Abstract

We extensively study the propagation features of higher-order modes in a photonic crystal fiber (PCF). Our analysis is based on a full-vector modal technique specially adapted to accurately describe light propagation in PCF’s. Unlike conventional fibers, PCF’s exhibit a somewhat unusual mechanism for the generation of higher-order modes. Accordingly, PCF’s are characterized by the constancy of the number of modes below a wavelength threshold. An explicit verification of this property is given through a complete analysis of the dispersion relations of higher-order modes in terms of the structural parameters of this kind of fiber. The transverse irradiance distributions for some of these higher-order modes are also presented, showing an excellent agreement with recent experimental measurements. In the same way, the full-vector nature of our approach allows us to analyze the rich polarization structure of the PCF mode spectrum.

© 2000 Optical Society of America

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  1. P. St. J. Russell, T. A. Birks, F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995); J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); erratum, 22, 484 (1997).
    [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987);E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [CrossRef] [PubMed]
  3. T. M. Monro, D. J. Richardson, N. G. R. Broderick, P. J. Bennett, “Holey fibers: an efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999).
    [CrossRef]
  4. J. C. Knight, J. Broeng, T. A. Birks, P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
    [CrossRef] [PubMed]
  5. J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
    [CrossRef]
  6. J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
    [CrossRef]
  7. T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  8. E. Silvestre, P. St. J. Russell, T. A. Birks, J. C. Knight, “Analysis and design of an endlessly single-mode finned dielectric waveguide,” J. Opt. Soc. Am. A 15, 3067–3075 (1998).
    [CrossRef]
  9. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
    [CrossRef]
  10. D. Mogilevtsev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1663 (1998).
    [CrossRef]
  11. A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
    [CrossRef]
  12. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, J. P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347–1348 (1998).
    [CrossRef]
  13. E. Silvestre, M. V. Andrés, P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber modes,” J. Lightwave Technol. 16, 923–928 (1998).
    [CrossRef]
  14. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Harcourt Brace College Publishers, Fort Worth, Tex., 1976), pp. 135–136.
  15. M. Creutz, Quarks, Gluons and Lattices (Cambridge U. Press, Cambridge, UK, 1985), pp. 10, 14.
  16. R. P. Feynman, Statistical Mechanics (Addison-Wesley, Reading, Mass., 1972), pp. 76–96; J. I. Kapusta, Finite-Temperature Field Theory (Cambridge U. Press, Cambridge, UK, 1989), pp. 9–16.
  17. A. Ferrando, A. Jaramillo, “Two dimensional quantum chromodynamics as the limit of higher dimensional theories,” Phys. Lett. B 341, 342–348 (1995);“The role of tem-perature in a dimensional approach to QCD3,” Nucl. Phys. B 457, 57–77 (1995).
    [CrossRef]
  18. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
    [CrossRef]
  19. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.
  20. J. C. Knight, T. A. Birks, P. St. J. Russell, J. P. de Sandro, “Properties of photonic crystal fiber and the effective index model,” J. Opt. Soc. Am. A 15, 748–752 (1998).
    [CrossRef]

1999 (3)

1998 (7)

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

E. Silvestre, M. V. Andrés, P. Andrés, “Biorthonormal-basis method for the vector description of optical-fiber modes,” J. Lightwave Technol. 16, 923–928 (1998).
[CrossRef]

E. Silvestre, P. St. J. Russell, T. A. Birks, J. C. Knight, “Analysis and design of an endlessly single-mode finned dielectric waveguide,” J. Opt. Soc. Am. A 15, 3067–3075 (1998).
[CrossRef]

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

D. Mogilevtsev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1663 (1998).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, 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, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

1997 (1)

1995 (1)

A. Ferrando, A. Jaramillo, “Two dimensional quantum chromodynamics as the limit of higher dimensional theories,” Phys. Lett. B 341, 342–348 (1995);“The role of tem-perature in a dimensional approach to QCD3,” Nucl. Phys. B 457, 57–77 (1995).
[CrossRef]

1994 (1)

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

1987 (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987);E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Andrés, M. V.

Andrés, P.

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Harcourt Brace College Publishers, Fort Worth, Tex., 1976), pp. 135–136.

Barkou, S. E.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

Bennett, P. J.

Birks, T. A.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

D. Mogilevtsev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1663 (1998).
[CrossRef]

E. Silvestre, P. St. J. Russell, T. A. Birks, J. C. Knight, “Analysis and design of an endlessly single-mode finned dielectric waveguide,” J. Opt. Soc. Am. A 15, 3067–3075 (1998).
[CrossRef]

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

T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

P. St. J. Russell, T. A. Birks, F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995); J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); erratum, 22, 484 (1997).
[CrossRef] [PubMed]

Bjarklev, A.

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

Broderick, N. G. R.

Broeng, J.

J. C. Knight, J. Broeng, T. A. Birks, 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, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Cregan, R. F.

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

Creutz, M.

M. Creutz, Quarks, Gluons and Lattices (Cambridge U. Press, Cambridge, UK, 1985), pp. 10, 14.

de Sandro, J. P.

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

Ferrando, A.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
[CrossRef]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
[CrossRef]

A. Ferrando, A. Jaramillo, “Two dimensional quantum chromodynamics as the limit of higher dimensional theories,” Phys. Lett. B 341, 342–348 (1995);“The role of tem-perature in a dimensional approach to QCD3,” Nucl. Phys. B 457, 57–77 (1995).
[CrossRef]

Feynman, R. P.

R. P. Feynman, Statistical Mechanics (Addison-Wesley, Reading, Mass., 1972), pp. 76–96; J. I. Kapusta, Finite-Temperature Field Theory (Cambridge U. Press, Cambridge, UK, 1989), pp. 9–16.

Jaramillo, A.

A. Ferrando, A. Jaramillo, “Two dimensional quantum chromodynamics as the limit of higher dimensional theories,” Phys. Lett. B 341, 342–348 (1995);“The role of tem-perature in a dimensional approach to QCD3,” Nucl. Phys. B 457, 57–77 (1995).
[CrossRef]

Joannopoulos, J. D.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987);E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Birks, 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, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

E. Silvestre, P. St. J. Russell, T. A. Birks, J. C. Knight, “Analysis and design of an endlessly single-mode finned dielectric waveguide,” J. Opt. Soc. Am. A 15, 3067–3075 (1998).
[CrossRef]

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

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

T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

Lloyd-Lucas, F. D.

P. St. J. Russell, T. A. Birks, F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995); J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); erratum, 22, 484 (1997).
[CrossRef] [PubMed]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

Meade, R. D.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Harcourt Brace College Publishers, Fort Worth, Tex., 1976), pp. 135–136.

Miret, J. J.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
[CrossRef]

A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, M. V. Andrés, “Full-vector analysis of a realistic photonic crystal fiber,” Opt. Lett. 24, 276–278 (1999).
[CrossRef]

Mogilevtsev, D.

Monro, T. M.

Monsoriu, J. A.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
[CrossRef]

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Richardson, D. J.

Silvestre, E.

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

St. J. Russell, P.

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
[CrossRef]

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

E. Silvestre, P. St. J. Russell, T. A. Birks, J. C. Knight, “Analysis and design of an endlessly single-mode finned dielectric waveguide,” J. Opt. Soc. Am. A 15, 3067–3075 (1998).
[CrossRef]

D. Mogilevtsev, T. A. Birks, P. St. J. Russell, “Group-velocity dispersion in photonic crystal fibers,” Opt. Lett. 23, 1662–1663 (1998).
[CrossRef]

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

J. C. Knight, J. Broeng, T. A. Birks, P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

T. A. Birks, J. C. Knight, P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

P. St. J. Russell, T. A. Birks, F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995); J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); erratum, 22, 484 (1997).
[CrossRef] [PubMed]

Winn, J. N.

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

Electron. Lett. (2)

A. Ferrando, E. Silvestre, J. J. Miret, J. A. Monsoriu, M. V. Andrés, P. St. J. Russell, “Designing a photonic crystal fibre with flattened chromatic dispersion,” Electron. Lett. 35, 325–326 (1999).
[CrossRef]

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

J. Lightwave Technol. (2)

J. Mod. Opt. (1)

J. N. Winn, R. D. Meade, J. D. Joannopoulos, “Two-dimensional photonic band-gap materials,” J. Mod. Opt. 41, 257–273 (1994);A. Mekkis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. Broeng, S. E. Barkou, A. Bjarklev, J. C. Knight, T. A. Birks, P. St. J. Russell, “Highly increased photonic band gaps in silica/air structures,” Opt. Commun. 156, 240–244 (1998);J. Broeng, D. Mogilevstev, S. E. Barkou, A. Bjarklev, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. Mater. Devices Syst. 5, 305–330 (1999).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. B (1)

A. Ferrando, A. Jaramillo, “Two dimensional quantum chromodynamics as the limit of higher dimensional theories,” Phys. Lett. B 341, 342–348 (1995);“The role of tem-perature in a dimensional approach to QCD3,” Nucl. Phys. B 457, 57–77 (1995).
[CrossRef]

Phys. Rev. B (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, O. L. Alerhand, “Accurate theoretical analysis of photonic band-gap materials,” Phys. Rev. B 48, 8434–8437 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987);E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, “Donor and acceptor modes in photonic band structures,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Science (1)

J. C. Knight, J. Broeng, T. A. Birks, P. St. J. Russell, “Photonic band gap guidance in optical fibers,” Science 282, 1476–1478 (1998).
[CrossRef] [PubMed]

Other (5)

P. St. J. Russell, T. A. Birks, F. D. Lloyd-Lucas, “Photonic Bloch waves and photonic band gaps,” in Confined Electrons and Photons: New Physics and Applications, E. Burstein, C. Weisbuch, eds. (Plenum, New York, 1995); J. C. Knight, T. A. Birks, P. St. J. Russell, D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996); erratum, 22, 484 (1997).
[CrossRef] [PubMed]

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983), pp. 595–606.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Saunders College Publishing, Harcourt Brace College Publishers, Fort Worth, Tex., 1976), pp. 135–136.

M. Creutz, Quarks, Gluons and Lattices (Cambridge U. Press, Cambridge, UK, 1985), pp. 10, 14.

R. P. Feynman, Statistical Mechanics (Addison-Wesley, Reading, Mass., 1972), pp. 76–96; J. I. Kapusta, Finite-Temperature Field Theory (Cambridge U. Press, Cambridge, UK, 1989), pp. 9–16.

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Figures (7)

Fig. 1
Fig. 1

(a) Transverse section of a hexagonally centered PCF, (b) replication of the unit cell of dimensions D×D for a hexagonally centered PCF configuration to construct the superlattice structure.

Fig. 2
Fig. 2

Modal dispersion relations for different configurations of a PCF: (a) single-polarization doublet (single-mode), a=0.3 μm and Λ=2.3 μm; (b) Two-multiplets configuration, a=0.7 μm and Λ=2.3 μm; (c) several-multiplets configuration, a=0.9 μm and Λ=2.3 μm.

Fig. 3
Fig. 3

V parameter of a PCF versus the normalized frequency for different filling fractions (or, equivalently, for different a/Λ ratios). The pitch Λ is 2.3 μm. From bottom to top, all curves are obtained by increasing a in steps of 0.2 μm. The lowest curve corresponds to a=0.1 μm. Below the a=0.5 μm curve, the configurations are single mode (single-polarization doublet). Notice the asymptotic flat behavior of all curves.

Fig. 4
Fig. 4

Irradiance and magnetic field distributions for the fundamental doublet of a PCF at λ=632.8 nm with a=0.3 μm and Λ=2.3 μm: (a) irradiance distribution of the two modes (level curve intervals, 2 dB); (b) magnetic field distribution of the almost-y-polarized member of this doublet; (c) magnetic field distribution for its partner, the quasi-x-polarized mode.

Fig. 5
Fig. 5

Irradiance distribution for the first higher-order multiplet of a PCF at λ=632.8 nm with a=0.7 μm and Λ=2.3 μm.

Fig. 6
Fig. 6

Magnetic field distribution of the four modes that constitute the first higher-order multiplet: (a) TE01 mode, (b) TM01 mode, (c) and (d) HE21 modes. The values of the structural parameters are the same as in Fig. 5.

Fig. 7
Fig. 7

Irradiance pattern corresponding to the linear combination of the TM01 mode [Fig. 6(b)] and one of the HE21 modes [Fig. 6(c)] belonging to the first almost-degenerated higher-order multiplet.

Equations (7)

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Lh=β2h,Le¯=β*2e¯,
Lγδ=(2+k2n2)δγδ-γσ σn2n2(δρρ),
γ, δ, σ, ρ=x, y,
hα(xt)=iˆciˆ,α exp(ikiˆxt),
j|L(x0)|i=exp[i(kiˆ-kjˆ)x0]j|L(0)|i.
j|L|i=x0Γ exp[i(kiˆ-kjˆ)x0]j|L(0)|i,
x0Γexp[i(kiˆ-kjˆ)x0]=N2-1(iˆ-jˆ)/NZ2-1otherwise;

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