Abstract

Using a ray-optics model, we analyze the guided modes of a slab waveguide that consists of a low-index layer sandwiched between two photonic bandgap structures. Normalized band diagrams and dispersion curves for the TE and TM waves are investigated in detail, and a nomenclature system for the guided modes based on the mode-field patterns in the waveguide is proposed. The cutoff conditions and the confinement factors of the modes are discussed. The effects of varying the physical parameters of the waveguide on the dispersion characteristics of the modes are also analyzed.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  20. S. Assefa, P. T. Rakich, P. Bienstman, S. G. Johnson, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, E. P. Ippen, and H. I. Smith, "Guiding 1.5 μm light in photonic crystals based on dielectric rods," Appl. Phys. Lett. 85, 6110-6112 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  23. S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
    [CrossRef] [PubMed]
  24. W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
    [CrossRef]
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2006 (3)

B. Nistad, M. W. Haakestad, and J. Skaar, "Dispersion properties of planar Bragg waveguides," Opt. Commun. 265, 153-160 (2006).
[CrossRef]

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

B. R. West and A. S. Helmy, "Properties of the quarter-wave Bragg reflection waveguide: theory," J. Opt. Soc. Am. B 23, 1207-1220 (2006).
[CrossRef]

2004 (4)

J.-S. I. Y. Park, and H. Jeon, "Optimal design for one-dimensional photonic crystal waveguide," J. Lightwave Technol. 22, 509-513 (2004).
[CrossRef]

A. Mizrahi and L. Schachter, "Bragg reflection waveguides with a matching layer," Opt. Express 12, 3156-3170 (2004).
[CrossRef] [PubMed]

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

T. Hori, "Enhancement of field confinement by deforming perfectly periodic structures in one-dimensional slab waveguides," Opt. Commun. 230, 161-165 (2004).
[CrossRef]

2003 (2)

2002 (3)

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

V. V. Pobochii, T. Tada, and T. Kanayama, "Photonic-band-gap properties of two-dimensional lattices of Si nanopillars," J. Appl. Phys. 91, 3299-3305 (2002).
[CrossRef]

H. Taniyama, "Waveguide structures using one-dimensional photonic crystal," J. Appl. Phys. 91, 3511-3515 (2002).
[CrossRef]

2001 (1)

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

2000 (2)

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

1999 (2)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

1998 (1)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1989 (1)

1978 (1)

1977 (1)

1976 (1)

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Assefa, S.

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

Berg, E.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Bhattacharya, P.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Bienstman, P.

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

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Brechet, F.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Chutinan, A.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

County, F.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Coupland, S.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Dainese, M.

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

Dods, S. R. A.

Dunn, S. C.

Eggleton, B. J.

Fan, S.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Farr, L.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Fink, Y.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Flea, R.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Haakestad, M. W.

B. Nistad, M. W. Haakestad, and J. Skaar, "Dispersion properties of planar Bragg waveguides," Opt. Commun. 265, 153-160 (2006).
[CrossRef]

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

Helmy, A. S.

Hong, C. S.

Hori, T.

T. Hori, "Enhancement of field confinement by deforming perfectly periodic structures in one-dimensional slab waveguides," Opt. Commun. 230, 161-165 (2004).
[CrossRef]

Imada, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Ippen, E. P.

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

Jeon, H.

Joannopoulos, J. D.

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

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

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

Kanayama, T.

V. V. Pobochii, T. Tada, and T. Kanayama, "Photonic-band-gap properties of two-dimensional lattices of Si nanopillars," J. Appl. Phys. 91, 3299-3305 (2002).
[CrossRef]

Knight, J. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Kochman, B.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Kolodziejski, L. A.

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

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Langford, A.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Lawman, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Litchinitser, N. M.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Marcou, J.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

Marom, E.

Mason, M.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

McPhedran, R. C.

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Mizrahi, A.

Mochizuki, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Nistad, B.

B. Nistad, M. W. Haakestad, and J. Skaar, "Dispersion properties of planar Bragg waveguides," Opt. Commun. 265, 153-160 (2006).
[CrossRef]

Noda, S.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Notomi, M.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Orazio, A. D.

Pagnoux, D.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

Pang, S.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Park, J.-S. I. Y.

Petrich, G. S.

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

Petruzzelli, V.

Pobochii, V. V.

V. V. Pobochii, T. Tada, and T. Kanayama, "Photonic-band-gap properties of two-dimensional lattices of Si nanopillars," J. Appl. Phys. 91, 3299-3305 (2002).
[CrossRef]

Prudenzano, F.

Qasaimeh, O.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Rakich, P. T.

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

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Roy, P.

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

Russell, P. St. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Sabarinathan, J.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Sabert, H.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Sario, M. D.

Schachter, L.

Shinya, A.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Skaar, J.

B. Nistad, M. W. Haakestad, and J. Skaar, "Dispersion properties of planar Bragg waveguides," Opt. Commun. 265, 153-160 (2006).
[CrossRef]

Smith, H. I.

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

Sterke, C. M.

Swillo, M.

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

Tada, T.

V. V. Pobochii, T. Tada, and T. Kanayama, "Photonic-band-gap properties of two-dimensional lattices of Si nanopillars," J. Appl. Phys. 91, 3299-3305 (2002).
[CrossRef]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

Takahashi, C.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Takahashi, J.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Taniyama, H.

H. Taniyama, "Waveguide structures using one-dimensional photonic crystal," J. Appl. Phys. 91, 3511-3515 (2002).
[CrossRef]

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Thylen, L.

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

Usner, B.

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

West, B. R.

White, T. P.

Williams, D. P.

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Wosinski, L.

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

Yamada, K.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Yariv, A.

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Yeh, P.

Yokohama, I.

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

Yokoyama, M.

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

Zhou, W. D.

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

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

Electron. Lett. (2)

F. Brechet, P. Roy, J. Marcou, and D. Pagnoux, "Singlemode propagation into depressed-core-index photonic-bandgap fibre designed for zero-dispersion propagation at short wavelengths," Electron. Lett. 36, 514-515 (2000).
[CrossRef]

W. D. Zhou, J. Sabarinathan, B. Kochman, E. Berg, O. Qasaimeh, S. Pang, and P. Bhattacharya, "Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature," Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Notomi, A. Shinya, K. Yamada, J. Takahashi, C. Takahashi, and I. Yokohama, "Structural tuning of guiding modes of line-defect waveguides of silicon-on-insulator photonic crystal slabs," IEEE J. Quantum Electron. 38, 736-742 (2002).
[CrossRef]

J. Appl. Phys. (2)

V. V. Pobochii, T. Tada, and T. Kanayama, "Photonic-band-gap properties of two-dimensional lattices of Si nanopillars," J. Appl. Phys. 91, 3299-3305 (2002).
[CrossRef]

H. Taniyama, "Waveguide structures using one-dimensional photonic crystal," J. Appl. Phys. 91, 3511-3515 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Opt. Commun. (4)

T. Hori, "Enhancement of field confinement by deforming perfectly periodic structures in one-dimensional slab waveguides," Opt. Commun. 230, 161-165 (2004).
[CrossRef]

B. Nistad, M. W. Haakestad, and J. Skaar, "Dispersion properties of planar Bragg waveguides," Opt. Commun. 265, 153-160 (2006).
[CrossRef]

M. Dainese, M. Swillo, L. Wosinski, and L. Thylen, "Directional coupler wavelength selective filter based on dispersive Bragg reflection waveguide," Opt. Commun. 260, 514-521 (2006).
[CrossRef]

P. Yeh and A. Yariv, "Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

Science (3)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional Reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

S. Noda, M. Yokoyama, M. Imada, A. Chutinan, and M. Mochizuki, "Polarization mode control of two-dimensional photonic crystal laser by unit cell structure design," Science 293, 1123-1125 (2001).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Other (2)

B. J. Mangan, L. Farr, A. Langford, P. J. Roberts, D. P. Williams, F. County, M. Lawman, M. Mason, S. Coupland, R. Flea, H. Sabert, T. A. Birks, J. C. Knight, and P. St. J. Russell, "Low loss (1.7 dB/km) hollow core photonic bandgap fiber," in Proceedings of Optical Fiber Communications Conference (IEEE, 2004), paper PDP24.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

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Figures (14)

Fig. 1
Fig. 1

Structure of a symmetric 1D PBG waveguide.

Fig. 2
Fig. 2

Refractive-index profile of a 1D PBG structure.

Fig. 3
Fig. 3

TE wave that corresponds to χ = 1.13 and ξ = 0.51 decays away in a semi-infinite PBG structure.

Fig. 4
Fig. 4

Normalized band diagrams for the TE polarization for p = ( a ) 0.5 and (b) 0.8, together with the contours of different ξ values in the forbidden bands.

Fig. 5
Fig. 5

Normalized band diagrams for the TM polarization with p = 0.5 for r 12 = ( a ) 2.25 and (b) 5.44, together with the contours of different ξ values in the forbidden bands.

Fig. 6
Fig. 6

Contours of the reflection phase 2 ϕ (in a unit of π) within the forbidden bands for (a) the TE polarization and (b) the TM polarization.

Fig. 7
Fig. 7

Normalized dispersion curves for the TE modes.

Fig. 8
Fig. 8

Electric-field patterns for a number of TE modes: V = 4.0 , b = 0.194 , Г = 80.3 % ; V = 8.5 , b = 0.063 , Г = 90.6 % ; V = 8.5 , b = 0.206 , Г = 76.2 % ; V = 15.0 , b = 0.018 , Г = 97.6 % ; V = 15.0 , b = 0.069 , Г = 90.8 % ; V = 12.0 , b = 0.242 , Г = 17.0 % ; V = 8.5 , b = 0.770 , Г = 36.8 % .

Fig. 9
Fig. 9

Normalized dispersion curves for the TM modes.

Fig. 10
Fig. 10

Magnetic-field patterns for a number of TM modes: V = 5.0 , b = 0.070 , Г = 55.9 % ; V = 2.6 , b = 0.758 , Г = 34.7 % ; V = 10.0 , b = 0.036 , Г = 85.4 % ; V = 9.0 , b = 0.140 , Г = 22.4 % ; V = 6.5 , b = 0.484 , Г = 30.2 % .

Fig. 11
Fig. 11

Variation of the confinement factor Г with the normalized frequency V for several guided modes.

Fig. 12
Fig. 12

Normalized dispersion curves calculated for p = 0.5 , a = 0 , q = 0.1 , and r 12 = 2.25 .

Fig. 13
Fig. 13

Mode-field patterns of several modes: V = 2.8 , b = 0.616 , Г = 0.06 % ; V = 4.5 , b = 0.028 , Г = 0.03 % ; V = 2.8 , b = 0.668 , Г = 6.66 % .

Fig. 14
Fig. 14

Normalized dispersion curves calculated for p = 0.5 , a = 0.4 , q = 1.6 , and r 12 = 2.25 .

Tables (1)

Tables Icon

Table 1 Cutoff Conditions for Some Guided Modes

Equations (17)

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2 k g d g + 4 ϕ = 2 m π for m = integer ,
φ 1 ( x , z ) = { a 1 , j exp [ i k 1 ( x j Λ + Λ ) ] + b 1 , j exp [ i k 1 ( x j Λ + Λ ) ] } exp ( i β z ) for ( j 1 ) Λ < x j Λ d 2 ,
φ 2 ( x , z ) = { a 2 , j exp [ i k 2 ( x j Λ ) ] + b 2 , j exp [ i k 2 ( x j Λ ) ] } exp ( i β z ) for j Λ d 2 < x j Λ ,
( a 1 , j b 1 , j ) = 1 2 ( ( 1 + K 2 K 1 ) exp [ i ( k 1 d 1 + k 2 d 2 ) ] ( 1 K 2 K 1 ) exp [ i ( k 1 d 1 k 2 d 2 ) ] ( 1 K 2 K 1 ) exp [ i ( k 1 d 1 k 2 d 2 ) ] ( 1 + K 2 K 1 ) exp [ i ( k 1 d 1 + k 2 d 2 ) ] ) ( a 2 , j b 2 , j ) ,
( a 2 , j 1 b 2 , j 1 ) = ( T 11 T 12 T 21 T 22 ) ( a 2 , j b 2 , j ) ,
T 11 = exp ( i k 2 d 2 ) [ cos k 1 d 1 1 2 i ( K 1 K 2 + K 2 K 1 ) sin k 1 d 1 ] ,
T 12 = exp ( i k 2 d 2 ) [ 1 2 i ( K 2 K 1 K 1 K 2 ) sin k 1 d 1 ] ,
T 21 = T 12 * , T 22 = T 11 * .
( a 2 , j b 2 , j ) = exp ( i K Λ ) ( a 2 , j 1 b 2 , j 1 ) ,
χ ( k 0 , n eff ) = cos ( k 1 d 1 ) cos ( k 2 d 2 ) 1 2 ( K 1 K 2 + K 2 K 1 ) sin ( k 1 d 1 ) sin ( k 2 d 2 ) .
χ = 1 4 ( K 1 K 2 + K 2 K 1 ) 2 cos ( k 1 d 1 + k 2 d 2 ) 1 4 ( K 1 K 2 K 2 K 1 ) 2 cos ( k 1 d 1 k 2 d 2 ) ,
k 1 d 1 + k 2 d 2 = n π for n = 1 , 2 , 3 , ,
( a 2 , j b 2 , j ) = C ( T 12 e i K Λ T 11 ) ,
( a g b g ) = 1 2 ( 1 + K 1 K g 1 K 1 K g 1 K 1 K g 1 + K 1 K g ) ( a 1 , 1 b 1 , 1 ) ,
ϕ g = arctan ( K 2 K g tan ϕ 0 ) ,
ϕ = { ϕ g π when ϕ g > 0 ϕ g when ϕ g < 0 } ,
b = a , b = b min , χ = 1 .

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