Abstract

An improved full-vectorial method exploiting the opposite-parity property of eigenmodes based on orthonormal-functions expansion is proposed to solve the wave equation for holey optical fibers. By use of the parity property of eigenmodes in symmetric structures, the number of orthonormal function integrals involved in the calculation is reduced, and the computation efficiency is greatly enhanced. The coupling between the two transverse field components is considered, and both dominant and minor field components can be calculated for the accurate modeling of fiber modes. This method is useful for efficiently modeling holey fibers, especially those with large air holes, in which the coupling effect that is due to refractive-index discontinuities is strong.

© 2003 Optical Society of America

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  1. T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
    [CrossRef]
  2. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
    [CrossRef]
  3. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, J. Lightwave Technol. 17, 1093 (1999).
    [CrossRef]
  4. T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, J. Lightwave Technol. 18, 50 (2000).
    [CrossRef]
  5. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, J. Lightwave Technol. 17, 2078 (1999).
    [CrossRef]
  6. T. M. Monro, N. G. Broderick, and D. J. Richardson, Nanoscale Linear and Nonlinear Optics, AIP Conf. Proc. 560, 123 (2000).
    [CrossRef]
  7. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)
  8. J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
    [CrossRef]

2000

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennett, J. Lightwave Technol. 18, 50 (2000).
[CrossRef]

T. M. Monro, N. G. Broderick, and D. J. Richardson, Nanoscale Linear and Nonlinear Optics, AIP Conf. Proc. 560, 123 (2000).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

1999

1998

1993

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Bennett, P. J.

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, J. Lightwave Technol. 17, 2078 (1999).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
[CrossRef]

Bjarklev, A.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Broderick, N. G.

T. M. Monro, N. G. Broderick, and D. J. Richardson, Nanoscale Linear and Nonlinear Optics, AIP Conf. Proc. 560, 123 (2000).
[CrossRef]

Broderick, N. G. R.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)

Knight, J. C.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Lumholt, O.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Mogilevtsev, D.

Monro, T. M.

Ortigosa-Blanch, A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

Pedersen, B.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Povlsen, J. H.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)

Rasmussen, T.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Richardson, D. J.

Rottwitt, K.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Russell, P. St. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, J. Lightwave Technol. 17, 2078 (1999).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, Opt. Lett. 23, 1662 (1998).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)

Wadsworth, W. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

AIP Conf. Proc.

T. M. Monro, N. G. Broderick, and D. J. Richardson, Nanoscale Linear and Nonlinear Optics, AIP Conf. Proc. 560, 123 (2000).
[CrossRef]

IEEE Photon. Technol. Lett.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, IEEE Photon. Technol. Lett. 12, 807 (2000).
[CrossRef]

J. Lightwave Technol.

J. Ligthwave Technol.

T. Rasmussen, J. H. Povlsen, A. Bjarklev, O. Lumholt, B. Pedersen, and K. Rottwitt, J. Ligthwave Technol. 11, 429 (1993).
[CrossRef]

Opt. Lett.

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C-The Art of Scientific Computing, 2nd ed. (Cambridge University, New York, 1992)

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Figures (2)

Fig. 1
Fig. 1

Field components of the x-polarized mode of an ultralarge air fraction holey fiber in Fig. 1(a) of Ref. 8. (a) Ex and (b) Ey. White and black represent positive and negative amplitudes, respectively. The dashed lines represent the holey fiber structure.

Fig. 2
Fig. 2

Calculated dispersion curves for the ultralarge air fraction holey fiber in Ref. 8. The x-polarized mode exhibits higher group-velocity dispersion (GVD) than the y-polarized mode in the vectorial results.

Equations (10)

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

Etx,yExxˆ+Eyyˆ=a,b=0Mϵa,bxψa1xψb2yxˆ+a,b=0Mϵa,byψa3xψb4yyˆ,
Fuxuy=β2k2uxuy,
FS+V+D=S00S+Vx00Vy+0DxyDyx0;
nx,y=n-x,y and nx,y=nx,-y.
2-β2+n2k2Ex+xEx ln n2x+Ey ln n2y=0.
2k2-β2k2+n2Ex-s,y+1k2-sEx-s,y ln n2-s+Ey-s,y ln n2y=0.
Exx,y=Ex-x,y.
2k2-β2k2+n2Exx,y+1k2xExx,yln n2x-1k2xEy-x,yln n2y=0,
1k2xEyx,y ln n2y=-1k2xEy-x,y ln n2y.
Eyx,y=-Ey-x,y.

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