Abstract

We extend our previous work on photonic-crystal fibers (PCFs) using the source-model technique to include leaky modes of fibers having a finite-sized photonic bandgap crystal (PBC) cladding. We concentrate on a hollow-core PCF and calculate the confinement losses by means of two different methods. The first method is more general but also more computationally expensive; we use sources that have a complex propagation constant and seek a transverse resonance in the complex plane. The second method, applicable only to modes with small confinement losses, uses sources with a real propagation constant to approximate leaky modes that have a propagation constant that is close to the real axis. We then apply Poynting’s theorem to calculate the attenuation constant in a manner akin to the perturbation methods used to calculate the losses in finite-conductivity metal waveguides. This first approximation can be improved through iterative application of the algorithm, i.e., by use of sources with the attenuation constant found in the first approximation. The two methods are shown to be in good agreement with each other and with previously published results for solid-core PCFs. Numerical results show that, for the hollow-core PCF analyzed, many layers of PBC cladding are needed to attain confinement losses that are acceptable for telecommunications.

© 2005 Optical Society of America

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References

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  1. K. Saitoh and M. Koshiba, "Confinement losses in air-guiding photonic bandgap fibers," IEEE Photonics Technol. Lett. 15, 236-238 (2003).
    [CrossRef]
  2. 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]
  3. D. Marcuse, Light Transmission Optics (Krieger, Malabar, Fla., 1989).
  4. R. Sammut and A. W. Snyder, "Leaky modes on a dielectric waveguide: orthogonality and excitation," Appl. Opt. 15, 1040-1044 (1976).
    [CrossRef] [PubMed]
  5. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002).
    [CrossRef]
  6. X. E. Lin, "Photonic band gap fiber accelerator," Phys. Rev. ST Accel. Beams 4, 051301 (2001).
    [CrossRef]
  7. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).
  8. R. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998).
  9. R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960).
  10. B. T. Kuhlmey, T. P. White, G. Renversez, D. Maystre, L. C. Botten, 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]
  11. L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces (Pergamon, Oxford, UK, 1964).
  12. S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, "Loss and dispersion analysis of microstructured fibers by finite-difference method," Opt. Express 12, 3341-3352 (2004), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  13. 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]
  14. C. G. Broyden, "The convergence of a class of double-rank minimization algorithms," J. Inst. Math. Appl. 6, 76-90 (1970).
    [CrossRef]
  15. T. P. White, R. C. McPhedran, L. C. Botten, G. H. Smith, and C. M. de Sterke, "Calculations of air-guiding modes in photonic crystal fibers using the multipole method," Opt. Express 9, 721-732 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]
  16. S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, "Low-loss asymptotically single-mode propagation in large-core omniguide fibers," Opt. Express 9, 748-779 (2001), http://www.opticsexpress.org.
    [CrossRef] [PubMed]

2004 (2)

2003 (2)

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]

K. Saitoh and M. Koshiba, "Confinement losses in air-guiding photonic bandgap fibers," IEEE Photonics Technol. Lett. 15, 236-238 (2003).
[CrossRef]

2002 (2)

2001 (3)

1976 (1)

1970 (1)

C. G. Broyden, "The convergence of a class of double-rank minimization algorithms," J. Inst. Math. Appl. 6, 76-90 (1970).
[CrossRef]

Albin, S.

Botten, L. C.

Broyden, C. G.

C. G. Broyden, "The convergence of a class of double-rank minimization algorithms," J. Inst. Math. Appl. 6, 76-90 (1970).
[CrossRef]

de Sterke, C. M.

Engeness, T.

Fink, Y.

Guo, S.

Hochman , A.

Ibanescu, M.

Issa , N. A.

Jacobs, S.

Joannopoulos, J.

Johnson, S.

Koshiba, M.

K. Saitoh and M. Koshiba, "Confinement losses in air-guiding photonic bandgap fibers," IEEE Photonics Technol. Lett. 15, 236-238 (2003).
[CrossRef]

Kuhlmey, B. T.

Leviatan, Y.

Lin, X. E.

X. E. Lin, "Photonic band gap fiber accelerator," Phys. Rev. ST Accel. Beams 4, 051301 (2001).
[CrossRef]

Maystre, D.

McPhedran, R. C.

Poladian, L.

Renversez, G.

Rogowski, R. S.

Saitoh , K.

K. Saitoh and M. Koshiba, "Confinement losses in air-guiding photonic bandgap fibers," IEEE Photonics Technol. Lett. 15, 236-238 (2003).
[CrossRef]

Sammut , R.

Skorobogatiy, M.

Smith, G. H.

Snyder, A. W.

Soljacic, M.

Tai, H.

Weisberg, O.

White, T. P.

Wu, F.

Appl. Opt. (1)

IEEE Photonics Technol. Lett. (1)

K. Saitoh and M. Koshiba, "Confinement losses in air-guiding photonic bandgap fibers," IEEE Photonics Technol. Lett. 15, 236-238 (2003).
[CrossRef]

J. Inst. Math. Appl. (1)

C. G. Broyden, "The convergence of a class of double-rank minimization algorithms," J. Inst. Math. Appl. 6, 76-90 (1970).
[CrossRef]

J. Lightwave Technol. (1)

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

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

Opt. Express (3)

Phys. Rev. ST Accel. Beams (1)

X. E. Lin, "Photonic band gap fiber accelerator," Phys. Rev. ST Accel. Beams 4, 051301 (2001).
[CrossRef]

Other (5)

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice-Hall, Englewood Cliffs, N.J., 1991).

R. Lehoucq, D. Sorensen, and C. Yang, ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods (SIAM, Philadelphia, 1998).

R. E. Collin, Field Theory of Guided Waves (McGraw-Hill, New York, 1960).

L. V. Kantorovich and G. P. Akilov, Functional Analysis in Normed Spaces (Pergamon, Oxford, UK, 1964).

D. Marcuse, Light Transmission Optics (Krieger, Malabar, Fla., 1989).

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Figures (3)

Fig. 1
Fig. 1

Hollow-core PCF. Gray areas are fused silica, white areas are air.

Fig. 2
Fig. 2

Images of ΔE-1 showing singularities of [Z] in the complex β plane. (a) Nr=2, (b) Nr=4. In both cases, k0=8.1/Λ.

Fig. 3
Fig. 3

Confinement losses for two modes at λ=1 µm and Λ=1.2732 µm. The real part of the propagation constant, βr, varies slightly with the number of rings of veins, Nr. For Nr=4, βr/k0=0.9855 for the mode of symmetry class p=1 and βr/k0=0.9920 for the mode of symmetry class p=2.

Tables (4)

Tables Icon

Table 1 Complex Propagation Constants for Ten Modes of a Solid-Core PCF. Comparison with the Results Obtained with the Multipole Method, Given in Ref. 5a

Tables Icon

Table 2 Propagation Constant of the Fundamental Mode as Found by Different Studiesa

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Table 3 Complex Propagation Constant. Comparison between Scanning the Complex β Plane (Subsection 4.A) and the Use of the Conservation of Energy (Subsection 4.B)a

Tables Icon

Table 4 Dependence of Confinement Losses on the Number of Rings of Veinsa

Equations (8)

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

[Z]I=0
E=βkρ4jωr0H1(2)(kρρ)uρ-kρ24ωr0H0(2)(kρρ)uz,
H=kρ4jH1(2)(kρρ)uϕ,
rk02=β2+kρ2,
δ=ΔLL=Δβi|βi|,
βi=-C Re(S)·nˆdl2S Re(Sz)da,
Verr=[Z˜]I,
ΔE=|[Z]I|max|Verr|,

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