Abstract

A 3D full-vectorial Beam Propagation Method is successfully applied to compute both the propagation constants and the modal profiles in high-contrast silica-air index-guiding Photonic Crystal Fibers. The approach is intrinsically suited to investigate longitudinally varying structures or propagation and polarization effects, which are of practical interest for advanced optical applications. As an example we model a dual-core coupler, showing that efficient polarization preserving coupling can be expected.

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References

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  1. J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russel, "Single mode photonic band gap guidance of light in air," Science 282, 1476-1478 (1998).
    [CrossRef] [PubMed]
  2. R. F. Cregan, B. J. Mangan J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, andD. C. Allan, "Single mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
    [CrossRef] [PubMed]
  3. T.A. Birks, and P. St. J. Russel, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  4. D. Mogilevtsev, T. A. Birks, and P. St. J. Russel, "Group-velocity dispersion in photonic crystal fibers," Opt. Lett. 23, 1662-1664 (1998).
    [CrossRef]
  5. J. C. Knight, T. A. Birks, P. St. J. Russel, and J. P. de Sandro, "Properties of photonic crystal fiber and the effective index model," J. Opt. Soc. Am. A 15, 748-752 (1998).
    [CrossRef]
  6. E. Silvestre, M. V. Andr?s, and P. Andr?s, "Biorthonormal-basis method for the vector description of optical-fiber modes," IEEE J. Lightwave Tecnol. 23, 923-928 (1998).
    [CrossRef]
  7. A. Ferrando, E. Silvestre, J. J. Miret, P. Andr?s, and M. V. Andr?s, "Full-vector analysis of a realistic photonic crystal fiber modes," Opt. Lett. 24, 276-278 (1999).
    [CrossRef]
  8. A. Ferrando, E. Silvestre, J. J. Miret, P. Andr?s, and M. V. Andr?s, "Vector description of higher-order modes in photonic crystal fibers," J. Opt. Soc. Am. A 17, 1333-1340 (2000).
    [CrossRef]
  9. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennet, "Modeling large air fraction holey optical fibers," IEEE J. Lightwave Tecnol. 18, 50-56 (2000).
    [CrossRef]
  10. J. Broeng, S. E. Barkou, T. Sondergaard, and A. Bjarklev, "Analysis of air-guiding photonic bandgap fibers," Opt. Lett. 25, 96-98 (2000).
    [CrossRef]
  11. M. J. Steel, T. P. White, C. M. de Sterke, R. C.McPhedran, and L. C. Botten, "Symmetry and degeneracy in microstructured optical fibers," Opt. Lett. 26, 488-490 (2001).
    [CrossRef]
  12. X. Liu, C. Xu, W. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, "Soliton selffrequency shift in short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-400 (2001).
    [CrossRef]
  13. T. Sorensen, J. Broeng, A. Bjarklev, E. Knudsen, and S. E. Barkou Libori, "Macro-bending loss properties of photonic crystal fibre," Electron. Lett. 37, 287-289 (2001).
    [CrossRef]
  14. B.J. Mangan, J.C. Knight, T. A. Birks, T.A. Roberts, P. St. J. Russel, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
    [CrossRef]
  15. M.D. Feit, and J. A. Fleck, "Computation of mode properties in optical fiber waveguides by a propagating beam method," Appl. Opt. 19, 1154-1164 (1980).
    [CrossRef] [PubMed]
  16. B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler and G. L. Burdge, "Cladddingmode-resonances in air-silica microstructure optical fibers," IEEE J. Lightwave Tecnol. 18, 1084-1100 (2000).
    [CrossRef]
  17. C. E. Kerbage, B. J. Eggleton, P. S. Westbrook, R. S. Windeler, "Experimental and scalar beam propagation analysis of an air-silica microstructure fiber," Opt. Express 7, 13-122 (2000).
    [CrossRef]
  18. F. Fogli, G. Bellanca, P. Bassi, I. Madden, andW. Johnstone, "Highly Efficient Full-Vectorial 3-D BPM Modeling of Fiber to Planar Waveguide Couplers," IEEE J. Lightwave Tecnol. 17, 136-143 (1999).
    [CrossRef]

Other (18)

J. C. Knight, J. Broeng, T. A. Birks, and P. St. J. Russel, "Single mode photonic band gap guidance of light in air," Science 282, 1476-1478 (1998).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan J. C. Knight, T. A. Birks, P. St. J. Russel, P. J. Roberts, andD. C. Allan, "Single mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

T.A. Birks, and P. St. J. Russel, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
[CrossRef] [PubMed]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russel, "Group-velocity dispersion in photonic crystal fibers," Opt. Lett. 23, 1662-1664 (1998).
[CrossRef]

J. C. Knight, T. A. Birks, P. St. J. Russel, and 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, M. V. Andr?s, and P. Andr?s, "Biorthonormal-basis method for the vector description of optical-fiber modes," IEEE J. Lightwave Tecnol. 23, 923-928 (1998).
[CrossRef]

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

A. Ferrando, E. Silvestre, J. J. Miret, P. Andr?s, and M. V. Andr?s, "Vector description of higher-order modes in photonic crystal fibers," J. Opt. Soc. Am. A 17, 1333-1340 (2000).
[CrossRef]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennet, "Modeling large air fraction holey optical fibers," IEEE J. Lightwave Tecnol. 18, 50-56 (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]

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

X. Liu, C. Xu, W. Knox, J. K. Chandalia, B. J. Eggleton, S. G. Kosinski, and R. S. Windeler, "Soliton selffrequency shift in short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-400 (2001).
[CrossRef]

T. Sorensen, J. Broeng, A. Bjarklev, E. Knudsen, and S. E. Barkou Libori, "Macro-bending loss properties of photonic crystal fibre," Electron. Lett. 37, 287-289 (2001).
[CrossRef]

B.J. Mangan, J.C. Knight, T. A. Birks, T.A. Roberts, P. St. J. Russel, and A. H. Greenaway, "Experimental study of dual-core photonic crystal fibre," Electron. Lett. 36, 1358-1359 (2000).
[CrossRef]

M.D. Feit, and J. A. Fleck, "Computation of mode properties in optical fiber waveguides by a propagating beam method," Appl. Opt. 19, 1154-1164 (1980).
[CrossRef] [PubMed]

B. J. Eggleton, P. S. Westbrook, C. A. White, C. Kerbage, R. S. Windeler and G. L. Burdge, "Cladddingmode-resonances in air-silica microstructure optical fibers," IEEE J. Lightwave Tecnol. 18, 1084-1100 (2000).
[CrossRef]

C. E. Kerbage, B. J. Eggleton, P. S. Westbrook, R. S. Windeler, "Experimental and scalar beam propagation analysis of an air-silica microstructure fiber," Opt. Express 7, 13-122 (2000).
[CrossRef]

F. Fogli, G. Bellanca, P. Bassi, I. Madden, andW. Johnstone, "Highly Efficient Full-Vectorial 3-D BPM Modeling of Fiber to Planar Waveguide Couplers," IEEE J. Lightwave Tecnol. 17, 136-143 (1999).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Real part of the transverse profiles of the launched field (the imaginary parts are set to zero). Left frame: fundamental mode excitation. Right frame: upper mode excitation.

Fig. 2.
Fig. 2.

Modal effective index vs. normalized frequency ʌ/λ (λ varies from 300 to 1600 nm) for the fundamental mode and the next higher-order one of a PCF with a = 0.6 and ʌ = 2.3 μm. The upper (red) and the lower (blue) curves refer to the fundamental and the higher order modes respectively. The open circles stand for BPM calculations whereas the solid lines show for comparison the data taken from Fig. 3 of Ref. [7].

Fig. 3.
Fig. 3.

Moduli of the x, y and z electric field components of the fundamental mode at the output section of the PCF for a normalized frequency ʌ/λ = 5.

Fig. 4.
Fig. 4.

Moduli of the x, y and z electric field components of the first upper mode at the output section of the fiber for a normalized frequency ʌ/λ = 5.

Fig. 5.
Fig. 5.

Moduli of the x electric field components in the dual-core PCF Coupler for a normalized frequency ʌ/λ = 2.7 overlaid with the investigated coupler geometry. Left: launched field in the starting section. Right: field distribution after a propagation distance of nearly 0.715 mm.

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