Abstract

We present a detailed analysis of the guided modes of a one-dimensional photonic bandgap (PBG) waveguide that consists of a high-index guiding layer placed between two identical Bragg reflectors. Using a zigzag wave model, we calculate the modal characteristics of the waveguide including dispersion curves, field distributions, cutoff conditions, and confinement factors. We also investigate the effects of truncating the Bragg reflectors with either a high- or a low-index medium on the modal characteristics of the waveguide. The study provides a rigorous discussion of the two guiding mechanisms in the waveguide, namely index guiding and bandgap guiding. The results are useful not only for the design of PBG slab waveguides but also for a better understanding of the more complicated two-dimensional structures of the same nature, such as photonic crystal fibers and waveguides, which are not amenable to rigorous analytical studies.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Yeh, A. Yariv, and C. Hong, “Electromagnetic propagation in periodic stratified media,” J. Opt. Soc. Am. 67, 423-438 (1977).
    [CrossRef]
  2. S. R. A. Dods, “Bragg reflection waveguide,” J. Opt. Soc. Am. A 6, 1465-1476 (1989).
    [CrossRef]
  3. A. Mizrahi and L. Schachter, “Bragg reflection waveguides with a matching layer,” Opt. Express 12, 3156-3170 (2004).
    [CrossRef] [PubMed]
  4. B. Nistad, M. W. Haakestad, and J. Skaar, “Dispersion properties of planar Bragg waveguides,” Opt. Commun. 265, 153-160 (2006).
    [CrossRef]
  5. G. Lenz and J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519-531 (1990).
    [CrossRef]
  6. P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Electron. 27, 824-828 (1991).
    [CrossRef]
  7. C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
    [CrossRef]
  8. J. Li and K. S. Chiang, “Guided modes of one-dimensional photonic bandgap waveguides,” J. Opt. Soc. Am. B 24, 1942-1950 (2007).
    [CrossRef]
  9. E. Simova and I. Golub, “Polarization splitter/combiner in high index contrast Bragg reflector waveguides,” Opt. Express 11, 3425-3430 (2003).
    [CrossRef] [PubMed]
  10. S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
    [CrossRef]
  11. J. Li and K. S. Chiang, “Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors,” Opt. Commun. 281, 5797-5803 (2008).
    [CrossRef]
  12. Y. Sakurai and F. Koyama, “Tunable hollow waveguide distributed Bragg reflectors with variable air core,” Opt. Express 12, 2851-2856 (2004).
    [CrossRef] [PubMed]
  13. A. S. Helmy, B. Bijlani, and P. Abolghasem, “Phase matching in monolithic Bragg reflection waveguides,” Opt. Lett. 32, 2399-2401 (2007).
    [CrossRef] [PubMed]
  14. N. Ponnampalam and R. G. DeCorby, “Self-assembled hollow waveguides with hybrid metal-dielectric Bragg claddings,” Opt. Express 15, 12595-12604 (2007).
    [CrossRef] [PubMed]
  15. R. Das and K. Thyagarajan, “A high efficiency scheme for phase-matched second-harmonic generation in GaN-based Bragg reflection waveguide,” IEEE Photonics Technol. Lett. 19, 1526-1528 (2007).
    [CrossRef]
  16. H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
    [CrossRef]
  17. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68, 1196-1201 (1978).
    [CrossRef]
  18. M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
    [CrossRef] [PubMed]
  19. J. C. Knight, “Photonic crystal fibers,” Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  20. 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]
  21. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  22. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  23. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
  24. K. S. Chiang, “Coupled-zigzag wave theory for guided waves in slab waveguide arrays,” J. Lightwave Technol. 10, 1380-1387 (1992).
    [CrossRef]
  25. X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
    [CrossRef]
  26. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).
  27. B. T. Kuhlmey, R. C. McPhedran, and C. M. de Sterke, “Modal cutoff in microstructured optical fibers,” Opt. Lett. 27, 1684-1686 (2002).
    [CrossRef]

2008 (2)

J. Li and K. S. Chiang, “Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors,” Opt. Commun. 281, 5797-5803 (2008).
[CrossRef]

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

2007 (5)

S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
[CrossRef]

A. S. Helmy, B. Bijlani, and P. Abolghasem, “Phase matching in monolithic Bragg reflection waveguides,” Opt. Lett. 32, 2399-2401 (2007).
[CrossRef] [PubMed]

N. Ponnampalam and R. G. DeCorby, “Self-assembled hollow waveguides with hybrid metal-dielectric Bragg claddings,” Opt. Express 15, 12595-12604 (2007).
[CrossRef] [PubMed]

R. Das and K. Thyagarajan, “A high efficiency scheme for phase-matched second-harmonic generation in GaN-based Bragg reflection waveguide,” IEEE Photonics Technol. Lett. 19, 1526-1528 (2007).
[CrossRef]

J. Li and K. S. Chiang, “Guided modes of one-dimensional photonic bandgap waveguides,” J. Opt. Soc. Am. B 24, 1942-1950 (2007).
[CrossRef]

2006 (1)

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

2005 (1)

H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
[CrossRef]

2004 (2)

2003 (2)

2002 (1)

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

2000 (1)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

1997 (1)

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]

1992 (2)

K. S. Chiang, “Coupled-zigzag wave theory for guided waves in slab waveguide arrays,” J. Lightwave Technol. 10, 1380-1387 (1992).
[CrossRef]

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

1991 (1)

P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Electron. 27, 824-828 (1991).
[CrossRef]

1990 (1)

G. Lenz and J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519-531 (1990).
[CrossRef]

1989 (1)

1978 (1)

1977 (1)

Abolghasem, P.

Bijlani, B.

Birks, T. A.

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]

Chiang, K. S.

J. Li and K. S. Chiang, “Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors,” Opt. Commun. 281, 5797-5803 (2008).
[CrossRef]

J. Li and K. S. Chiang, “Guided modes of one-dimensional photonic bandgap waveguides,” J. Opt. Soc. Am. B 24, 1942-1950 (2007).
[CrossRef]

K. S. Chiang, “Coupled-zigzag wave theory for guided waves in slab waveguide arrays,” J. Lightwave Technol. 10, 1380-1387 (1992).
[CrossRef]

Das, R.

R. Das and K. Thyagarajan, “A high efficiency scheme for phase-matched second-harmonic generation in GaN-based Bragg reflection waveguide,” IEEE Photonics Technol. Lett. 19, 1526-1528 (2007).
[CrossRef]

Dasgupta, S.

S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
[CrossRef]

de Sterke, C. M.

DeCorby, R. G.

Dods, S. R. A.

Fan, S.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[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]

Fink, Y.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Ghatak, A.

S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
[CrossRef]

Golub, I.

Gu, B. Y.

H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
[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.

Ibanescu, M.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Joannopoulos, J. D.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[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]

Knight, J. C.

Koyama, F.

Kuhlmey, B. T.

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]

Lambkin, P. M.

P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Electron. 27, 824-828 (1991).
[CrossRef]

Lederer, F.

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Leine, L.

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Lenz, G.

G. Lenz and J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519-531 (1990).
[CrossRef]

Li, J.

J. Li and K. S. Chiang, “Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors,” Opt. Commun. 281, 5797-5803 (2008).
[CrossRef]

J. Li and K. S. Chiang, “Guided modes of one-dimensional photonic bandgap waveguides,” J. Opt. Soc. Am. B 24, 1942-1950 (2007).
[CrossRef]

Li, Z. Y.

H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
[CrossRef]

Mann, M.

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Marom, E.

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]

Mizrahi, A.

Nistad, B.

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

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Pal, B. P.

S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
[CrossRef]

Ponnampalam, N.

Ren, G. B.

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

Russell, P. St. J.

Sakurai, Y.

Salzman, J.

G. Lenz and J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519-531 (1990).
[CrossRef]

Sang, H. Y.

H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
[CrossRef]

Schachter, L.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Shore, K. A.

P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Electron. 27, 824-828 (1991).
[CrossRef]

Shum, P.

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

Simova, E.

Skaar, J.

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

Taflove, A.

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

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Thomas, E. L.

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Thyagarajan, K.

R. Das and K. Thyagarajan, “A high efficiency scheme for phase-matched second-harmonic generation in GaN-based Bragg reflection waveguide,” IEEE Photonics Technol. Lett. 19, 1526-1528 (2007).
[CrossRef]

Trutschel, U.

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

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]

Wachter, C.

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yan, M.

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

Yariv, A.

Yeh, P.

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yu, X.

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

IEEE J. Quantum Electron. (2)

G. Lenz and J. Salzman, “Bragg reflection waveguide composite structures,” IEEE J. Quantum Electron. 26, 519-531 (1990).
[CrossRef]

P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Electron. 27, 824-828 (1991).
[CrossRef]

IEEE Photonics Technol. Lett. (2)

R. Das and K. Thyagarajan, “A high efficiency scheme for phase-matched second-harmonic generation in GaN-based Bragg reflection waveguide,” IEEE Photonics Technol. Lett. 19, 1526-1528 (2007).
[CrossRef]

X. Yu, P. Shum, M. Yan, and G. B. Ren, “Silica-based birefringent large-mode-area fiber with a nanostructure core,” IEEE Photonics Technol. Lett. 20, 246-248 (2008).
[CrossRef]

J. Appl. Phys. (2)

H. Y. Sang, Z. Y. Li, and B. Y. Gu, “Propagation properties of planar Bragg waveguides studied by an analytical Blochmode method,” J. Appl. Phys. 98, 043114 (2005).
[CrossRef]

C. Wachter, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. 71, 3688-3692 (1992).
[CrossRef]

J. Lightwave Technol. (1)

K. S. Chiang, “Coupled-zigzag wave theory for guided waves in slab waveguide arrays,” J. Lightwave Technol. 10, 1380-1387 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

Nature (1)

J. C. Knight, “Photonic crystal fibers,” Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Commun. (3)

S. Dasgupta, A. Ghatak, and B. P. Pal, “Analysis of Bragg reflection waveguides with finite cladding: an accurate matrix method formulation,” Opt. Commun. 279, 83-88 (2007).
[CrossRef]

J. Li and K. S. Chiang, “Light guidance in a photonic bandgap slab waveguide consisting of two different Bragg reflectors,” Opt. Commun. 281, 5797-5803 (2008).
[CrossRef]

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

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

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]

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, “Extremely large group velocity dispersion of line-defect waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Science (1)

M. Ibanescu, Y. Fink, S. Fan, E. L. Thomas, and J. D. Joannopoulos, “An all-dielectric coaxial waveguide,” Science 289, 415-419 (2000).
[CrossRef] [PubMed]

Other (2)

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

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, 1984).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Symmetric 1D PBG waveguide that consists of a high-index guiding layer sandwiched between two identical periodic structures.

Fig. 2
Fig. 2

Refractive-index profile of a 1D periodic structure.

Fig. 3
Fig. 3

Band diagrams of a 1D periodic structure for TE and TM waves where the curves in the band gaps are the contours of constant ξ values.

Fig. 4
Fig. 4

Interface between the guiding layer and the periodic structure.

Fig. 5
Fig. 5

Dispersion curves for the TE and TM modes of a waveguide with p = 0.5 , q = 1.5 , and r 12 = 2.25 .

Fig. 6
Fig. 6

Field distributions of the TE 0 ( 0 ) mode ( V = 4.5 , b = 0.874 , Γ = 96.3%), the TE 1 ( 0 ) mode ( V = 6.2 , b = 0.701 , Γ = 86.6%), the TE 2 ( 1 ) mode ( V = 4.65 , b = 0 , Γ = 62.9%), the TE 3 ( 1 ) mode ( V = 8.5 , b = 0.361 , Γ = 55.2%), the TM 0 ( 0 ) mode ( V = 4.5 , b = 0.835 , Γ = 97.2%), the TM 1 ( 0 ) mode ( V = 6.2 , b = 0.635 , Γ = 93.3%), the TM 2 ( 1 ) mode ( V = 5.0 , b = 0 , Γ = 39.0%), and the TM 3 ( 1 ) mode ( V = 8.5 , b = 0.309 , Γ = 55.4%).

Fig. 7
Fig. 7

Variation of the confinement factor Γ with V for a number of TE and TM modes of a PBG waveguide with p = 0.5 , q = 1.5 , and r 12 = 2.25 .

Fig. 8
Fig. 8

Field distributions of the TE 4 ( 1 ) mode ( V = 13.48 , b = 0.510 , Γ = 56.2%) and the TE 4 ( 2 ) mode ( V = 13.15 , b = 0.487 , Γ = 53.9%).

Fig. 9
Fig. 9

Refractive-index profile of a 1D PBG waveguide truncated with a low-index external medium.

Fig. 10
Fig. 10

Dispersion curves for a number of TE and TM modes of a PBG waveguide with p = 0.5 , q = 1.5 , and r 12 = 2.25 , truncated to N = 2 with a low-index external medium.

Fig. 11
Fig. 11

Field distributions calculated at V = 4.5 for the TE modes ( M = 0 , b = 0.874 and Γ = 96.3%; M = 1 , b = 0.577 and Γ = 21.8%; M = 2 , b = 0.557 and Γ = 0.88%; M = 3 , b = 0.507 and Γ = 41.6%; M = 4 , b = 0.443 and Γ = 1.50%; M = 5 , b = 0.410 and Γ = 24.4 %) and the TM modes ( M = 0 , b = 0.835 and Γ = 97.2%; M = 1 , b = 0.429 and Γ = 55.2%; M = 2 , b = 0.360 and Γ = 1.28%; M = 3 , b = 0.331 and Γ = 18.5%; M = 4 , b = 0.211 and Γ=4.08%; M = 5 , b = 0.167 and Γ = 12.3%).

Fig. 12
Fig. 12

Field distributions calculated at V = 6.2 for the TE modes ( M = 0 , b = 0.923 and Γ = 98.5%; M = 1 , b = 0.701 and Γ = 86.7%; M = 2 , b = 0.658 and Γ = 0.22%; M = 3 , b = 0.655 and Γ = 4.73%; M = 4 , b = 0.624 and Γ = 0.31%; M = 5 , b = 0.622 and Γ = 2.57%; M = 6 , b = 0.339 and Γ = 82.6%) and the TM modes ( M = 0 , b = 0.906 and Γ = 99.0%; M = 1 , b = 0.635 and Γ = 93.3%; M = 2 , b = 0.495 and Γ = 0.47%; M = 3 , b = 0.494 and Γ = 0.87%; M = 4 , b = 0.446 and Γ = 0.91%; M = 5 , b = 0.443 and Γ = 0.86%; M = 6 , b = 0.236 and Γ = 74.0%).

Fig. 13
Fig. 13

Refractive-index profile of a PBG waveguide truncated with a high-index external medium.

Fig. 14
Fig. 14

Variation of the attenuation coefficient αΛ with V for a truncated PBG waveguide with N = 2 , p = 0.5 , q = 1.5 , and r 12 = 2.25 .

Fig. 15
Fig. 15

Variation of the attenuation coefficient αΛ with N at V = 6.2 for a number of core modes and cladding modes of a truncated PBG waveguide with p = 0.5 , q = 1.5 , and r 12 = 2.25 .

Fig. 16
Fig. 16

Variation of the attenuation coefficient αΛ with N at V = 4.5 for the TE and TM modes ( M = 1 ) of a truncated PBG waveguide with p = 0.5 , q = 1.5 , and r 12 = 2.25 .

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

2 k g d g + 4 ϕ = 2 m π for m = integer ,
( a 1 , j b 1 , j ) = 1 2 ( 1 + r 12 2 γ 2 2 k 1 2 ) 1 2 ( e γ 2 d 2 exp [ i ( k 1 d 1 ϕ b ) ] e γ 2 d 2 exp [ i ( k 1 d 1 + ϕ b ) ] e γ 2 d 2 exp [ i ( k 1 d 1 ϕ b ) ] e γ 2 d 2 exp [ i ( k 1 d 1 + ϕ b ) ] ) ( a 2 , j b 2 , j ) ,
( a 1 , j b 1 , j ) = ( T 11 T 12 T 21 T 22 ) ( a 1 , j + 1 b 1 , j + 1 ) ,
χ = 1 2 χ 1 exp ( γ 2 d 2 ) + 1 2 χ 2 exp ( γ 2 d 2 ) ,
{ χ 1 = cos k 1 d 1 + 1 2 ( r 12 γ 2 k 1 k 1 r 12 γ 2 ) sin k 1 d 1 χ 2 = cos k 1 d 1 1 2 ( r 12 γ 2 k 1 k 1 r 12 γ 2 ) sin k 1 d 1 } .
2 k 1 d 1 + 4 ϕ b = 2 m b π for m b = 0 , 1 , 2 , ,
k 1 d 1 = n π for n = 0 , 1 , 2 , ,
δ = 1 1 1 χ 2 = 1 2 χ 2 + 1 8 χ 4 + 1 16 χ 6 + 5 128 χ 8 + .
exp ( i 2 ϕ ) = 1 2 ( k 1 r 12 γ 2 r 12 γ 2 k 1 ) sinh ( γ 2 d 2 ) + χ δ sin k 1 d 1 i [ cosh ( γ 2 d 2 ) χ δ cos k 1 d 1 ] 1 2 ( k 1 r 12 γ 2 + r 12 γ 2 k 1 ) sinh ( γ 2 d 2 ) .
2 ϕ = 2 tan 1 { r 12 γ 2 k 1 1 + exp ( 2 γ 2 d 2 ) [ χ 1 + χ 2 exp ( 2 γ 2 d 2 ) ] δ cos k 1 d 1 1 exp ( 2 γ 2 d 2 ) + r 12 γ 2 k 1 [ χ 1 + χ 2 exp ( 2 γ 2 d 2 ) ] δ sin k 1 d 1 } .
α = 4.343 ( d P d z ) ( 1 P )
P = ( β 2 ω μ ) | E y | 2 d x , H z = ( 1 i ω μ ) ( E y x ) ,
P = ( β 2 ω ϵ ) | H y | 2 d x , E z = ( 1 i ω ϵ ) ( H y x ) ,

Metrics