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[CrossRef] [PubMed]

Sipe, J. E.

C. M. de Sterke, D. Salinas, J. E. Sipe, “Coupled-mode theory for light propagation through deep nonlinear gratings,” Phys. Rev. E 54, 1969–1989 (1996).
[CrossRef]

Skolnick, M. S.

Smith, C. J. M.

C. J. M. Smith, R. M. De La Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. F. Krauss, U. Oesterle, R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Stevenson, R. M.

Taflove, A.

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Figures (10)

Fig. 1
Fig. 1

Schematic view of a PPC and a waveguide oriented in the Γ X direction above the photonic crystal.

Fig. 2
Fig. 2

Band diagram for the coupled PPC waveguide system. The x axis gives the k-vector component imposed by the Bloch boundary condition in the Γ X direction, and the y axis gives the inverse wavelength 1 / λ = f / c of the resulting modes (where f is the frequency and c is the speed of light in vacuum). Labels indicate modes that correspond to the photonic crystal and to the waveguide far from the coupling region. The second band of the photonic crystal anticrosses with the waveguide. The dispersion diagram of the waveguide ends abruptly because the lower-frequency modes were not resolved with the numerical method used (badly confined modes).

Fig. 3
Fig. 3

FDTD simulation of a decaying field in the mini stop band for a discretization of 20 nm and λ = 1.48   μ m . The mode of the stand-alone waveguide is launched into the waveguide. (a) B z in the xy-symmetry plane of the waveguide, (b) B z in the xy-symmetry plane of the PPC. The decay of the coupled field is clearly seen. The field in the PPC propagates in the opposite direction from the field in the waveguide.

Fig. 4
Fig. 4

FDTD simulation of a decaying field in the mini stop band for a discretization of 20 nm and λ = 1.48   μ m . The mode of the stand-alone waveguide is launched into the waveguide. The figure shows B z in the yz-symmetry plane of the coupled structure. The field couples into the PPC and propagates in the opposite direction.

Fig. 5
Fig. 5

(a) Spatial Fourier transform of a typical Bloch mode of the second band of PC1 and (b) the spatial Fourier transform of the corresponding Bloch mode (same frequency and same main component k vector) of PC2. The first Brillouin zone of PC1 is indicated by the solid-line square, and the second Brillouin zone is indicated by the dashed-line square. The PC2 Bloch mode misses the component in the first Brillouin zone that is coupled to the waveguide. Thus, by transmission of a beam from PC1 to PC2, the coupling to the waveguide can be switched on and off. Note that, because PC2 is rescaled and rotated as compared with PC1, the first Brillouin zone of PC2 corresponds to both the first and the second Brillouin zones of PC1. This explains why a Bloch mode of PC2 has only one Fourier component, whereas a Bloch mode of PC1 has two. k-vector components are given in dimensionless units of k a , where a is the lattice parameter of PC1.

Fig. 6
Fig. 6

A waveguide is situated above a photonic crystal with a transition between lattices PC2 and PC1. This way the anticrossing between the photonic crystal and the waveguide can be turned on and off, and a self-collimated beam can be launched into PC2.

Fig. 7
Fig. 7

Excited modes can be determined by conservation of the k-vector component in the Γ M direction (modulo an inverse lattice vector). (a) The idealized equifrequency contour in the first Brillouin zone (dashed-line square), as well as its multiple higher-order copies. The horizontal line is determined by the k vector of the waveguide mode and intersects all the PPC modes to which the waveguide couples. Four modes are excited, labeled 1 to 4. The high-symmetry points are shown on the diagram (Γ, M, and X). The directions of propagation (given by the group velocity) are indicated in (b) for each of the excited modes.

Fig. 8
Fig. 8

Spatial Fourier transform of B z on the left side of the waveguide, on the center plane of the PPC ( z = 0 ) . Modes 1 and 2 that propagate to the left of the waveguide are present. The field was simulated by a FDTD with a 10-nm discretization, waveguide dimensions are 520   nm × 100   nm , and λ = 1.54   μ m . The device is in the regime illustrated in Fig. 7. The Fourier components are labeled in the same way as in Fig. 7. k-vector components are given in dimensionless units of k a , where a is the lattice parameter.

Fig. 9
Fig. 9

Excited modes can be determined by conservation of the k-vector component in the Γ M direction (modulo an inverse lattice vector). (a) The idealized equifrequency contour in the first Brillouin zone (dashed-line square), as well as its multiple higher-order copies. The horizontal line is determined by the k vector of the waveguide mode and intersects all the PPC modes to which the waveguide couples. Two modes are excited, labeled 1 and 2. The high-symmetry points are shown on the diagram (Γ, M and X). The directions of propagation (given by the group velocity) are indicated in (b) for each of the excited modes.

Fig. 10
Fig. 10

Spatial Fourier transform of B z on the left side of the waveguide, on the center plane of the PPC ( z = 0 ) . The field was simulated by FDTD with a 10-nm discretization, waveguide dimensions are 400   nm × 200   nm , and λ = 1.54 . All the Fourier components belong to the same Bloch mode, and true single-mode excitation is achieved on either side of the waveguide. The device is in the same regime as that illustrated in Fig. 9. k-vector components are given in dimensionless units of k a , where a is the lattice parameter.

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