Abstract

We measure the propagation properties of a highly nonlinear photonic crystal fiber (PCF). The spatial, temporal and frequency dependent properties of the propagating modes are measured under conditions of high power, seven picosecond excitation, white light continuum generation. The experimentally determined multi-mode nature of the white light continuum is found to be in good agreement with numerical simulations.

© 2005 Optical Society of America

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References

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  1. P. Russell , “ Photonic Crystal Fibers ,” Science   299 , 358 – 362 ( 2003 ).
    [Crossref] [PubMed]
  2. S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
    [Crossref]
  3. S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
    [Crossref]
  4. W. Wadsworth , N. Joly , J. Knight , T. Birks , F. Biancalana , and P. Russell , “ Supercontinuum and four-wave mixing with Q-swiched pulses in endlessly single-mode photonic crystal fibers ,” Opt. Express   12 , 299 – 309 ( 2004 ).
    [Crossref] [PubMed]
  5. T. A. Birks , J. Knight , and P. Russell , “ Endlessly single-mode photonic crystal fibre ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
    [Crossref] [PubMed]
  6. J. Knight , T. Birks , P. Russell , and D. Atkin , “ All-silica single-mode fiber with photonic crystal cladding ,” Opt. Lett.   21 , 1547 – 1549 ( 1996 ); Errata, Opt. Lett.   22 , 484 – 485 ( 1997 ).
    [Crossref] [PubMed]
  7. J. Knight , T. Birks , and P. Russell , “ Properties of photonic crystal fiber and the effective index model ,” J. Opt. Soc. Am. A   15 , 748 – 752 ( 1998 ).
    [Crossref]
  8. A. Ferrando , E. Silvestre , J. Miret , P. Andres , and M. Andres , “ Full-vector analysis of a realistic photonic crystal fiber ,” Opt. Lett.   24 , 276 – 278 ( 1999 ).
    [Crossref]
  9. N. Mortensen , J. Folkenberg , M. Nielsen , and K. Hansen , “ Modal cutoff and the V parameter in photonic crystal fibers ,” Opt. Lett.   28 , 1879 – 1881 ( 2003 ).
    [Crossref] [PubMed]
  10. J. Folkenberg , N. Mortensen , K. Hansen , T. Hansen , H. Simonsen , and C. Jakobsen , “ Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers ,” Opt. Lett.   28 , 1882 – 1884 ( 2003 ).
    [Crossref] [PubMed]
  11. B. Kuhlmey , “ Modal cutoff in microstructured optical fibers ,” Opt. Lett.   27 , 1684 – 1686 ( 2002 ).
    [Crossref]
  12. M. Nielsen and N. Mortensen , “ Photonic crystal fiber design based on the V-parameter ,” Opt. Express   11 , 2762 – 2768 ( 2003 ).
    [Crossref] [PubMed]
  13. C. Kerbage , B. Eggleton , P. Westbrook , and R. Windeler , “ Experimental and scalar beam propagation analysis of an air-silica microstructure fiber ,” Opt. Express   7 , 113 – 122 ( 2000 ).
    [Crossref] [PubMed]
  14. A. Efimov and A. Taylor , “ Nonlinear generation of very high-order UV modes in microstructured fibers ,” Opt. Express   11 , 910 – 918 ( 2003 ).
    [Crossref] [PubMed]
  15. J. Ranka , R. Windeler , and A. Stentz , “ Optical properties of high-delta air-silica microstructure optical fibers ,” Opt. Lett.   25 , 796 – 798 ( 2000 ).
    [Crossref]
  16. G. Agrawal , Nonlinear fiber optics , ( Academic Press , 2nd edition, 1995 ).
  17. R. Guobin , W. Zhi , L. Shuqin , and J. Shuisheng , “ Mode classification and degeneracy in photonic crystal fibers ,” Opt. Express   11 , 1310 – 1321 ( 2003 ).
    [Crossref] [PubMed]
  18. R. Rokitski and S. Fainman , “ Propagation of ultrashort pulses in multimode fiber in space and time ,” Opt. Express   11 , 1497 – 1502 ( 2003 ).
    [Crossref] [PubMed]
  19. N. A. Mortensen , M. Stach , J. Broeng , A. Petersson , H. R. Simonsen , and R. Michalzik ,“ Multi-mode photonic crystal fibers for VCSEL based data transmission ,” Opt. Express   11 , 1953 – 1959 ( 2003 ).
    [Crossref] [PubMed]
  20. http://www.stanfordcomputeroptics.com
  21. http://www.lumerical.com
  22. A. Ward and J. Pendry , “ A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method ,” Comput. Phys. Commun.   28 , 590 – 621 ( 2000 ).
    [Crossref]
  23. T. White , C. Martijn de Sterke , and R. McPhedran , “ Symmetry and degeneracy in microstructured optical fibers ,” Opt. Lett.   26 , 488 – 490 ( 2001 ).
    [Crossref]
  24. The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
    [Crossref]

2004 (2)

W. Wadsworth , N. Joly , J. Knight , T. Birks , F. Biancalana , and P. Russell , “ Supercontinuum and four-wave mixing with Q-swiched pulses in endlessly single-mode photonic crystal fibers ,” Opt. Express   12 , 299 – 309 ( 2004 ).
[Crossref] [PubMed]

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

2003 (8)

2002 (2)

B. Kuhlmey , “ Modal cutoff in microstructured optical fibers ,” Opt. Lett.   27 , 1684 – 1686 ( 2002 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

2001 (2)

2000 (3)

1999 (1)

1998 (1)

1997 (1)

1996 (1)

Agrawal, G.

G. Agrawal , Nonlinear fiber optics , ( Academic Press , 2nd edition, 1995 ).

Andres, M.

Andres, P.

Atkin, D.

Biancalana, F.

Birks, T.

Birks, T. A.

Broeng, J.

Chau, A.

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
[Crossref]

Coen, S.

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
[Crossref]

de Sterke, C. Martijn

Efimov, A.

Eggleton, B.

Fainman, S.

Ferrando, A.

Folkenberg, J.

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

N. Mortensen , J. Folkenberg , M. Nielsen , and K. Hansen , “ Modal cutoff and the V parameter in photonic crystal fibers ,” Opt. Lett.   28 , 1879 – 1881 ( 2003 ).
[Crossref] [PubMed]

J. Folkenberg , N. Mortensen , K. Hansen , T. Hansen , H. Simonsen , and C. Jakobsen , “ Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers ,” Opt. Lett.   28 , 1882 – 1884 ( 2003 ).
[Crossref] [PubMed]

Guobin, R.

Hansen, K.

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

J. Folkenberg , N. Mortensen , K. Hansen , T. Hansen , H. Simonsen , and C. Jakobsen , “ Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers ,” Opt. Lett.   28 , 1882 – 1884 ( 2003 ).
[Crossref] [PubMed]

N. Mortensen , J. Folkenberg , M. Nielsen , and K. Hansen , “ Modal cutoff and the V parameter in photonic crystal fibers ,” Opt. Lett.   28 , 1879 – 1881 ( 2003 ).
[Crossref] [PubMed]

Hansen, T.

Harvey, J.

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
[Crossref]

Jakobsen, C.

Joly, N.

Kerbage, C.

Knight, J.

Kuhlmey, B.

Lægsgaard, J.

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

Leonhardt, R.

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
[Crossref]

McPhedran, R.

Michalzik, R.

Miret, J.

Mortensen, N.

Mortensen, N. A.

Nielsen, M.

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

N. Mortensen , J. Folkenberg , M. Nielsen , and K. Hansen , “ Modal cutoff and the V parameter in photonic crystal fibers ,” Opt. Lett.   28 , 1879 – 1881 ( 2003 ).
[Crossref] [PubMed]

M. Nielsen and N. Mortensen , “ Photonic crystal fiber design based on the V-parameter ,” Opt. Express   11 , 2762 – 2768 ( 2003 ).
[Crossref] [PubMed]

Pendry, J.

A. Ward and J. Pendry , “ A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method ,” Comput. Phys. Commun.   28 , 590 – 621 ( 2000 ).
[Crossref]

Petersson, A.

Ranka, J.

Rokitski, R.

Russell, P.

Shuisheng, J.

Shuqin, L.

Silvestre, E.

Simonsen, H.

Simonsen, H. R.

Stach, M.

Stentz, A.

Taylor, A.

Wadsworth, W.

Ward, A.

A. Ward and J. Pendry , “ A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method ,” Comput. Phys. Commun.   28 , 590 – 621 ( 2000 ).
[Crossref]

Westbrook, P.

White, T.

Windeler, R.

Zhi, W.

Comput. Phys. Commun. (1)

A. Ward and J. Pendry , “ A program for calculating photonic band structures, Green’s functions and transmission/reflection coefficients using a non-orthogonal FDTD method ,” Comput. Phys. Commun.   28 , 590 – 621 ( 2000 ).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

The effects of small disorder in the holes nearest the core has been shown to break the mode symmetry. N. Mortensen , M. Nielsen , J. Folkenberg , K. Hansen , and J. Lægsgaard , “ Small-core photonic crystal fibers with weakly disordered air-hole claddings ,” J. Opt. A: Pure Appl. Opt.   6 , 221 – 223 ( 2004 ).
[Crossref]

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

J. Opt. Soc. Am. B3 (1)

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers ,” J. Opt. Soc. Am. B3   19 , 753 – 764 ( 2002 ).
[Crossref]

Opt. Express (7)

Opt. Lett. (9)

J. Ranka , R. Windeler , and A. Stentz , “ Optical properties of high-delta air-silica microstructure optical fibers ,” Opt. Lett.   25 , 796 – 798 ( 2000 ).
[Crossref]

T. A. Birks , J. Knight , and P. Russell , “ Endlessly single-mode photonic crystal fibre ,” Opt. Lett.   22 , 961 – 963 ( 1997 ).
[Crossref] [PubMed]

J. Knight , T. Birks , P. Russell , and D. Atkin , “ All-silica single-mode fiber with photonic crystal cladding ,” Opt. Lett.   21 , 1547 – 1549 ( 1996 ); Errata, Opt. Lett.   22 , 484 – 485 ( 1997 ).
[Crossref] [PubMed]

A. Ferrando , E. Silvestre , J. Miret , P. Andres , and M. Andres , “ Full-vector analysis of a realistic photonic crystal fiber ,” Opt. Lett.   24 , 276 – 278 ( 1999 ).
[Crossref]

N. Mortensen , J. Folkenberg , M. Nielsen , and K. Hansen , “ Modal cutoff and the V parameter in photonic crystal fibers ,” Opt. Lett.   28 , 1879 – 1881 ( 2003 ).
[Crossref] [PubMed]

J. Folkenberg , N. Mortensen , K. Hansen , T. Hansen , H. Simonsen , and C. Jakobsen , “ Experimental investigation of cutoff phenomena in nonlinear photonic crystal fibers ,” Opt. Lett.   28 , 1882 – 1884 ( 2003 ).
[Crossref] [PubMed]

B. Kuhlmey , “ Modal cutoff in microstructured optical fibers ,” Opt. Lett.   27 , 1684 – 1686 ( 2002 ).
[Crossref]

T. White , C. Martijn de Sterke , and R. McPhedran , “ Symmetry and degeneracy in microstructured optical fibers ,” Opt. Lett.   26 , 488 – 490 ( 2001 ).
[Crossref]

S. Coen , A. Chau , R. Leonhardt , J. Harvey , J. Knight , W. Wadsworth , and P. Russell , “ White-light supercontinuum with 60 ps pump pulses in a photonic crystal fiber ,” Opt. Lett.   26 , 1356 – 1358 ( 2001 ).
[Crossref]

Science (1)

P. Russell , “ Photonic Crystal Fibers ,” Science   299 , 358 – 362 ( 2003 ).
[Crossref] [PubMed]

Other (3)

G. Agrawal , Nonlinear fiber optics , ( Academic Press , 2nd edition, 1995 ).

http://www.stanfordcomputeroptics.com

http://www.lumerical.com

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Figures (10)

Fig. 1.
Fig. 1.

Single mode vs multimode phase diagram as predicted by Eq. (4). The dashed lines indicate the uncertainty of the constants used. The arrow indicates the value of d/Λ for the PCF fiber used in the experiments while the shaded region represents the range of observed wavelengths in the white light continuum generated by the PCF fiber.

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Fig. 2.
Fig. 2.

Effective indices of the spatial modes as calculated by simulation, the blue dashed lines represent the effective indices extremes of the core and cladding.

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Fig. 3.
Fig. 3.

SEM image of PCF showing the core surrounded by air holes as supplied by the manufacturer (Thorlabs NL 2.3).

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Fig. 4.
Fig. 4.

Broadband SC generation in 6 m of fiber pumped by 7 ps long pulses at 790 nm from a 82 MHz, 1.5 W average power, mode-locked Ti:Sapphire laser.

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Fig. 5.
Fig. 5.

Experimental setup for measuring the spectral, temporal and spatial structure of the supercontinuum generated in the PCF.

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Fig. 6.
Fig. 6.

PCF structure in simulation (a) manufacturer supplied SEM image of PCF core and cladding structure (b).

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Fig. 7.
Fig. 7.

Intensity distribution of the first 20 spatial modes.

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Fig. 8.
Fig. 8.

Group delay of the first 12 modes as calculated by the simulation

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Fig. 9.
Fig. 9.

The lowest order modes of the PCF in the time domain at a wavelength near 790nm.

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Fig. 10.
Fig. 10.

Far field images of the spatial modes after spectral and intensity filtering. The images were obtained on a gated camera with 300 ps between images (a) and (b), 450 ps between (b) and (c) and 150 ps time difference between (c) and (d).

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Equations (3)

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V = 2 πρ λ [ n c 2 − n cl 2 ] 1 2
V PCF = 2 π Λ λ [ n c 2 ( λ ) − n cl 2 ( λ ) ] 1 2
λ Λ ≅ α ( d Λ − d * Λ ) γ

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