Abstract

We study Cross Phase Modulational Instability (CPMI) -a particular form of vector modulational instability- in the anomalous dispersion regime in highly birefringent, strongly dispersive, optical fibers. When the pump power is high, the detuning of the Scalar Modulational Instability (SMI) is comparable to the detuning of the CPMI. The gain of the CPMI -which is usually much smaller than the gain of the SMI-, is then strongly enhanced and becomes much larger than the gain of the SMI. This theoretical prediction is well verified experimentally using small core photonic crystal fibers.

© 2006 Optical Society of America

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  1. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986).
    [CrossRef] [PubMed]
  2. G. P. Agrawal, Nonlinear Fiber Optics, third ed., (Academic Press, San Diego, 2001).
  3. J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
    [CrossRef] [PubMed]
  4. 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, 137-142 (1990).
    [CrossRef]
  5. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, "Polarization modulation instability in weakly birefringent fibers," Opt. Lett. 20, 866-868 (1995).
    [CrossRef] [PubMed]
  6. D. Amans, E. Brainis, M. Haelterman, Ph. Emplit, and S. Massar "Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous-dispersion regime," Opt. Lett. 30, 1051-1053 (2005).
    [CrossRef] [PubMed]
  7. F. Biancalana, and D. V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A: Pure Appl. Opt. 6301-306 (2004).
    [CrossRef]
  8. 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, 695-697 (2002).
    [CrossRef]
  9. 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, 1903-1905 (2004).
    [CrossRef] [PubMed]
  10. A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, "Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber," Opt. Express 14, 397-404 (2006).
    [CrossRef] [PubMed]
  11. J. S. Y. Chen, G. K. L. 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, 873-875 (2006).
    [CrossRef] [PubMed]
  12. 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, 1379-1381 (2006).
    [CrossRef] [PubMed]
  13. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
    [CrossRef]
  14. J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005).
    [CrossRef] [PubMed]
  15. E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
    [CrossRef]
  16. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L.C. Botten, "Multipole method for microstructured optical fibers. I. Formulation," J. Opt. Soc. Am. B 19, 2322-2330 (2002).
    [CrossRef]
  17. T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
    [CrossRef]

2006 (3)

2005 (4)

J. Rarity, J. Fulconis, J. Duligall, W. Wadsworth, and P. Russell, "Photonic crystal fiber source of correlated photon pairs," Opt. Express 13, 534-544 (2005).
[CrossRef] [PubMed]

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

E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

2004 (2)

2002 (3)

1995 (1)

1990 (2)

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 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, 137-142 (1990).
[CrossRef]

1986 (1)

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

Amans, D.

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

E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

Berghmans, F.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Biancalana, F.

F. Biancalana, and D. V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A: Pure Appl. Opt. 6301-306 (2004).
[CrossRef]

Billet, C.

Botten, L.C.

Brainis, E.

E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

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

Chen, J. S.

Chen, J. S. Y.

Conforti, M.

De Angelis, C.

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, 137-142 (1990).
[CrossRef]

Dudley, J. M.

Duligall, J.

Emplit, Ph.

Fiorentino, M.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Fulconis, J.

Golojuch, G.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

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, 135-138 (1986).
[CrossRef] [PubMed]

Joly, N. Y.

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, 137-142 (1990).
[CrossRef]

Kibler, B.

Knight, J. C.

Kruhlak, R. J.

Kuhlmey, B. T.

Kumar, P.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Leonhardt, R.

Locatelli, A.

Makara, M.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Martijn de Sterke, C.

Martynkien, T.

A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, "Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber," Opt. Express 14, 397-404 (2006).
[CrossRef] [PubMed]

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Massar, S.

E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

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

Maystre, D.

McPhedran, R. C.

Mergo, P.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Millot, G.

Murdoch, S. G.

Nasilowski, T.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Olszewski, J.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Pitois, S.

Provino, L.

Rarity, J.

Renversez, G.

Rothenberg, J. E.

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
[CrossRef] [PubMed]

Russell, P.

Sauter, A.

Sharping, J. E.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Skryabin, D. V.

F. Biancalana, and D. V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A: Pure Appl. Opt. 6301-306 (2004).
[CrossRef]

Statkiewicz, G.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Szpulak, M.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Tai, K.

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

Thienpont, H.

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Tomita, A.

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

Tonello, A.

Urbanczyk, W.

A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, "Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber," Opt. Express 14, 397-404 (2006).
[CrossRef] [PubMed]

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Voss, P. L.

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[CrossRef]

Wabnitz, S.

Wadsworth, W.

White, T. P.

Windeler, R. S.

Wojcik, J.

A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, "Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber," Opt. Express 14, 397-404 (2006).
[CrossRef] [PubMed]

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

Wong, G. K.

Wong, G. K. L.

Appl. Phys. B (1)

T. Nasilowski, T. Martynkien, G. Statkiewicz, M. Szpulak, J. Olszewski, G. Golojuch, W. Urbanczyk, J. Wojcik, P. Mergo, M. Makara, F. Berghmans, and H. Thienpont, "Temperature and pressure sensitivities of the highly birefringent photonic crystal fiber with core asymmetry," Appl. Phys. B 81, 325-331 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, "All-fibre photon pair source for quantum communications," IEEE Photon. Technol. Lett. 14, 983-985 (2002).
[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. 6301-306 (2004).
[CrossRef]

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

Opt. Commun. (1)

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, 137-142 (1990).
[CrossRef]

Opt. Express (2)

Opt. Lett. (6)

Phys. Rev. A (2)

E. Brainis, D. Amans, and S. Massar, "Scalar and vector modulation instabilities induced by vacuum fluctuations in fibers: Numerical study," Phys. Rev. A 71, 023808 (2005).
[CrossRef]

J. E. Rothenberg, "Modulational instability for normal dispersion," Phys. Rev. A 42, 682-685 (1990).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics, third ed., (Academic Press, San Diego, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

Gain spectra for MI in highly birefringent fibers in the anomalous dispersion regime for different values of the birefringence Δβ 1. The horizontal and vertical axes are the dimensionless units ω ˜ = ω γ P 0 β 2 and = (2/γ P 0)k. In the different panels we change the value of the dimensionless parameter α = Δ β 1 γ P 0 β 2 . In Panel (a) to (f) α successively takes the values 3, 1.43, 1, 0.75, 0.6 and 0.

Fig. 2.
Fig. 2.

Scanning Electron Micrograph of fiber 030904p4

Fig. 3.
Fig. 3.

Spectra measured at the output of 6.6 meters of fiber 030904p4 when the light is injected at 45° to the axes of the fiber. The peak powers P 0 are 33.2 W (blue), 37.7 W (red), 39.8 W (green). Note that the pump at 1536 nm is not observed in the spectra as it is removed by the FBG.(The noise level in the case P 0 = 39.8 W is higher than in the other cases due to a different setting of the OSA.)

Fig. 4.
Fig. 4.

Spectra measured at the output of 6.6 meters of fiber 030904p4 when the injected peak power at 1536 nm is 61W. The red and the blue curves represent the light polarized along the slow and fast axis of the fiber respectively as measured after a PBS, whereas the black curve represents the total spectrum. Note that the pump has been removed by a FBG, and does not appear in the spectrum. The noise level is higher than in Fig. 4 due to other experimental conditions. The SMI peaks are barely visible above the background.

Equations (6)

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

A x z + Δ β 1 2 A x t + i β 2 2 2 A x t 2 = ( A x 2 + B A y 2 ) A x
A y z Δ β 1 2 A y t + i β 2 2 2 A y t 2 = ( A y 2 + B A x 2 ) A y
α = Δ β 1 γ P 0 β 2 .
A x = A x 0 e ( P x + B P y ) z ( 1 + 0 e iωt e ik ( ω ) z a x ( ω ) + e + iωt e i k * ( ω ) z a x ( ω ) )
A y = A y 0 e ( P y + B P x ) z ( 1 + 0 e iωt e ik ( ω ) z a y ( ω ) + e + iωt e i k * ( ω ) z a y ( ω ) )
k ˜ 2 = ± 2 ω ˜ 4 ( B 2 + α 2 ( ω ˜ 2 + 2 sgn ( β 2 ) ) ) + ω ˜ 2 ( ω ˜ 2 + α 2 + 2 sgn ( β 2 ) )

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