Abstract

We report the experimental observation of scalar and cross-phase modulation instabilities by pumping a highly birefringent photonic crystal fiber in the normal dispersion regime at 45° to its principal polarization axes. Five sideband pairs (two scalar and three vector ones) are observed simultaneously in the spontaneous regime, four of which have a large frequency shift from the pump, in the range 79-93 THz. These results are in excellent agreement with phase-matching arguments and numerical simulations.

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  1. V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D238(5), 540–548 (2009).
    [CrossRef]
  2. G. P. Agrawal, Nonlinear Fiber Optics, Fourth Edition (Academic Press, 2006).
  3. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
    [CrossRef] [PubMed]
  4. S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun.226(1-6), 415–422 (2003).
    [CrossRef]
  5. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett.28(22), 2225–2227 (2003).
    [CrossRef] [PubMed]
  6. S. Trillo and S. Wabnitz, “Bloch wave theory of modulational polarization instabilities in birefringent optical fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(1), 1048–1058 (1997).
    [CrossRef]
  7. A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP31, 486 (1970).
  8. S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38(4), 2018–2021 (1988).
    [CrossRef] [PubMed]
  9. J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A42(1), 682–685 (1990).
    [CrossRef] [PubMed]
  10. P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun.78(2), 137–142 (1990).
    [CrossRef]
  11. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett.20(8), 866–868 (1995).
    [CrossRef] [PubMed]
  12. G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B15(4), 1266–1277 (1998).
    [CrossRef]
  13. P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett.75(19), 2873–2875 (1999).
    [CrossRef]
  14. D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett.30(9), 1051–1053 (2005).
    [CrossRef] [PubMed]
  15. J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett.21(19), 1547–1549 (1996).
    [CrossRef] [PubMed]
  16. J. S. Chen, G. K. Wong, S. G. Murdoch, R. J. Kruhlak, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Cross-phase modulation instability in photonic crystal fibers,” Opt. Lett.31(7), 873–875 (2006).
    [CrossRef] [PubMed]
  17. S. Virally, N. Godbout, S. Lacroix, and L. Labonté, “Two-fold symmetric geometries for tailored phase-matching in birefringent solid-core air-silica microstructured fibers,” Opt. Express18(10), 10731–10741 (2010).
    [CrossRef] [PubMed]
  18. F. Biancalana and D. V. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A, Pure Appl. Opt.6(4), 301–306 (2004).
    [CrossRef]
  19. A. Tonello and S. Wabnitz, “Switching off polarization modulation instabilities in photonic crystal fibers,” IEEE Photon. Technol. Lett.18(8), 953–955 (2006).
    [CrossRef]
  20. G. Millot, A. Sauter, J. M. Dudley, L. Provino, and R. S. Windeler, “Polarization mode dispersion and vectorial modulational instability in air-silica microstructure fiber,” Opt. Lett.27(9), 695–697 (2002).
    [CrossRef] [PubMed]
  21. R. J. Kruhlak, G. K. Wong, J. S. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett.31(10), 1379–1381 (2006).
    [CrossRef] [PubMed]
  22. E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B29(8), 1959–1967 (2012).
    [CrossRef]
  23. B. Kibler, C. Billet, J. M. Dudley, R. S. Windeler, and G. Millot, “Effects of structural irregularities on modulational instability phase matching in photonic crystal fibers,” Opt. Lett.29(16), 1903–1905 (2004).
    [CrossRef] [PubMed]
  24. A. T. Nguyen, K. Phan Huy, E. Brainis, P. Mergo, J. Wojcik, T. Nasilowski, J. Van Erps, H. Thienpont, and S. Massar, “Enhanced cross phase modulation instability in birefringent photonic crystal fibers in the anomalous dispersion regime,” Opt. Express14(18), 8290–8297 (2006).
    [CrossRef] [PubMed]
  25. C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23(2), 174–176 (1987).
    [CrossRef]
  26. A. Mussot, A. Kudlinski, R. Habert, I. Dahman, G. Mélin, L. Galkovsky, A. Fleureau, S. Lempereur, L. Lago, D. Bigourd, T. Sylvestre, M. W. Lee, and E. Hugonnot, “20 THz-bandwidth continuous-wave fiber optical parametric amplifier operating at 1 µm using a dispersion-stabilized photonic crystal fiber,” Opt. Express20(27), 28906–28911 (2012).
    [CrossRef] [PubMed]
  27. B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express18(19), 20136–20142 (2010).
    [CrossRef] [PubMed]
  28. R. T. Murray, E. J. R. Kelleher, S. V. Popov, A. Mussot, A. Kudlinski, and J. R. Taylor, “Synchronously pumped photonic crystal fiber-based optical parametric oscillator,” Opt. Lett.37(15), 3156–3158 (2012).
    [CrossRef] [PubMed]
  29. J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express13(2), 534–544 (2005).
    [CrossRef] [PubMed]
  30. J. A. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fiber source of photon pairs at widely separated wavelengths,” Opt. Lett.35(4), 499–501 (2010).
    [CrossRef] [PubMed]
  31. S. Lefrancois, D. Fu, G. R. Holtom, L. Kong, W. J. Wadsworth, P. Schneider, R. Herda, A. Zach, X. Sunney Xie, and F. W. Wise, “Fiber four-wave mixing source for coherent anti-Stokes Raman scattering microscopy,” Opt. Lett.37(10), 1652–1654 (2012).
    [CrossRef] [PubMed]
  32. T. Gottschall, M. Baumgartl, A. Sagnier, J. Rothhardt, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber-based source for multiplex-CARS microscopy based on degenerate four-wave mixing,” Opt. Express20(11), 12004–12013 (2012).
    [CrossRef] [PubMed]

2012 (5)

2010 (3)

2009 (1)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D238(5), 540–548 (2009).
[CrossRef]

2006 (4)

2005 (2)

2004 (2)

2003 (2)

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett.28(22), 2225–2227 (2003).
[CrossRef] [PubMed]

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun.226(1-6), 415–422 (2003).
[CrossRef]

2002 (1)

1999 (1)

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett.75(19), 2873–2875 (1999).
[CrossRef]

1998 (1)

1997 (1)

S. Trillo and S. Wabnitz, “Bloch wave theory of modulational polarization instabilities in birefringent optical fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(1), 1048–1058 (1997).
[CrossRef]

1996 (1)

1995 (1)

1990 (2)

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A42(1), 682–685 (1990).
[CrossRef] [PubMed]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun.78(2), 137–142 (1990).
[CrossRef]

1988 (1)

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38(4), 2018–2021 (1988).
[CrossRef] [PubMed]

1987 (1)

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23(2), 174–176 (1987).
[CrossRef]

1986 (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
[CrossRef] [PubMed]

1970 (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP31, 486 (1970).

Amans, D.

Atkin, D. M.

Babin, S. A.

Baumgartl, M.

Berkhoer, A. L.

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP31, 486 (1970).

Beugnot, J.-C.

Biancalana, F.

F. Biancalana and D. V. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A, Pure Appl. Opt.6(4), 301–306 (2004).
[CrossRef]

Bigourd, D.

Billet, C.

Birks, T. A.

Bouwmans, G.

Brainis, E.

Bussières, F.

Chen, J. S.

Coen, S.

Corbeil, J.-S.

Dahman, I.

Delqué, M.

Drummond, P. D.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun.78(2), 137–142 (1990).
[CrossRef]

Dudley, J. M.

Duligall, J.

Emplit, P.

Fleureau, A.

Foaleng, S. M.

Fu, D.

Fulconis, J.

Galkovsky, L.

Godbout, N.

Gottschall, T.

Habert, R.

Haelterman, M.

Harvey, J. D.

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
[CrossRef] [PubMed]

Herda, R.

Holtom, G. R.

Hugonnot, E.

Jauregui, C.

Joly, N. Y.

Kablukov, S. I.

Kelleher, E. J. R.

Kennedy, T. A. B.

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun.78(2), 137–142 (1990).
[CrossRef]

Kibler, B.

Knight, J. C.

Kockaert, P.

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett.75(19), 2873–2875 (1999).
[CrossRef]

Kong, L.

Kruhlak, R. J.

Kudlinski, A.

Labonté, L.

Lacroix, S.

Lago, L.

Lee, M. W.

Lefrancois, S.

Lempereur, S.

Leonhardt, R.

Limpert, J.

Maillotte, H.

Massar, S.

Mélin, G.

Menyuk, C. R.

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23(2), 174–176 (1987).
[CrossRef]

Mergo, P.

Millot, G.

Murdoch, S. G.

Murray, R. T.

Mussot, A.

Nasilowski, T.

Nguyen, A. T.

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D238(5), 540–548 (2009).
[CrossRef]

Phan Huy, K.

Pitois, S.

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun.226(1-6), 415–422 (2003).
[CrossRef]

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett.75(19), 2873–2875 (1999).
[CrossRef]

Popov, S. V.

Provino, L.

Rarity, J.

Rothenberg, J. E.

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A42(1), 682–685 (1990).
[CrossRef] [PubMed]

Rothhardt, J.

Russell, P.

Russell, P. St. J.

Sagnier, A.

Sauter, A.

Schneider, P.

Seve, E.

Skryabin, D. V.

F. Biancalana and D. V. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A, Pure Appl. Opt.6(4), 301–306 (2004).
[CrossRef]

Slater, J. A.

Stiller, B.

Sunney Xie, X.

Sylvestre, T.

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
[CrossRef] [PubMed]

Taylor, J. R.

Thévenaz, L.

Thienpont, H.

Tittel, W.

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
[CrossRef] [PubMed]

Tonello, A.

A. Tonello and S. Wabnitz, “Switching off polarization modulation instabilities in photonic crystal fibers,” IEEE Photon. Technol. Lett.18(8), 953–955 (2006).
[CrossRef]

Trillo, S.

S. Trillo and S. Wabnitz, “Bloch wave theory of modulational polarization instabilities in birefringent optical fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(1), 1048–1058 (1997).
[CrossRef]

Tünnermann, A.

Van Erps, J.

Virally, S.

Wabnitz, S.

A. Tonello and S. Wabnitz, “Switching off polarization modulation instabilities in photonic crystal fibers,” IEEE Photon. Technol. Lett.18(8), 953–955 (2006).
[CrossRef]

G. Millot, E. Seve, S. Wabnitz, and M. Haelterman, “Observation of induced modulational polarization instabilities and pulse-train generation in the normal-dispersion regime of a birefringent optical fiber,” J. Opt. Soc. Am. B15(4), 1266–1277 (1998).
[CrossRef]

S. Trillo and S. Wabnitz, “Bloch wave theory of modulational polarization instabilities in birefringent optical fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(1), 1048–1058 (1997).
[CrossRef]

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38(4), 2018–2021 (1988).
[CrossRef] [PubMed]

Wadsworth, W.

Wadsworth, W. J.

Windeler, R. S.

Wise, F. W.

Wojcik, J.

Wong, G. K.

Wong, G. K. L.

Zach, A.

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D238(5), 540–548 (2009).
[CrossRef]

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP31, 486 (1970).

Zlobina, E. A.

Appl. Phys. Lett. (1)

P. Kockaert, M. Haelterman, S. Pitois, and G. Millot, “Isotropic polarization modulational instability and domain walls in spun fibers,” Appl. Phys. Lett.75(19), 2873–2875 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

C. R. Menyuk, “Nonlinear pulse propagation in birefringent optical fibers,” IEEE J. Quantum Electron.23(2), 174–176 (1987).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Tonello and S. Wabnitz, “Switching off polarization modulation instabilities in photonic crystal fibers,” IEEE Photon. Technol. Lett.18(8), 953–955 (2006).
[CrossRef]

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

F. Biancalana and D. V. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A, Pure Appl. Opt.6(4), 301–306 (2004).
[CrossRef]

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

Opt. Commun. (2)

S. Pitois and G. Millot, “Experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber,” Opt. Commun.226(1-6), 415–422 (2003).
[CrossRef]

P. D. Drummond, T. A. B. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun.78(2), 137–142 (1990).
[CrossRef]

Opt. Express (6)

T. Gottschall, M. Baumgartl, A. Sagnier, J. Rothhardt, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber-based source for multiplex-CARS microscopy based on degenerate four-wave mixing,” Opt. Express20(11), 12004–12013 (2012).
[CrossRef] [PubMed]

A. Mussot, A. Kudlinski, R. Habert, I. Dahman, G. Mélin, L. Galkovsky, A. Fleureau, S. Lempereur, L. Lago, D. Bigourd, T. Sylvestre, M. W. Lee, and E. Hugonnot, “20 THz-bandwidth continuous-wave fiber optical parametric amplifier operating at 1 µm using a dispersion-stabilized photonic crystal fiber,” Opt. Express20(27), 28906–28911 (2012).
[CrossRef] [PubMed]

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express13(2), 534–544 (2005).
[CrossRef] [PubMed]

A. T. Nguyen, K. Phan Huy, E. Brainis, P. Mergo, J. Wojcik, T. Nasilowski, J. Van Erps, H. Thienpont, and S. Massar, “Enhanced cross phase modulation instability in birefringent photonic crystal fibers in the anomalous dispersion regime,” Opt. Express14(18), 8290–8297 (2006).
[CrossRef] [PubMed]

S. Virally, N. Godbout, S. Lacroix, and L. Labonté, “Two-fold symmetric geometries for tailored phase-matching in birefringent solid-core air-silica microstructured fibers,” Opt. Express18(10), 10731–10741 (2010).
[CrossRef] [PubMed]

B. Stiller, S. M. Foaleng, J.-C. Beugnot, M. W. Lee, M. Delqué, G. Bouwmans, A. Kudlinski, L. Thévenaz, H. Maillotte, and T. Sylvestre, “Photonic crystal fiber mapping using Brillouin echoes distributed sensing,” Opt. Express18(19), 20136–20142 (2010).
[CrossRef] [PubMed]

Opt. Lett. (11)

S. Lefrancois, D. Fu, G. R. Holtom, L. Kong, W. J. Wadsworth, P. Schneider, R. Herda, A. Zach, X. Sunney Xie, and F. W. Wise, “Fiber four-wave mixing source for coherent anti-Stokes Raman scattering microscopy,” Opt. Lett.37(10), 1652–1654 (2012).
[CrossRef] [PubMed]

J. A. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fiber source of photon pairs at widely separated wavelengths,” Opt. Lett.35(4), 499–501 (2010).
[CrossRef] [PubMed]

D. Amans, E. Brainis, M. Haelterman, P. Emplit, and S. Massar, “Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime,” Opt. Lett.30(9), 1051–1053 (2005).
[CrossRef] [PubMed]

J. S. Chen, G. K. Wong, S. G. Murdoch, R. J. Kruhlak, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Cross-phase modulation instability in photonic crystal fibers,” Opt. Lett.31(7), 873–875 (2006).
[CrossRef] [PubMed]

R. J. Kruhlak, G. K. Wong, J. S. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett.31(10), 1379–1381 (2006).
[CrossRef] [PubMed]

R. T. Murray, E. J. R. Kelleher, S. V. Popov, A. Mussot, A. Kudlinski, and J. R. Taylor, “Synchronously pumped photonic crystal fiber-based optical parametric oscillator,” Opt. Lett.37(15), 3156–3158 (2012).
[CrossRef] [PubMed]

J. C. Knight, T. A. Birks, P. St. J. Russell, and D. M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett.21(19), 1547–1549 (1996).
[CrossRef] [PubMed]

G. Millot, A. Sauter, J. M. Dudley, L. Provino, and R. S. Windeler, “Polarization mode dispersion and vectorial modulational instability in air-silica microstructure fiber,” Opt. Lett.27(9), 695–697 (2002).
[CrossRef] [PubMed]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett.28(22), 2225–2227 (2003).
[CrossRef] [PubMed]

B. Kibler, C. Billet, J. M. Dudley, R. S. Windeler, and G. Millot, “Effects of structural irregularities on modulational instability phase matching in photonic crystal fibers,” Opt. Lett.29(16), 1903–1905 (2004).
[CrossRef] [PubMed]

S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett.20(8), 866–868 (1995).
[CrossRef] [PubMed]

Phys. Rev. A (2)

S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A38(4), 2018–2021 (1988).
[CrossRef] [PubMed]

J. E. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A42(1), 682–685 (1990).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

S. Trillo and S. Wabnitz, “Bloch wave theory of modulational polarization instabilities in birefringent optical fibers,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics56(1), 1048–1058 (1997).
[CrossRef]

Phys. Rev. Lett. (1)

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett.56(2), 135–138 (1986).
[CrossRef] [PubMed]

Physica D (1)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: the beginning,” Physica D238(5), 540–548 (2009).
[CrossRef]

Sov. Phys. JETP (1)

A. L. Berkhoer and V. E. Zakharov, “Self excitation of waves with different polarizations in nonlinear media,” Sov. Phys. JETP31, 486 (1970).

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, Fourth Edition (Academic Press, 2006).

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Figures (3)

Fig. 1
Fig. 1

SMI (dashed lines) and XPMI (solid lines) phase-matching curves as a function of pump wavelength calculated for the PCF described in the text. The pump power is set to 430 W. Red and blue lines represent sidebands generated respectively on the fast and slow axis of the PCF. The vertical line corresponds to the 1064 nm pump wavelength. Inset: scanning electron image of the fabricated PCF.

Fig. 2
Fig. 2

Numerical simulation of the output spectra on the fast (red line) and slow (blue line) PCF polarization axes. Arrows depict expected phase-matched wavelengths from Fig. 1, with the same style code.

Fig. 3
Fig. 3

(a) Measured output spectrum for a pump peak power of 430 W and input polarization state at 45° of the PCF principal axes. (b), (c), (d) Close-up on the anti-Stokes (b), pump (c) and Stokes (d) spectral regions for the fast axis (red lines) and slow axis (blue lines).

Tables (1)

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Table 1 Polarization state of the pump (top row) and sidebands (middle row) with respect to fiber principle axes (represented as black dotted lines) for various types of MI with a linearly polarized pump. The bottom row indicates required typical values of phase birefringence Bp.

Equations (3)

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β P,x + β P,y = β S + β AS +γ( P x + P y ) and 2 ω P = ω S + ω AS
A x z k1 i k+1 k! β k,x k A x t k =iγ( | A x | 2 + 2 3 | A y | 2 ) A x
A y z k1 i k+1 k! β k,y k A y t k =iγ( | A y | 2 + 2 3 | A x | 2 ) A y

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