Abstract

Guided modes in a dielectric waveguide structure with a coaxial periodic multi-layer are investigated by using a matrix formula with Bessel functions. We show that guided modes exist in the structure, and that the field is confined in the core which consists of the optically thinner medium. The dispersion curves are discontinuous, so that the modes can exist only in particular wavelength bands corresponding to the stop bands of the periodic structure of the clad. It is possible that the waveguide structure can be applied to filters or optical fibers to reduce nonlinear effects.

© 2000 Optical Society of America

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  1. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
    [Crossref] [PubMed]
  2. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding: errata,” Opt. Lett. 22, 484–485 (1997).
    [Crossref] [PubMed]
  3. 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]
  4. J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
    [Crossref]
  5. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
    [Crossref]
  6. J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
    [Crossref]
  7. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
    [Crossref] [PubMed]
  8. S. E. Barkou, J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett. 24, 46–48 (1999).
    [Crossref]
  9. A. Ferrando, E. Silverstre, J. J. Miret, P. Andés, and M. V. Andés “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
    [Crossref]
  10. Z. Xue-Heng, “Theory of two-dimensional ‘Fingerprint’ resonators,” Electron.Lett. 25, 1311–1312 (1989).
    [Crossref]
  11. M. Toda, “Single-mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473–481 (1990).
    [Crossref]
  12. T. Erdogan and D. G. Hall, “Circularly symmetric distribution feedback semiconductor laser: An analysis,” J.Appl.Phys. 68, 1435–1444 (1990).
    [Crossref]
  13. X. H. Zheng and S. Lacroix, “Mode coupling in circular-cylindrical system and its application to fingerprint resonators,” J.Lightwave Technol. 8, 1509–1516 (1990).
    [Crossref]
  14. C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
    [Crossref]
  15. C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
    [Crossref]
  16. S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
    [Crossref]
  17. A. Yariv and A. Gover, “Equivalence of the coupled-mode and Floquet-Bloch formalisms in periodic optical waveguides,” Appl. Phys. Lett. 26, 537–539 (1975).
    [Crossref]
  18. A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
    [Crossref]
  19. P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
    [Crossref]
  20. W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
    [Crossref]

1999 (2)

1998 (4)

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

1997 (2)

1996 (1)

1995 (1)

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

1992 (1)

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

1991 (1)

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

1990 (3)

M. Toda, “Single-mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473–481 (1990).
[Crossref]

T. Erdogan and D. G. Hall, “Circularly symmetric distribution feedback semiconductor laser: An analysis,” J.Appl.Phys. 68, 1435–1444 (1990).
[Crossref]

X. H. Zheng and S. Lacroix, “Mode coupling in circular-cylindrical system and its application to fingerprint resonators,” J.Lightwave Technol. 8, 1509–1516 (1990).
[Crossref]

1989 (1)

Z. Xue-Heng, “Theory of two-dimensional ‘Fingerprint’ resonators,” Electron.Lett. 25, 1311–1312 (1989).
[Crossref]

1978 (2)

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[Crossref]

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

1977 (1)

A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
[Crossref]

1975 (1)

A. Yariv and A. Gover, “Equivalence of the coupled-mode and Floquet-Bloch formalisms in periodic optical waveguides,” Appl. Phys. Lett. 26, 537–539 (1975).
[Crossref]

Andés, M. V.

Andés, P.

Atkin, D. M.

Barkou, S. E.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett. 24, 46–48 (1999).
[Crossref]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

Birks, T. A.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding: errata,” Opt. Lett. 22, 484–485 (1997).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[Crossref] [PubMed]

Bjarklev, A.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett. 24, 46–48 (1999).
[Crossref]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

Broeng, J.

S. E. Barkou, J. Broeng, and A. Bjarklev, “Silica-air photonic crystal fiber design that permits waveguiding by a true photonic bandgap effect,” Opt. Lett. 24, 46–48 (1999).
[Crossref]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

Chen, P. C.

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

Cho, A. Y.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[Crossref]

A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
[Crossref]

Cregan, R. F.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

de Sandro, J. P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

Erdogan, T.

T. Erdogan and D. G. Hall, “Circularly symmetric distribution feedback semiconductor laser: An analysis,” J.Appl.Phys. 68, 1435–1444 (1990).
[Crossref]

Ferrando, A.

Glinski, J.

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

Gover, A.

A. Yariv and A. Gover, “Equivalence of the coupled-mode and Floquet-Bloch formalisms in periodic optical waveguides,” Appl. Phys. Lett. 26, 537–539 (1975).
[Crossref]

Hall, D. G.

T. Erdogan and D. G. Hall, “Circularly symmetric distribution feedback semiconductor laser: An analysis,” J.Appl.Phys. 68, 1435–1444 (1990).
[Crossref]

Imada, M.

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

Ishikawa, T.

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

Knight, J. C.

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding: errata,” Opt. Lett. 22, 484–485 (1997).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[Crossref] [PubMed]

Lacroix, S.

X. H. Zheng and S. Lacroix, “Mode coupling in circular-cylindrical system and its application to fingerprint resonators,” J.Lightwave Technol. 8, 1509–1516 (1990).
[Crossref]

Maciejko, R.

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

Makino, T.

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

Miret, J. J.

Najafi, S. I.

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

Ng, W.

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

Noda, S.

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

Russell, P. St. J.

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

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]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding: errata,” Opt. Lett. 22, 484–485 (1997).
[Crossref] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996).
[Crossref] [PubMed]

Sasaki, A.

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

Silverstre, E.

Svilans, M.

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

Toda, M.

M. Toda, “Single-mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473–481 (1990).
[Crossref]

Wu, C.

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

Xue-Heng, Z.

Z. Xue-Heng, “Theory of two-dimensional ‘Fingerprint’ resonators,” Electron.Lett. 25, 1311–1312 (1989).
[Crossref]

Yariv, A.

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[Crossref]

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
[Crossref]

A. Yariv and A. Gover, “Equivalence of the coupled-mode and Floquet-Bloch formalisms in periodic optical waveguides,” Appl. Phys. Lett. 26, 537–539 (1975).
[Crossref]

Yeh, P.

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[Crossref]

A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
[Crossref]

Zheng, X. H.

X. H. Zheng and S. Lacroix, “Mode coupling in circular-cylindrical system and its application to fingerprint resonators,” J.Lightwave Technol. 8, 1509–1516 (1990).
[Crossref]

Appl. Phys. Lett. (4)

A. Yariv and A. Gover, “Equivalence of the coupled-mode and Floquet-Bloch formalisms in periodic optical waveguides,” Appl. Phys. Lett. 26, 537–539 (1975).
[Crossref]

A. Y. Cho, A. Yariv, and P. Yeh, “Observation of confined propagation in Bragg waveguides,” Appl. Phys. Lett. 30, 471–472 (1977).
[Crossref]

P. Yeh, A. Yariv, and A. Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32, 104–105 (1978).
[Crossref]

W. Ng, P. Yeh, P. C. Chen, and A. Yariv, “Optical surface waves in periodic layered medium grown by liquid phase epitaxy,” Appl. Phys. Lett. 32, 370–371 (1978).
[Crossref]

Electron. Lett. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
[Crossref]

Electron.Lett. (1)

Z. Xue-Heng, “Theory of two-dimensional ‘Fingerprint’ resonators,” Electron.Lett. 25, 1311–1312 (1989).
[Crossref]

IEEE J. Quantum Electron. (1)

M. Toda, “Single-mode behavior of a circular grating for potential disk-shaped DFB lasers,” IEEE J. Quantum Electron. 26, 473–481 (1990).
[Crossref]

IEEE J.Photon.Technol.Lett (1)

S. Noda, T. Ishikawa, M. Imada, and A. Sasaki, “Surface-emitting device with embedded circular grating coupler for possible application on optoelectronic integrated devices,” IEEE J.Photon.Technol.Lett 7, 1397–1399 (1995).
[Crossref]

J. Opt. Soc. Am. (1)

J. C. Knight, T. A. Birks, P. St. J. Russell, and J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. 15, 748–752 (1998).
[Crossref]

J.Appl.Phys. (1)

T. Erdogan and D. G. Hall, “Circularly symmetric distribution feedback semiconductor laser: An analysis,” J.Appl.Phys. 68, 1435–1444 (1990).
[Crossref]

J.Lightwave Technol. (3)

X. H. Zheng and S. Lacroix, “Mode coupling in circular-cylindrical system and its application to fingerprint resonators,” J.Lightwave Technol. 8, 1509–1516 (1990).
[Crossref]

C. Wu, T. Makino, J. Glinski, R. Maciejko, and S. I. Najafi, “Self-consistent coupled-wave theory for circular gratings on planar dielectric waveguides,” J.Lightwave Technol. 8, 1264–1277 (1991).
[Crossref]

C. Wu, T. Makino, R. Maciejko, S. I. Najafi, and M. Svilans, “Simplified coupled-wave equations for cylindrical waves in circular grating planar waveguides,” J.Lightwave Technol. 10, 1575–1589 (1992).
[Crossref]

Opt. Commun. (1)

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, and P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998).
[Crossref]

Opt. Lett. (5)

Science (1)

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russell, “Photonic Band Gap Guidance in Optical Fibers,” Science 282, 1476–1478 (1998).
[Crossref] [PubMed]

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Figures (14)

Fig. 1.
Fig. 1.

A waveguide structure with one-dimensional periodic structures.

Fig. 2.
Fig. 2.

Definition of propagation direction of a wave in a periodic structure.

Fig. 3.
Fig. 3.

Coaxial periodic optical waveguide.

Fig. 4.
Fig. 4.

Cross-section.

Fig. 5.
Fig. 5.

Dispersion curves for k 0 c=1.0

Fig. 6.
Fig. 6.

Dispersion curves for k 0 c=5.0

Fig. 7.
Fig. 7.

Stopband of a coaxial periodic optical waveguide.

Fig. 8.
Fig. 8.

Stopband of a one-dimensonal photonic band gap structure.

Fig. 9.
Fig. 9.

z-direction components of magnetic field of TE-polarized mode and electric field of TM-polarized mode, where k=1.2k 0 and β=0.7859[TE], 0.5270[TM].

Fig. 10.
Fig. 10.

z-direction components of magnetic field of TE-polarized mode and electric field of TM-polarized mode, where k=3.0k 0 and β=0.9672[TE], 0.9672[TM].

Fig. 11.
Fig. 11.

Intensity of EM wave field in CPOW, excited by TE01 mode. |T|=0.986, |R|=0.007.

Fig. 12.
Fig. 12.

Intensity of EM wave field in CPOW, excited by TE21 mode. |T|=0.479, |R|=0.049.

Fig. 13.
Fig. 13.

Intensity of EM wave field in CPOW, excited by TM01 mode. |T|=0.440, |R|=0.106.

Fig. 14.
Fig. 14.

Intensity of EM wave field in CPOW, excited by TM21 mode. |T|=0.049, |R|=0.493.

Equations (16)

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cos k TE ( a + b ) = n 1 2 cos 2 θ 1 + n 2 2 cos 2 θ 2 2 n 1 n 2 cos θ 1 cos θ 2 sin ( n 1 cos θ 1 k a ) sin ( n 2 cos θ 2 k b )
+ cos ( n 1 cos θ 1 k a ) cos ( n 2 cos θ 2 k b )
cos k TM ( a + b ) = n 2 2 cos 2 θ 1 + n 1 2 cos 2 θ 2 2 n 1 n 2 cos θ 1 cos θ 2 sin ( n 1 cos θ 1 k a ) sin ( n 2 cos θ 2 k b )
+ cos ( n 1 cos θ 1 k a ) cos ( n 2 cos θ 2 k b ) ,
cos k TE ( a + b ) > 1 ,
cos k TM ( a + b ) > 1 ,
r i = { n ( b + a ) + c i = 2 n n ( b + a ) + b + c i = 2 n + 1 ( n = 0 , 1 , 2 , 3 , ) .
i = { I i = 2 n II i = 2 n + 1 ( n = 0 , 1 , 2 , 3 , ) .
E z ( r ) = { A i J m ( q i r ) + B i Y m ( q i r ) } sin ( m ϕ + θ m )
H z ( r ) = { C i J m ( q i r ) + D i Y m ( q i r ) } cos ( m ϕ + θ m ) ,
[ E z ( r ) H z ( r ) E ϕ ( r ) H ϕ ( r ) ] = U · T ( r , i ) · u i
U [ sin ( m ϕ + θ m ) 0 0 0 0 cos ( m ϕ + θ m ) 0 0 0 0 cos ( m ϕ + θ m ) 0 0 0 0 sin ( m ϕ + θ m ) ]
T ( r , i ) [ J m ( q i r ) Y m ( q i r ) 0 0 0 0 J m ( q i r ) Y m ( q i r ) j β m J m ( q i r ) q i 2 r j β m Y m ( q i r ) q i 2 r + j ω μ 0 J ' m ( q i r ) q i + j ω μ 0 Y ' m ( q i r ) q i j ω i J ' m ( q i r ) q i j ω i Y ' m ( q i r ) q i + j β m J m ( q i r ) q i 2 r + j β m Y m ( q i r ) q i 2 r ]
u i = [ A i , B i , C i , D i ] t .
T ( r i , i ) · u i = T ( r i , i + 1 ) · u i + 1 .
u 0 = i = 0 n R i · u n + 1 , R i T 1 ( r i , i ) · T ( r i , i + 1 ) ,

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