Abstract

We present a summary of the simulation exercise carried out within the EC Cost Action P11 on the rigorous modeling of photonic crystal fiber (PCF) with an elliptically deformed core and noncircular air holes with a high fill factor. The aim of the exercise is to calculate using different numerical methods and to compare several fiber characteristics, such as the spectral dependence of the phase and the group effective indices, the birefringence, the group velocity dispersion and the confinement losses. The simulations are performed using four rigorous approaches: the finite element method (FEM), the source model technique (SMT), the plane wave method (PWM), and the localized function method (LFM). Furthermore, we consider a simplified equivalent fiber method (EFM), in which the real structure of the holey fiber is replaced by an equivalent step index waveguide composed of an elliptical glass core surrounded by air cladding. All these methods are shown to converge well and to provide highly consistent estimations of the PCF characteristics. Qualitative arguments based on the general properties of the wave equation are applied to explain the physical mechanisms one can utilize to tailor the propagation characteristics of nonlinear PCFs.

© 2006 Optical Society of America

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  1. P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
    [CrossRef] [PubMed]
  2. J. C. Knight, "Photonic crystal fibers," Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  3. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
    [CrossRef]
  4. C. M. Bowden and A. M. Zheltikov, eds., "Nonlinear optics of Photonic Crystals," Feature issue of J. Opt. Soc. Am. B 19, (2002).
  5. W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
    [CrossRef] [PubMed]
  6. T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
    [CrossRef] [PubMed]
  7. S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
    [CrossRef]
  8. H. N. Paulsen, K.M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003).
    [CrossRef] [PubMed]
  9. I. Hartl, X. D. Li, C. Chudoba, R. K. Rhanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
    [CrossRef]
  10. M. T. Myaing, J. Y. Ye, T. B. Norris, T. Thomas, J. R. BakerJr., W. J. Wadsworth, G. Bouwmans, J. C. Knight, and P. St. J. Russell, "Enhanced two-photon biosensing with double-clad photonic crystal fibers," Opt. Lett. 28, 1224-1226 (2003).
    [CrossRef] [PubMed]
  11. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10,609-613 (2002).
    [PubMed]
  12. 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]
  13. A. Ferrando, E. Silvestre, J. J. Miret, P. Andrés, and M. V. Andrés, "Full-vector analysis of a realistic photonic crystal fiber modes," Opt. Lett. 24,276-278 (1999).
    [CrossRef]
  14. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8,173-190 (2001).
    [CrossRef] [PubMed]
  15. N. A. Issa and L. Poladian, "Vector wave expansion method for leaky modes of microstructured optical fibers," J. Lightwave Technol. 21, 1005-1012 (2003).
    [CrossRef]
  16. 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]
  17. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
    [CrossRef]
  18. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennet, "Modelling large air fraction holey optical fibers," J. Lightwave Technol. 18, 50-56 (2000).
    [CrossRef]
  19. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botton, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19,2322-2330 (2002).
    [CrossRef]
  20. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botton, C. M. de Sterke, and R. C. McPhedran, "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. Am. B 19,2331-2340 (2002).
    [CrossRef]
  21. A. Hochman and Y. Leviatan, "Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique," J. Opt. Soc. Am. A 21, 1073-1081, (2004).
    [CrossRef]
  22. Z. Zhu and T. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Express 10, 853-864 (2002).
    [PubMed]
  23. S. O. Konorov and A. M. Zheltikov, "Frequency conversion of subnanojoule femtosecond laser pulses in a microstructure fiber for photochromism initiation," Opt. Express 11,2440-2445 (2003).
    [CrossRef] [PubMed]
  24. R. B. Dyott, Elliptical fiber waveguides (Artech House Optoelectronics Library, 1995).
  25. M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
    [CrossRef]
  26. H. S. Sözüer and J. W. Haus, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
    [CrossRef]
  27. M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, "Symmetry and degeneracy in microstructured optical fibers, " Opt. Lett. 26, 488-490 (2001).
    [CrossRef]
  28. A. Hochman and Y. Leviatan, "Calculation of confinement losses in photonic crystal fibers by use of a source-model technique," J. Opt. Soc. Am. B 22, 474-480 (2005).
    [CrossRef]
  29. A. Hochman and Y. Leviatan, "A spurious-free Source-Model Technique for modal waveguide analysis," CCIT Report #521, EE Dept., Technion Israel Inst. of Technology, March 2005, online: http://www2.ee.technion.ac.il/CCIT/info/Publications/Articles/521.pdf.
  30. A. Hochman and Y. Leviatan, "Modal dynamics in hollow-core photonic-crystal fibers with elliptical veins," Opt. Express 13,6193-6201 (2005).
    [CrossRef] [PubMed]
  31. R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
    [CrossRef]
  32. A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
    [CrossRef]
  33. C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys. 33,3235-3243 (1962).
    [CrossRef]
  34. A. W. Snydera and J. D. Love, Optical Waveguide Theory (London, Chapman and Hall, 1983).
  35. T. P. White, R. C. McPhedram, C. M. de Sterke, L. C. Botten, and M. J. Steel, "Confinement losses in microstructured optical fibers," Opt. Lett. 26,1660-1662 (2001).
    [CrossRef]
  36. D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
    [PubMed]
  37. V. Rastogi and K. S. Chiang, "Holey optical fiber with circularly distributed holes, analyzed by the radial effective-index method," Opt. Lett. 28, 2449-2451 (2003).
    [CrossRef] [PubMed]

2005 (3)

2004 (3)

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

A. Hochman and Y. Leviatan, "Analysis of strictly bound modes in photonic crystal fibers by use of a source-model technique," J. Opt. Soc. Am. A 21, 1073-1081, (2004).
[CrossRef]

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

2003 (8)

H. N. Paulsen, K.M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003).
[CrossRef] [PubMed]

M. T. Myaing, J. Y. Ye, T. B. Norris, T. Thomas, J. R. BakerJr., W. J. Wadsworth, G. Bouwmans, J. C. Knight, and P. St. J. Russell, "Enhanced two-photon biosensing with double-clad photonic crystal fibers," Opt. Lett. 28, 1224-1226 (2003).
[CrossRef] [PubMed]

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

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

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

N. A. Issa and L. Poladian, "Vector wave expansion method for leaky modes of microstructured optical fibers," J. Lightwave Technol. 21, 1005-1012 (2003).
[CrossRef]

S. O. Konorov and A. M. Zheltikov, "Frequency conversion of subnanojoule femtosecond laser pulses in a microstructure fiber for photochromism initiation," Opt. Express 11,2440-2445 (2003).
[CrossRef] [PubMed]

V. Rastogi and K. S. Chiang, "Holey optical fiber with circularly distributed holes, analyzed by the radial effective-index method," Opt. Lett. 28, 2449-2451 (2003).
[CrossRef] [PubMed]

2002 (8)

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
[PubMed]

Z. Zhu and T. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Express 10, 853-864 (2002).
[PubMed]

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]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botton, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19,2322-2330 (2002).
[CrossRef]

B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botton, C. M. de Sterke, and R. C. McPhedran, "Multipole method for microstructured optical fibers. II. Implementation and results," J. Opt. Soc. Am. B 19,2331-2340 (2002).
[CrossRef]

T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10,609-613 (2002).
[PubMed]

2001 (4)

2000 (2)

1999 (1)

1997 (1)

1994 (1)

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

1992 (1)

H. S. Sözüer and J. W. Haus, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

1962 (1)

C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys. 33,3235-3243 (1962).
[CrossRef]

Akimov, D. A.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

Alfimov, M. V.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

Andrés, M. V.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

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

Andrés, P.

Antkowiak, M.

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Baker, J. R.

Bennet, P. J.

Berghmans, F.

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Biancalana, F.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Birks, T. A.

Botten, L. C.

Botton, L. C.

Bouwmans, G.

Broderick, N. G. R.

Brown, T.

Chiang, K. S.

Chudoba, C.

Cruz, J. L.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

Cucinotta, A.

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
[PubMed]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

de Sterke, C. M.

Delgado-Pinar, M.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

Díez, A.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

Efimov, A.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Ferrando, A.

Ferrarini, D.

Fujimoto, J. G.

Hänsch, T. W.

T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Hartl, I.

Haus, J. W.

H. S. Sözüer and J. W. Haus, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Hilligsøe, K.M.

Hirayama, K.

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

Hochman, A.

Holzwarth, R.

T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Issa, N. A.

Ivanov, A. A.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Keiding, S. R.

Knight, J. C.

Ko, T. H.

Konorov, S. O.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

S. O. Konorov and A. M. Zheltikov, "Frequency conversion of subnanojoule femtosecond laser pulses in a microstructure fiber for photochromism initiation," Opt. Express 11,2440-2445 (2003).
[CrossRef] [PubMed]

Koshiba, M.

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]

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

Kotynski, R.

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Kuhlmey, B. T.

Larsen, J. J.

Leviatan, Y.

Li, X. D.

Martijn de Sterke, C.

Maruyama, S.

M. Koshiba, S. Maruyama, and K. Hirayama, "A vector finite element method with the higher order mixed-interpolation-type triangular elements for optical waveguide problems," J. Lightwave Technol. 12, 495-502 (1994).
[CrossRef]

Maystre, D.

McPhedram, R. C.

McPhedran, R. C.

Miret, J. J.

Monro, T. M.

Myaing, M. T.

Norris, T. B.

Omenetto, F. G.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

Panajotov, K.

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Paulsen, H. N.

Poladian, L.

Ranka, J. K.

Rastogi, V.

Reeves, W. H.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10,609-613 (2002).
[PubMed]

Renversez, G.

Rhanta, R. K.

Richardson, D. J.

Roberts, P. J.

Russell, P. St. J.

Saitoh, K.

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]

Selleri, S.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
[PubMed]

Serebryannikov, E. E.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

Silvestre, E.

Skryabin, D. V.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Sözüer, H. S.

H. S. Sözüer and J. W. Haus, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Steel, M. J.

Stentz, A. J.

Taylor, A. J.

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

Thienpont, H.

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Thøgersen, J.

Thomas, T.

Udem, T.

T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Vincetti, L.

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
[PubMed]

Wadsworth, W. J.

White, T. P.

Windeler, R. S.

Ye, J. Y.

Yeh, C.

C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys. 33,3235-3243 (1962).
[CrossRef]

Zheltikov, A. M.

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

S. O. Konorov and A. M. Zheltikov, "Frequency conversion of subnanojoule femtosecond laser pulses in a microstructure fiber for photochromism initiation," Opt. Express 11,2440-2445 (2003).
[CrossRef] [PubMed]

Zhu, Z.

Zoboli, M.

D. Ferrarini, L. Vincetti, M. Zoboli, A. Cucinotta, and S. Selleri, "Leakage properties of photonic crystal fibers," Opt. Express 10, 1314-1319 (2002).
[PubMed]

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

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 Photon. Technol. Lett. (2)

A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, "Holey fiber analysis through the finite element method," IEEE Photon. Technol. Lett. 14, 1530-1532 (2002).
[CrossRef]

A. Ortigosa-Blanch, A. Díez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrés, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16,1667-1669 (2004).
[CrossRef]

J. Appl. Phys. (1)

C. Yeh, "Elliptical dielectric waveguides," J. Appl. Phys. 33,3235-3243 (1962).
[CrossRef]

J. Lightwave Technol. (3)

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

J. Opt. Soc. Am. B (3)

Nature (3)

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

W. H. Reeves, D. V. Skryabin, F. Biancalana, J. C. Knight, P. St. J. Russell, F. G. Omenetto, A. Efimov, and A. J. Taylor, "Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres," Nature 424, 511-515 (2003).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (9)

V. Rastogi and K. S. Chiang, "Holey optical fiber with circularly distributed holes, analyzed by the radial effective-index method," Opt. Lett. 28, 2449-2451 (2003).
[CrossRef] [PubMed]

T. P. White, R. C. McPhedram, C. M. de Sterke, L. C. Botten, and M. J. Steel, "Confinement losses in microstructured optical fibers," Opt. Lett. 26,1660-1662 (2001).
[CrossRef]

M. J. Steel, T. P. White, C. Martijn de Sterke, R. C. McPhedran, and L. C. Botten, "Symmetry and degeneracy in microstructured optical fibers, " Opt. Lett. 26, 488-490 (2001).
[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]

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

H. N. Paulsen, K.M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen, "Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source," Opt. Lett. 28, 1123-1125 (2003).
[CrossRef] [PubMed]

I. Hartl, X. D. Li, C. Chudoba, R. K. Rhanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001).
[CrossRef]

M. T. Myaing, J. Y. Ye, T. B. Norris, T. Thomas, J. R. BakerJr., W. J. Wadsworth, G. Bouwmans, J. C. Knight, and P. St. J. Russell, "Enhanced two-photon biosensing with double-clad photonic crystal fibers," Opt. Lett. 28, 1224-1226 (2003).
[CrossRef] [PubMed]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

Opt. Quantum. Electron. (1)

R. Kotynski, M. Antkowiak, F. Berghmans, H. Thienpont, and K. Panajotov, "Photonic crystal fibers with material anisotropy," Opt. Quantum. Electron. 37,253-264 (2005).
[CrossRef]

Phys. Rev. B (1)

H. S. Sözüer and J. W. Haus, "Photonic bands: convergence problems with the plane-wave method," Phys. Rev. B 45, 13962-13972 (1992).
[CrossRef]

Phys. Rev. E (1)

S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, "Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers," Phys. Rev. E 70, 057601 (2004).
[CrossRef]

Science (1)

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other (4)

A. Hochman and Y. Leviatan, "A spurious-free Source-Model Technique for modal waveguide analysis," CCIT Report #521, EE Dept., Technion Israel Inst. of Technology, March 2005, online: http://www2.ee.technion.ac.il/CCIT/info/Publications/Articles/521.pdf.

A. W. Snydera and J. D. Love, Optical Waveguide Theory (London, Chapman and Hall, 1983).

C. M. Bowden and A. M. Zheltikov, eds., "Nonlinear optics of Photonic Crystals," Feature issue of J. Opt. Soc. Am. B 19, (2002).

R. B. Dyott, Elliptical fiber waveguides (Artech House Optoelectronics Library, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

SEM image of the nonlinear PCF.

Fig. 2.
Fig. 2.

Mesh used in finite element method (a) and super cell used in plane-wave method (b) with indicated co-ordinate system.

Fig. 3.
Fig. 3.

Sources placed in a homogeneous air region that are used to approximate the fields in an air-hole and normal vectors used to construct the curve on which the sources are placed (a). Location of sources and testing points are shown in (b). Testing points are marked by x’s, sources used to approximate the fields in the air-holes are marked by hollow circles, while sources used to approximate the fields in the dielectric are marked by solid circles.

Fig. 4.
Fig. 4.

Overlap coefficient vs. minor and major axes of the equivalent elliptical core (a) and the optimal elliptical core superimposed on the cross-section the considered PCF (b).

Fig. 5.
Fig. 5.

Field intensity profiles with polarization maps calculated with FEM for x-polarized LP 01 (a), LP11e (b), and LP11o (c) spatial modes.

Fig. 6.
Fig. 6.

Spectral dependence of phase effective index (a) and group effective index (b) of x-polarized LP 01 , LP11e , and LP11o spatial modes calculated using FEM.

Fig. 7.
Fig. 7.

Group velocity dispersion calculated for x-and y-polarized LP 01 (a–b), LP11e (c–d), and LP11o (e–f) modes using FEM, SMT, PWM, LFM, and equivalent fiber method EFM.

Fig. 8.
Fig. 8.

Phase and group modal birefringence calculated for LP 01 (a), LP11e (b), and LP11o (c) modes using FEM, SMT, PWM, LFM, and equivalent fiber method EFM.

Fig. 9.
Fig. 9.

Confinement losses for x-polarized (a) and y-polarized (b) LP 01 , LP11e, and LP11o modes calculated as a function of wavelength using FEM with PML boundary conditions (solid lines) and SMT (dashed lines).

Tables (2)

Tables Icon

Table 1. Results of the convergence test carried out for the LP01x mode at λ=1.55 µm.

Tables Icon

Table 2. Results on the PCF characteristics obtained with the different methods at λ=0.4 µm (first row) and 1.55 µm (second row).

Equations (9)

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

[ × × k 0 2 n 2 ( r ) 0 0 0 ] [ E E z ] = β 2 [ 1 Δ + k 0 2 n 2 ( r ) ] [ E E z ] .
( [ k 0 2 n 2 ( r ) + 2 ] + [ ln n 2 ( r ) × × ] ) H = β 2 H .
β 2 β ̃ 2 = k 0 2 ( n 2 n ̃ 2 ) Ψ Ψ ̃ d x d y Ψ Ψ ̃ d x d y ,
Ψ k ( x , y ) = j a j Ψ ˜ j ( x , j ) + j 0 a j ( q ) Ψ ˜ j ( x , y , q ) d q ,
Ψ k Ψ ˜ k , β k β ˜ k , a k 1 .
a j = k 0 2 β ̃ k 2 β ̃ j 2 ( n 2 n ̃ 2 ) Ψ ̃ j Ψ ̃ k d x d y Ψ ̃ j 2 d x d y ,
β k 2 = β ̃ k 2 + k 0 2 ( n 2 n ̃ 2 ) Ψ ̃ k 2 d x d y Ψ ̃ k 2 d x d y .
Δ n = [ ( β x β y ) c ] ω ,
Δ n g = c ( β x ω β y ω ) = Δ n λ ( Δ n ) λ ,

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