Abstract

The dispersion and loss in microstructured fibers are studied using a full-vectorial compact-2D finite-difference method in frequency-domain. This method solves a standard eigen-value problem from the Maxwell’s equations directly and obtains complex propagation constants of the modes using anisotropic perfectly matched layers. A dielectric constant averaging technique using Ampere’s law across the curved media interface is presented. Both the real and the imaginary parts of the complex propagation constant can be obtained with a high accuracy and fast convergence. Material loss, dispersion and spurious modes are also discussed.

© 2004 Optical Society of America

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2004 (5)

2003 (5)

2002 (5)

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J Quantum Electron. 38, 927–933 (2002).
[Crossref]

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructuredd optical fibers,” Opt. Express 10, 853–864 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853
[Crossref] [PubMed]

T. P. White, B. T. Kuhlmey, R. C. Mcphedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, “Multipole method for microstructuredd optical fibers. I. Formulation,” J. Opt. Soc. Am. B 19, 2322 (2002).
[Crossref]

T. Tischler and W. Heinrich, “Accuracy limitations of perfectly matched layers in 3D Finite-difference frequency domain method,” IEEE Microwave Theory Tech. 50, 1885–1888 (2002).

2001 (2)

2000 (5)

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A 17, 1333–1339 (2000).
[Crossref]

J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andres, “Nearly zero ultra-flattened dispersion in photonic crystal fibers,” Opt. Lett. 25, 79–792 (2000).
[Crossref]

M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000).
[Crossref]

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

1999 (8)

M. Koshiba, Y. Tsuji, and M. Hikari, “Finite element beam propagation method with perfectly matched layer boundary conditions,” IEEE Trans. Magnetics 35, 1482–1485 (1999).
[Crossref]

J. Broeng, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[Crossref]

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

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

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

F. L. Teixeira and W. C. Chew, “Unified analysis of perfectly matched layers using differential forms,” Microwave Opt. Technol. Lett. 20, 124–126 (1999).
[Crossref]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE Trans. Magnetics 35, 1506–1509 (1999).
[Crossref]

1998 (1)

1997 (3)

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonantors with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645–1649 (1997).
[Crossref]

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[Crossref]

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microwave & Opt. Technol. Lett. 7, 363–369 (1997).
[Crossref]

1996 (1)

H. Y. D. Yang, “Finite difference analysis of 2D photonic crystals,” IEEE Trans. Microwave Theory Technol. 44, 2688–2695 (1996).
[Crossref]

1995 (3)

A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal, “Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin’s method with Hermite-Gauss basis functions,” J. Lightwave Technol. 13, 1795–1780 (1995).
[Crossref]

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

U. Pekel and R. Mittra, “An application of the perfectly matched layer (PML) concept to the finite element method frequency domain analysis of scattering problems,” IEEE Microwave Guided Wave Lett. 5, 258–260 (1995).
[Crossref]

1994 (2)

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J Comp. Phys. 114, 185–200 (1994).
[Crossref]

1993 (1)

A. C. Cangellaris, “Numerical stability and numerical dispersion of a compact 2D FDTD method used for the dispersion analysis of waveguides,” IEEE Microwave Guided Wave Lett. 3, 3–5 (1993).
[Crossref]

1992 (3)

A. Asi and L. Shafai, “Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD,” Electron. Lett. 28, 1451–1452 (1992).
[Crossref]

S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microwave Guided Wave Lett. 2, 165–167 (1992).
[Crossref]

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J Quantum Electron. 28, 459–465 (1992).
[Crossref]

1986 (2)

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 34, 1104–1113 (1986).
[Crossref]

D. H. Choi and W. J. R. Hoeffer, “The finite-difference time-domain method and its application to eigen-value problems,” IEEE Trans. Microwave Theory Tech. 34, 1464–1470 (1986).
[Crossref]

1975 (1)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides-II:Theory,” IEEE Trans. Microwave Theory Tech. 23, 429–433 (1975).
[Crossref]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1966).
[Crossref]

Albin, S.

Alimenti, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Andres, M. V.

Andres, P.

Arndt, F.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 34, 1104–1113 (1986).
[Crossref]

Asi, A.

A. Asi and L. Shafai, “Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD,” Electron. Lett. 28, 1451–1452 (1992).
[Crossref]

Barkou, S. E.

Bassi, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Bennett, P. J.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J Comp. Phys. 114, 185–200 (1994).
[Crossref]

Bierwirth, K.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 34, 1104–1113 (1986).
[Crossref]

Birks, T. A.

Bjarklev, A.

J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic crystal fibres (Kluwer Academic Publishers, Boston/Dordrecht/London, 2003).
[Crossref]

Bjarklev, A. S.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic crystal fibres (Kluwer Academic Publishers, Boston/Dordrecht/London, 2003).
[Crossref]

Botten, L. C.

Brechet, F.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Broderick, N. G. R.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

Broeng, J.

J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, “Analysis of air-guiding photonic bandgap fibers,” Opt. Lett. 25, 96–98 (2000).
[Crossref]

J. Broeng, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[Crossref]

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic crystal fibres (Kluwer Academic Publishers, Boston/Dordrecht/London, 2003).
[Crossref]

Brown, T. G.

Cangellaris, A. C.

A. C. Cangellaris, “Numerical stability and numerical dispersion of a compact 2D FDTD method used for the dispersion analysis of waveguides,” IEEE Microwave Guided Wave Lett. 3, 3–5 (1993).
[Crossref]

Chang, H. C.

Chew, W. C.

F. L. Teixeira and W. C. Chew, “Unified analysis of perfectly matched layers using differential forms,” Microwave Opt. Technol. Lett. 20, 124–126 (1999).
[Crossref]

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[Crossref]

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microwave & Opt. Technol. Lett. 7, 363–369 (1997).
[Crossref]

Choi, D. H.

D. H. Choi and W. J. R. Hoeffer, “The finite-difference time-domain method and its application to eigen-value problems,” IEEE Trans. Microwave Theory Tech. 34, 1464–1470 (1986).
[Crossref]

Cucinotta, A.

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

de Sterke, C. M.

Ferrando, A.

Gallawa, R. L.

A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal, “Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin’s method with Hermite-Gauss basis functions,” J. Lightwave Technol. 13, 1795–1780 (1995).
[Crossref]

Goyal, I. C.

A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal, “Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin’s method with Hermite-Gauss basis functions,” J. Lightwave Technol. 13, 1795–1780 (1995).
[Crossref]

Grattan, K. T. V.

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

Guenneau, S.

S. Guenneau, A. Nicolet, F. Zolla, and S. Lasquellec, “Numerical and theoretical study of photonic crystal fibers,” Progress in Electromagnetics Research 41, 271–305 (2003).

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

Guo, S.

Guobing, R.

Hadjicharalambous, A.

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

Hasegawa, T.

Heinrich, W.

T. Tischler and W. Heinrich, “Accuracy limitations of perfectly matched layers in 3D Finite-difference frequency domain method,” IEEE Microwave Theory Tech. 50, 1885–1888 (2002).

Hikari, M.

M. Koshiba, Y. Tsuji, and M. Hikari, “Finite element beam propagation method with perfectly matched layer boundary conditions,” IEEE Trans. Magnetics 35, 1482–1485 (1999).
[Crossref]

Hoeffer, W. J. R.

D. H. Choi and W. J. R. Hoeffer, “The finite-difference time-domain method and its application to eigen-value problems,” IEEE Trans. Microwave Theory Tech. 34, 1464–1470 (1986).
[Crossref]

Houshmand, B.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonantors with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645–1649 (1997).
[Crossref]

Ikram, K.

Issa, N. A.

Itoh, T.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonantors with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645–1649 (1997).
[Crossref]

Jin, H.

S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microwave Guided Wave Lett. 2, 165–167 (1992).
[Crossref]

Jin, J. M.

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microwave & Opt. Technol. Lett. 7, 363–369 (1997).
[Crossref]

Kaneda, N.

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonantors with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645–1649 (1997).
[Crossref]

Koshiba, M.

Kuhlmey, B. T.

Lasquellec, S.

S. Guenneau, A. Nicolet, F. Zolla, and S. Lasquellec, “Numerical and theoretical study of photonic crystal fibers,” Progress in Electromagnetics Research 41, 271–305 (2003).

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

Li, J.

A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal, “Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin’s method with Hermite-Gauss basis functions,” J. Lightwave Technol. 13, 1795–1780 (1995).
[Crossref]

Lusse, P.

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

Marcou, J.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Marcuse, D.

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J Quantum Electron. 28, 459–465 (1992).
[Crossref]

Marengo, E. A.

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE Trans. Magnetics 35, 1506–1509 (1999).
[Crossref]

Maystre, D.

McIsaac, P. R.

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides-II:Theory,” IEEE Trans. Microwave Theory Tech. 23, 429–433 (1975).
[Crossref]

Mcphedran, R. C.

Mezzanotte, P.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Michielssen, E.

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microwave & Opt. Technol. Lett. 7, 363–369 (1997).
[Crossref]

Miller, E. L.

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE Trans. Magnetics 35, 1506–1509 (1999).
[Crossref]

Milton, G. W.

G. W. Milton, The theory of composites (Cambridge University Press, Cambridge, UK, 2002).
[Crossref]

Miret, J. J.

Mittra, R.

U. Pekel and R. Mittra, “An application of the perfectly matched layer (PML) concept to the finite element method frequency domain analysis of scattering problems,” IEEE Microwave Guided Wave Lett. 5, 258–260 (1995).
[Crossref]

Mogilevtsev, D.

Monro, T. M.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

Nicolet, A.

S. Guenneau, A. Nicolet, F. Zolla, and S. Lasquellec, “Numerical and theoretical study of photonic crystal fibers,” Progress in Electromagnetics Research 41, 271–305 (2003).

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

Pagnoux, D.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Peiosi, G.

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

Pekel, U.

U. Pekel and R. Mittra, “An application of the perfectly matched layer (PML) concept to the finite element method frequency domain analysis of scattering problems,” IEEE Microwave Guided Wave Lett. 5, 258–260 (1995).
[Crossref]

Poladian, L.

Rahman, B. M. A.

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

Rappaport, C. M.

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE Trans. Magnetics 35, 1506–1509 (1999).
[Crossref]

Renversez, G.

Richardson, D. J.

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

Rogowski, R. S

Rogowski, R. S.

Roselli, L.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Roy, P.

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Russel, P. St. J.

Russell, P.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Saitoh, K.

Sasaoka, E.

Schule, J.

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

Schulz, N.

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 34, 1104–1113 (1986).
[Crossref]

Selleri, S.

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

Shafai, L.

A. Asi and L. Shafai, “Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD,” Electron. Lett. 28, 1451–1452 (1992).
[Crossref]

Shuisheng, J.

Shuqin, L.

Silvestre, E.

Sondergaard, T.

Sorrentino, R.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Stuwe, P.

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

Tartarini, G.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Teixeira, F. L.

F. L. Teixeira and W. C. Chew, “Unified analysis of perfectly matched layers using differential forms,” Microwave Opt. Technol. Lett. 20, 124–126 (1999).
[Crossref]

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[Crossref]

Themistos, C.

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

Tischler, T.

T. Tischler and W. Heinrich, “Accuracy limitations of perfectly matched layers in 3D Finite-difference frequency domain method,” IEEE Microwave Theory Tech. 50, 1885–1888 (2002).

Tsuji, Y.

M. Koshiba and Y. Tsuji, “Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems,” J. Lightwave Technol. 18, 737–743 (2000).
[Crossref]

M. Koshiba, Y. Tsuji, and M. Hikari, “Finite element beam propagation method with perfectly matched layer boundary conditions,” IEEE Trans. Magnetics 35, 1482–1485 (1999).
[Crossref]

Unger, H. G.

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

Vahldieck, R.

S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microwave Guided Wave Lett. 2, 165–167 (1992).
[Crossref]

Vincetti, L.

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

Weisshaar, A.

A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal, “Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin’s method with Hermite-Gauss basis functions,” J. Lightwave Technol. 13, 1795–1780 (1995).
[Crossref]

White, T. P.

Wu, F.

Xiao, S.

S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microwave Guided Wave Lett. 2, 165–167 (1992).
[Crossref]

Yang, H. Y. D.

H. Y. D. Yang, “Finite difference analysis of 2D photonic crystals,” IEEE Trans. Microwave Theory Technol. 44, 2688–2695 (1996).
[Crossref]

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1966).
[Crossref]

Yu, C. P.

Zepparelli, F.

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Zhi, W.

Zhu, Z.

Zoboli, M.

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

Zolla, F.

S. Guenneau, A. Nicolet, F. Zolla, and S. Lasquellec, “Numerical and theoretical study of photonic crystal fibers,” Progress in Electromagnetics Research 41, 271–305 (2003).

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

Electron. Lett. (1)

A. Asi and L. Shafai, “Dispersion analysis of anisotropic inhomogeneous waveguides using compact 2D-FDTD,” Electron. Lett. 28, 1451–1452 (1992).
[Crossref]

IEEE J Quantum Electron. (2)

D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J Quantum Electron. 28, 459–465 (1992).
[Crossref]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J Quantum Electron. 38, 927–933 (2002).
[Crossref]

IEEE Microwave Guided Wave Lett. (4)

A. C. Cangellaris, “Numerical stability and numerical dispersion of a compact 2D FDTD method used for the dispersion analysis of waveguides,” IEEE Microwave Guided Wave Lett. 3, 3–5 (1993).
[Crossref]

S. Xiao, R. Vahldieck, and H. Jin, “Full-wave analysis of guided wave structures using a novel 2-D FDTD,” IEEE Microwave Guided Wave Lett. 2, 165–167 (1992).
[Crossref]

F. L. Teixeira and W. C. Chew, “Systematic derivation of anisotropic PML absorbing media in cylindrical and spherical coordinates,” IEEE Microwave Guided Wave Lett. 7, 371–373 (1997).
[Crossref]

U. Pekel and R. Mittra, “An application of the perfectly matched layer (PML) concept to the finite element method frequency domain analysis of scattering problems,” IEEE Microwave Guided Wave Lett. 5, 258–260 (1995).
[Crossref]

IEEE Microwave Theory Tech. (1)

T. Tischler and W. Heinrich, “Accuracy limitations of perfectly matched layers in 3D Finite-difference frequency domain method,” IEEE Microwave Theory Tech. 50, 1885–1888 (2002).

IEEE Trans. Antennas Propagat. (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1966).
[Crossref]

IEEE Trans. Magnetics (2)

M. Koshiba, Y. Tsuji, and M. Hikari, “Finite element beam propagation method with perfectly matched layer boundary conditions,” IEEE Trans. Magnetics 35, 1482–1485 (1999).
[Crossref]

E. A. Marengo, C. M. Rappaport, and E. L. Miller, “Optimum PML ABC conductivity profile in FDFD,” IEEE Trans. Magnetics 35, 1506–1509 (1999).
[Crossref]

IEEE Trans. Microwave Theory Tech. (4)

P. R. McIsaac, “Symmetry-induced modal characteristics of uniform waveguides-II:Theory,” IEEE Trans. Microwave Theory Tech. 23, 429–433 (1975).
[Crossref]

D. H. Choi and W. J. R. Hoeffer, “The finite-difference time-domain method and its application to eigen-value problems,” IEEE Trans. Microwave Theory Tech. 34, 1464–1470 (1986).
[Crossref]

N. Kaneda, B. Houshmand, and T. Itoh, “FDTD analysis of dielectric resonantors with curved surfaces,” IEEE Trans. Microwave Theory Tech. 45, 1645–1649 (1997).
[Crossref]

K. Bierwirth, N. Schulz, and F. Arndt, “Finite-difference analysis of rectangular dielectric waveguide structures,” IEEE Trans. Microwave Theory Tech. 34, 1104–1113 (1986).
[Crossref]

IEEE Trans. Microwave Theory Technol. (1)

H. Y. D. Yang, “Finite difference analysis of 2D photonic crystals,” IEEE Trans. Microwave Theory Technol. 44, 2688–2695 (1996).
[Crossref]

International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL (1)

S. Guenneau, S. Lasquellec, A. Nicolet, and F. Zolla, “Design of photonic crystal fibers using finite elements,” International J. Computation and Mathematics in Electrical & Electronics Engineering COMPEL 21, 534–539 (2002).
[Crossref]

J Comp. Phys. (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J Comp. Phys. 114, 185–200 (1994).
[Crossref]

J Lightwave Technol. (3)

P. Lusse, P. Stuwe, J. Schule, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J Lightwave Technol. 12, 487–494 (1994).
[Crossref]

C. Themistos, B. M. A. Rahman, A. Hadjicharalambous, and K. T. V. Grattan, “Loss/gain characterization of optical waveguides,” J Lightwave Technol. 13, 1760–1765 (1995).
[Crossref]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, “Holey optical fibers: an efficient modal model,” J Lightwave Technol. 17, 1093–1102 (1999).
[Crossref]

J. Lightwave Technol. (4)

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

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

Microwave & Opt. Technol. Lett. (1)

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microwave & Opt. Technol. Lett. 7, 363–369 (1997).
[Crossref]

Microwave Opt. Techn. Lett. (1)

A. Cucinotta, G. Peiosi, S. Selleri, L. Vincetti, and M. Zoboli, “Perfectly matched anisotropic layers for optical waveguide analysis through the finite-element beam-propagation method,” Microwave Opt. Techn. Lett. 23, 67–69 (1999).
[Crossref]

Microwave Opt. Technol. Lett. (1)

F. L. Teixeira and W. C. Chew, “Unified analysis of perfectly matched layers using differential forms,” Microwave Opt. Technol. Lett. 20, 124–126 (1999).
[Crossref]

Opt. and Quantum Electron. (1)

F. Zepparelli, P. Mezzanotte, F. Alimenti, L. Roselli, R. Sorrentino, G. Tartarini, and P. Bassi, “Rigorous analysis of 3D optical and optoelectronic devices by the Compact-2D-FDTD method,” Opt. and Quantum Electron. 31, 827–841 (1999).
[Crossref]

Opt. Express (8)

S. Guo, F. Wu, S. Albin, and R. S Rogowski, “Photonic band gap analysis using finite-difference frequency-domain method,” Opt. Express 12, 1741–1746 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1741
[Crossref] [PubMed]

C. P. Yu and H. C. Chang, “Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals,” Opt. Express 12, 1397–1408 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1397
[Crossref] [PubMed]

Z. Zhu and T. G. Brown, “Full-vectorial finite-difference analysis of microstructuredd optical fibers,” Opt. Express 10, 853–864 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-853
[Crossref] [PubMed]

Z. Zhu and T. G. Brown, “Analysis of the space filling modes of photonic crystal fibers,” Opt. Express 8, 547–554 (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-10-547
[Crossref] [PubMed]

K. Saitoh, M. Koshiba, T. Hasegawa, and E. Sasaoka, “Chromatic dispersion control in photonic crystal fibers: application to ultra-flattened dispersion,” Opt. Express 11, 843–852 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-8-843
[Crossref] [PubMed]

W. Zhi, R. Guobing, L. Shuqin, and J. Shuisheng, “Supercell lattice method for photonic crystal fibers,” Opt. Express 11, 980–991 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-9-980
[Crossref] [PubMed]

S. Guo, S. Albin, and R. S. Rogowski, “Comparative analysis of Bragg fibers,” Opt. Express 12, 198–207 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-207
[Crossref] [PubMed]

R. Guobing, W. Zhi, L. Shuqin, and J. Shuisheng, “Full-vectorial analysis of complex refractive index photonic crystal fibers,” Opt. Express 12, 1126–1135 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1135
[Crossref]

Opt. Fiber Technol. (2)

J. Broeng, “Photonic crystal fibers: a new class of optical waveguides,” Opt. Fiber Technol. 5, 305–330 (1999).
[Crossref]

F. Brechet, J. Marcou, D. Pagnoux, and P. Roy, “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite-element method,” Opt. Fiber Technol. 6, 181–191 (2000).
[Crossref]

Opt. Lett. (5)

Progress in Electromagnetics Research (1)

S. Guenneau, A. Nicolet, F. Zolla, and S. Lasquellec, “Numerical and theoretical study of photonic crystal fibers,” Progress in Electromagnetics Research 41, 271–305 (2003).

Science (1)

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003).
[Crossref] [PubMed]

Other (2)

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic crystal fibres (Kluwer Academic Publishers, Boston/Dordrecht/London, 2003).
[Crossref]

G. W. Milton, The theory of composites (Cambridge University Press, Cambridge, UK, 2002).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1.

The PCF under study. A quarter of the PCF is used in calculation, which can obtain the third and fourth mode classes with a 90-degree rotation symmetry.

Fig. 2.
Fig. 2.

The relative error of the calculated complex mode index of the fundamental mode. The y-axis is the relative error of the real and imaginary part of the mode index of the fundamental mode. Note the different scales of the two y-axes.

Fig. 3.
Fig. 3.

The six field components and the discretization of the transverse index profile in the x-y plane. The E and H components are in red and blue colors respectively. The orange line denotes the curved interface across the cells, and the dotted cells show the integration plane for Ex and Ey respectively.

Fig. 4.
Fig. 4.

Calculation of Ex, Ey and Ez using Ampere’s law. The orange line denotes the dielectric boundary in the integration plane. From left to right are the integration cells for Ex, Ey and Ez respectively.

Fig. 5.
Fig. 5.

The accuracy and convergence of the complex effective mode index using a more reasonable averaging technique. Note that the scale of the right y-axis is at least an order of magnitude smaller than the corresponding one in Fig. 2.

Fig. 6.
Fig. 6.

The mode field patterns of the fundamental mode (top three) and 2nd-order mode (bottom three) in the degenerate mode class 3 and 4.

Fig. 7.
Fig. 7.

Some spurious cladding modes created by the artificial waveguide between the PML + zero boundary and the air holes. These modes are weak and highly lossy.

Tables (2)

Tables Icon

Table 1. Calculated mode index of the fundamental mode. The accurate value is 1.445395345+3.15×10-8i (by multipole method in [32])

Tables Icon

Table 2. The complex mode index with a lossy core material

Equations (30)

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

ξ ( x , y , z , t ) = { ξ t ( x , y ) + ξ z ( x , y ) } exp [ j ( ω t β z ) ]
( t 2 + k 0 2 n 2 β 2 ) E t = t ( E t · t ln n 2 )
( t 2 + k 0 2 n 2 β 2 ) H t = ( t × H t ) × t ln n 2
( t 2 + k 0 2 n 2 β 2 ) E z = j β E t · t ln n 2
( t 2 + k 0 2 n 2 β 2 ) H z = ( t H z + j β H t ) · t ln n 2
j k 0 s ε r E = × H
j k 0 s μ r H = × E
s = [ s y s x s x s y s x s y ]
s x = 1 σ x j w ε 0 , s y = 1 σ y j w ε 0
j k 0 [ s y s x ε rx s x s y ε ry s x s y ε rz ] [ E x E y E z ] = [ 0 j β I V y j β I 0 V x V y V x 0 ] [ H x H y H z ]
j k 0 [ s y s x μ rx s x s y μ ry s x s y μ rz ] [ H x H y H z ] = [ 0 j β I U y j β I 0 U x U y U x 0 ] [ E x E y E z ]
ε rx = s y s x ε rx , ε ry = s x s y ε ry , ε rz = s x s y ε rz
μ rx = s y s x μ rx , μ ry = s x s y μ ry , μ rz = s x s y μ rz
[ Q xx Q xy Q yx Q yy ] [ H x H y ] = β 2 [ H x H y ]
[ P xx P xy P yx P yy ] [ E x E y ] = β 2 [ E x E y ]
P xx = μ ry V y μ rz 1 U y + U x ε rz 1 V x ε rx + k 0 2 μ ry ε rx + k 0 2 U x ε rz 1 { V x V y V y V x } μ rz 1 U y
P xy = μ ry V y μ rz 1 U x + U x ε rz 1 V y ε ry + k 0 2 U x ε rz 1 { V y V x V x V y } μ rz 1 U x
P yx = μ rx V x μ rz 1 U y + U y ε rz 1 V x ε rx + k 0 2 U y ε rz 1 { V x V y V y V x } μ rz 1 U y
P yy = μ rx V x μ rz 1 U x + k 0 2 μ rx ε ry + U y ε rz 1 V y ε ry + k 0 2 U y ε rz 1 { V y V x V x V y } μ rz 1 U x
Q xx = ε ry U y ε rz 1 V y + V x μ rz 1 U x μ rx + k 0 2 ε ry μ rx + k 0 2 V x μ rz 1 { U x U y U y U x } ε rz 1 V y
Q xy = ε ry U y ε rz 1 V x + V x μ rz 1 U y μ ry + k 0 2 V x μ rz 1 { U y U x U x U y } ε rz 1 V x
Q yx = ε rx U x ε rz 1 V y + V y μ rz 1 U x μ rx + k 0 2 V y μ rz 1 { U x U y U y U x } ε rz 1 V y
Q yy = ε rx U x ε rz 1 V x + k 0 2 ε rx μ ry + V y μ rz 1 U y μ ry + k 0 2 V y μ rz 1 { U y U x U x U y } ε rz 1 V x
ε = ε a f + ε b ( 1 f )
t A 1 ε x E x dydz = L 1 H · dl
t A 2 ε y E y dydz = L 2 H · dl
t A 1 ε z E z dydy = L 3 H · dl
t ( ε ¯ z E ¯ z Δ x Δ y ) = L 3 H · dl and ε ¯ z = f ε a + ( 1 f ) ε b
ε ¯ x = [ 1 Δ x x x + Δ x 1 ε a f ( x ) + ε b ( 1 f ( x ) ) dx ] 1
ε ¯ y = [ 1 Δy y y + Δ y 1 ε a f ( y ) + ε b ( 1 f ( y ) ) dy ] 1

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