Abstract

For optical fibers exhibiting a radially symmetric refractive index profile, there exists an analytical relation that connects waveguide dispersion and the Petermann-II mode field radius. We extend the usefulness of this relation to the nonradially symmetric case of microstructure fibers in the anomalous dispersion regime, yielding a simple relation between dispersion and effective mode field area. Assuming a Gaussian mode distribution, we derive a fundamental upper limit for the effective mode field area that is required to obtain a certain amount of anomalous waveguide dispersion. This relation is demonstrated to show excellent agreement for fiber designs suited for supercontinuum generation and soliton lasers in the near infrared.

© 2006 Optical Society of America

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  1. P. St. J. Russel, Science 19, 299 (2003).
  2. D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
    [CrossRef]
  3. J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
    [CrossRef]
  4. K. Saitoh and M. Koshiba, Opt. Express 13, 267 (2005).
    [CrossRef] [PubMed]
  5. M. D. Nielsen and N. A. Mortensen, Opt. Express 11, 2762 (2003).
    [CrossRef] [PubMed]
  6. A. M. Zheltikov, Appl. Phys. B 84, 69 (2006).
    [CrossRef]
  7. K. Petermann, Electron. Lett. 19, 712 (1983).
    [CrossRef]
  8. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L. C. Botten, J. Opt. Soc. Am. B 19, 2322 (2002).
    [CrossRef]
  9. M. Koshiba and K. Saitoh, Opt. Express 11, 1746 (2003).
    [CrossRef] [PubMed]
  10. M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
    [CrossRef] [PubMed]
  11. M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).
  12. 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]
  13. L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
    [CrossRef] [PubMed]
  14. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
    [CrossRef]

2006 (1)

A. M. Zheltikov, Appl. Phys. B 84, 69 (2006).
[CrossRef]

2005 (2)

2003 (5)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

M. D. Nielsen and N. A. Mortensen, Opt. Express 11, 2762 (2003).
[CrossRef] [PubMed]

P. St. J. Russel, Science 19, 299 (2003).

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

M. Koshiba and K. Saitoh, Opt. Express 11, 1746 (2003).
[CrossRef] [PubMed]

2002 (1)

2000 (2)

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (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]

1998 (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

1983 (1)

K. Petermann, Electron. Lett. 19, 712 (1983).
[CrossRef]

Akimov, D. A.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[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]

Ashcom, J. B.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

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]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

Botten, L. C.

Bretschneider, M.

Cregan, R. F.

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

de Sandro, J. P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

Dukel'skii, K. V.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Gattass, R. R.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Glas, P.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
[CrossRef] [PubMed]

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

He, S. L.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Iliew, R.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
[CrossRef] [PubMed]

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

Khokhlov, A. V.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Kiefer, W.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

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]

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

Kondrat'ev, Y. N.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Koshiba, M.

Kuhlmey, B. T.

Lebedev, N.

Lou, J. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Maksimenka, R.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Martijn de Sterke, C.

Maxwell, I.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Maystre, D.

Mazur, E.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

McPhedran, R. C.

Moenster, M.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
[CrossRef] [PubMed]

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

Mortensen, N. A.

Nielsen, M. D.

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]

Petermann, K.

K. Petermann, Electron. Lett. 19, 712 (1983).
[CrossRef]

Renversez, G.

Russel, P. St. J.

P. St. J. Russel, Science 19, 299 (2003).

Russell, P. S.

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[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]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

Saitoh, K.

Schmitt, M.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Shen, M. Y.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Shevandin, V. S.

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Steinmeyer, G.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
[CrossRef] [PubMed]

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

Tong, L. M.

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

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]

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, Opt. Lett. 25, 1415 (2000).
[CrossRef]

Wedell, R.

M. Moenster, P. Glas, G. Steinmeyer, R. Iliew, N. Lebedev, R. Wedell, and M. Bretschneider, Opt. Express 13, 8671 (2005).
[CrossRef] [PubMed]

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

White, T. P.

Zheltikov, A. M.

A. M. Zheltikov, Appl. Phys. B 84, 69 (2006).
[CrossRef]

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

Appl. Phys. B (2)

D. A. Akimov, M. Schmitt, R. Maksimenka, K. V. Dukel'skii, Y. N. Kondrat'ev, A. V. Khokhlov, V. S. Shevandin, W. Kiefer, and A. M. Zheltikov, Appl. Phys. B 77, 299 (2003).
[CrossRef]

A. M. Zheltikov, Appl. Phys. B 84, 69 (2006).
[CrossRef]

Electron. Lett. (2)

K. Petermann, Electron. Lett. 19, 712 (1983).
[CrossRef]

J. C. Knight, T. A. Birks, R. F. Cregan, P. S. Russell, and J. P. de Sandro, Electron. Lett. 34, 1347 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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. Opt. Soc. Am. B (1)

Nature (1)

L. M. Tong, R. R. Gattass, J. B. Ashcom, S. L. He, J. Y. Lou, M. Y. Shen, I. Maxwell, and E. Mazur, Nature 426, 816 (2003).
[CrossRef] [PubMed]

Opt. Express (4)

Opt. Lett. (1)

Science (1)

P. St. J. Russel, Science 19, 299 (2003).

Other (1)

M. Moenster, P. Glas, R. Iliew, R. Wedell, and G. Steinmeyer, "Microstructure fiber soliton laser," (submitted to IEEE Photon. Technol. Lett.).

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Figures (3)

Fig. 1
Fig. 1

Normalized effective area of the fundamental mode A eff Λ 2 versus the normalized wavelength λ Λ for a hexagonal MSF design with a central defect for different values of air-fill parameter d Λ . An example calculation of the mode field intensity distribution for λ Λ = 0.3 and d Λ = 0.62 is shown as an inset.

Fig. 2
Fig. 2

Normalized waveguide dispersion β 2 , wg Λ versus the normalized wavelength λ Λ for different air-fill parameters d Λ , as calculated by numerical simulations (solid curve) and as derived from Eq. (5) under the assumption of a Gaussian mode field (dashed curve). Different ordinate scales have been used for the normal and the anomalous dispersion regimes.

Fig. 3
Fig. 3

Upper limit for the allowed effective mode field area for compensating for the material dispersion of phosphate glass ( β 2 , total = 0 ) at 1060 nm (upper graph, β 2 , mat = + 26 ps 2 km ) and 800 nm (lower graph, β 2 , mat = + 45 ps 2 km ) versus the air-fill parameter d Λ . Circles have been calculated by numerically searching the maximum pitch providing dispersion compensation. The dashed line represents the prediction from Eq. (6).

Equations (6)

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

β 2 , wg = λ 3 4 π 3 c 2 d d λ [ λ n mat w II 2 ] .
w II = 2 0 F 2 r d r 0 ( d F d r ) 2 r d r ,
β 2 , wg = λ 3 4 π 2 c 2 n mat A II [ λ A II d A II d λ 1 + λ n mat d n mat d λ ] ,
A eff = [ F 2 d x d y ] 2 F 4 d x d y .
β 2 , wg = λ 3 4 π 2 c 2 n mat [ λ A eff 2 d A eff d λ 1 A eff ] .
A eff , max λ 3 4 π 2 c 2 n mat β 2 , wg .

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