Abstract

Precise knowledge of the group velocity dispersion in gas-filled hollow-core photonic crystal fiber is essential for accurate modeling of ultrafast nonlinear dynamics. Here we study the validity of the capillary approximation commonly used to calculate the modal refractive index in kagomé-style photonic crystal fibers. For area-preserving core radius aAP and core wall thickness t, measurements and finite element simulations show that the approximation has an error greater than 15% for wavelengths longer than 0.56(aAPt), independently of the gas-filling pressure. By introducing an empirical wavelength-dependent core radius, the range of validity of the capillary approximation is extended out to a wavelength of at least 0.98(aAPt).

© 2014 Optical Society of America

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  1. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
    [CrossRef]
  2. F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
    [CrossRef]
  3. J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2922 (2010).
    [CrossRef]
  4. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
    [CrossRef]
  5. K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 10942 (2013).
    [CrossRef]
  6. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (2)

2012 (1)

2011 (4)

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

2010 (2)

2009 (2)

S. J. Im, A. Husakou, and J. Herrmann, Opt. Express 17, 13052 (2009).

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

2008 (1)

2007 (1)

2003 (1)

2002 (1)

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

1999 (1)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

1981 (1)

M. Tateda, N. Shibata, and S. Seikai, IEEE J. Quantum Electron. 17, 404 (1981).
[CrossRef]

1964 (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Allan, D. C.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Antonopolous, G.

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

Azhar, M.

Baer, C. R. E.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Beaudou, B.

Benabid, F.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011).
[CrossRef]

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

Biancalana, F.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

Birks, T. A.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Börzsönyi, A.

Burger, S.

Chang, W.

M. Azhar, G. K. L. Wong, W. Chang, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 4405 (2013).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

Couny, F.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011).
[CrossRef]

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Février, S.

Heckl, O. H.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Heiner, Z.

Herrmann, J.

S. J. Im, A. Husakou, and J. Herrmann, Opt. Express 17, 13052 (2009).

Holler, M.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Hölzer, P.

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 10942 (2013).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2922 (2010).
[CrossRef]

Husakou, A.

S. J. Im, A. Husakou, and J. Herrmann, Opt. Express 17, 13052 (2009).

Im, S. J.

S. J. Im, A. Husakou, and J. Herrmann, Opt. Express 17, 13052 (2009).

Joly, N. Y.

Kalashnikov, M. P.

Keller, U.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Knight, J. C.

F. Yu, W. J. Wadsworth, and J. C. Knight, Opt. Express 20, 11153 (2012).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Kovács, A. P.

Kränkel, C.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Light, P.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Mak, K. F.

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Marchese, S. V.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Nazarkin, A.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2922 (2010).
[CrossRef]

Nold, J.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2922 (2010).
[CrossRef]

Osvay, K.

Pearce, G. J.

Podlipensky, A.

Poulton, C. G.

Roberts, P. J.

Y. Y. Wang, N. V. Wheeler, F. Couny, P. J. Roberts, and F. Benabid, Opt. Lett. 36, 669 (2011).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Robinson, J. S.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Russell, P. St.J.

M. Azhar, G. K. L. Wong, W. Chang, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 4405 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 10942 (2013).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, Opt. Lett. 35, 2922 (2010).
[CrossRef]

G. J. Pearce, G. S. Wiederhecker, C. G. Poulton, S. Burger, and P. St.J. Russell, Opt. Express 15, 12680 (2007).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

Saleh, M. F.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

Scharrer, M.

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

Schnapper, F.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Seikai, S.

M. Tateda, N. Shibata, and S. Seikai, IEEE J. Quantum Electron. 17, 404 (1981).
[CrossRef]

Shibata, N.

M. Tateda, N. Shibata, and S. Seikai, IEEE J. Quantum Electron. 17, 404 (1981).
[CrossRef]

Südmeyer, T.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Tateda, M.

M. Tateda, N. Shibata, and S. Seikai, IEEE J. Quantum Electron. 17, 404 (1981).
[CrossRef]

Tee, C. W.

Tisch, J. W. G.

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Travers, J. C.

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, Opt. Express 21, 10942 (2013).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, J. Opt. Soc. Am. B 28, A11 (2011).
[CrossRef]

Viale, P.

Wadsworth, W. J.

Wang, Y. Y.

Wheeler, N. V.

Wiederhecker, G. S.

Wong, G. K. L.

Yu, F.

Yu, S. F.

Appl. Opt. (1)

Appl. Phys. B (1)

O. H. Heckl, C. R. E. Baer, C. Kränkel, S. V. Marchese, F. Schnapper, M. Holler, T. Südmeyer, J. S. Robinson, J. W. G. Tisch, F. Couny, P. Light, F. Benabid, and U. Keller, Appl. Phys. B 97, 369 (2009).
[CrossRef]

Bell Syst. Tech. J. (1)

E. A. J. Marcatili and R. A. Schmeltzer, Bell Syst. Tech. J. 43, 1783 (1964).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Tateda, N. Shibata, and S. Seikai, IEEE J. Quantum Electron. 17, 404 (1981).
[CrossRef]

J. Lightwave Technol. (1)

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

Opt. Express (6)

Opt. Lett. (2)

Phys. Rev. Lett. (2)

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

Science (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St.J. Russell, P. J. Roberts, and D. C. Allan, Science 285, 1537 (1999).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopolous, and P. St.J. Russell, Science 298, 399 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Generic set-up for ultrafast nonlinear optical experiments using gas-filled kagomé-PCF. In most cases fiber lengths of less than 1 m are sufficient. The observed dynamics depend on the filling gas, the pressure and the pump pulse characteristics.

Fig. 2.
Fig. 2.

(a) Measured relative group delay, fitted to a third-order polynomial, for a 725 mm length of five-ring kagomé PCF. (b) 1: GVD calculated using the MSM for an area-preserving (AP) diameter of 21.4 μm and a flat-to-flat (FF) diameter of 20.4 μm. 2: GVD for a thin capillary (inner radius 10.2 μm, wall thickness 190 nm, calculated analytically). 3: a fifth-order polynomial fit to FEM simulations of the simplified kagomé PCF (structure shown in the inset). 4: measured GVD using (a).

Fig. 3.
Fig. 3.

Comparison between the MSM [Eq. (1)], measurement, FEM, and the modified MSM, including a(λ) [Eq. (3)] for the FEM determined and experimental s-parameter.

Fig. 4.
Fig. 4.

Measured GVD of argon-filled kagomé PCF minus the GVD of the evacuated fiber. The MSM and mMSM (s=0.065) were calculated for 10 bars argon filling and an area-preserving radius of 10.71 μm.

Equations (3)

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

nmp(λ)=ngas2(λ)ump2k02a2,
λ<λcrit=0.56aAPt,
a(λ)=aAP1+sλ2/(aAPt),

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