Abstract

We investigate theoretically and experimentally the modulation instability process in a dispersion oscillating fiber characterized by an amplitude modulation of its group velocity dispersion. We developed an analytical model that allows us to calculate the parametric gain in these fibers and to predict the position of the quasi-phase matched modulation instability sidelobes. The two fundamental frequencies characterizing the dispersion profile lead to the splitting of the original multiple sidelobes generated in basic sinusoidally varying dispersion oscillating fibers. These theoretical predictions are confirmed by experiments.

© 2015 Optical Society of America

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References

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  1. E. A. Golovchenko and A. N. Pilipetskii, “Unified analysis of four-photon mixing, modulational instability, and stimulated Raman scattering under various polarization conditions in fibers,” J. Opt. Soc. Am. B 11, (1)92–101 (1994).
    [Crossref]
  2. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum. Electron 18(7), 1062–1072 (1982).
    [Crossref]
  3. A. Kudlinski, A. Bendahmane, D. Labat, S. Virally, R. T. Murray, E. J. R. Kelleher, and A. Mussot, “Simultaneous scalar and cross-phase modulation instabilities in highly birefringent photonic crystal fiber,” Opt. Express 21(7), 8437–8443 (2013).
    [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. Russel, “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. F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett. 18(18), 1499–1501 (1993).
    [Crossref] [PubMed]
  7. N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett. 21(8), 570–572 (1996).
    [Crossref] [PubMed]
  8. F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
    [Crossref]
  9. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, “Experimental demonstration of modulation instability in an optical fiber with a periodic dispersion landscape,” Opt. Lett. 37(23), 4832–4834 (2012).
    [Crossref] [PubMed]
  10. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, “Dynamics of the modulation instability spectrum in optical fibers with oscillating dispersion,” Phys. Rev. A 87(1), 013813 (2013).
    [Crossref]
  11. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38(17), 3464–3467 (2013).
    [Crossref] [PubMed]
  12. C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
    [Crossref]
  13. A. Armaroli and F. Biancalana, “Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers,” Phys. Rev. A 87(6), 063848 (2013).
    [Crossref]
  14. X. Wang, D. Bigourd, A. Kudlinski, K. K. Y. Wong, M. Douay, L. Bigot, A. Lerouge, Y. Quiquempois, and A. Mussot, “Correlation between multiple modulation instability side lobes in dispersion oscillating fiber,” Opt. Lett. 39(7), 1881–1884 (2014).
    [Crossref] [PubMed]
  15. S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
    [Crossref] [PubMed]
  16. G. Agrawal, Nonlinear Fiber Optics, 5. (Academic, 2013).
  17. M. E. Marhic, F. S. Yang, M. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” J. Lightwave Technol. 17(2), 210–215 (1999).
    [Crossref]
  18. K. Saitoh and M. Koshiba, “Empirical relations for simple design of photonic crystal fibers,” Opt. Express 13(1), 267–274 (2005).
    [Crossref] [PubMed]

2014 (2)

2013 (4)

A. Armaroli and F. Biancalana, “Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers,” Phys. Rev. A 87(6), 063848 (2013).
[Crossref]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, “Dynamics of the modulation instability spectrum in optical fibers with oscillating dispersion,” Phys. Rev. A 87(1), 013813 (2013).
[Crossref]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38(17), 3464–3467 (2013).
[Crossref] [PubMed]

A. Kudlinski, A. Bendahmane, D. Labat, S. Virally, R. T. Murray, E. J. R. Kelleher, and A. Mussot, “Simultaneous scalar and cross-phase modulation instabilities in highly birefringent photonic crystal fiber,” Opt. Express 21(7), 8437–8443 (2013).
[Crossref] [PubMed]

2012 (1)

2005 (1)

2003 (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]

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

1999 (1)

1996 (2)

N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett. 21(8), 570–572 (1996).
[Crossref] [PubMed]

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

1994 (1)

1993 (1)

1991 (1)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum. Electron 18(7), 1062–1072 (1982).
[Crossref]

Abdullaev, F. K.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 5. (Academic, 2013).

Armaroli, A.

A. Armaroli and F. Biancalana, “Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers,” Phys. Rev. A 87(6), 063848 (2013).
[Crossref]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38(17), 3464–3467 (2013).
[Crossref] [PubMed]

Bendahmane, A.

Biancalana, F.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38(17), 3464–3467 (2013).
[Crossref] [PubMed]

A. Armaroli and F. Biancalana, “Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers,” Phys. Rev. A 87(6), 063848 (2013).
[Crossref]

Bigot, L.

Bigourd, D.

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum. Electron 18(7), 1062–1072 (1982).
[Crossref]

Bouwmans, G.

Chembo, Y.

C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
[Crossref]

Coen, S.

Darmanyan, S. A.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

Doran, N. J.

Douay, M.

Droques, M.

Feng, F.

C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
[Crossref]

Finot, C.

C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
[Crossref]

Golovchenko, E. A.

Harvey, J. D.

Ho, M.

Kazovsky, L. G.

Kelleher, E. J. R.

Knight, J. C.

Kobyakov, A.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

Koshiba, M.

Kudlinski, A.

Labat, D.

Lederer, F.

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

Leonhardt, R.

Lerouge, A.

Marhic, M. E.

Martinelli, G.

Matera, F.

Mecozzi, A.

Millot, G.

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]

Murray, R. T.

Mussot, A.

Pilipetskii, A. N.

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]

Quiquempois, Y.

Romagnoli, M.

Russel, P. St. J.

Saitoh, K.

Settembre, M.

Smith, N. J.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum. Electron 18(7), 1062–1072 (1982).
[Crossref]

Trillo, S.

Virally, S.

Wabnitz, S.

C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
[Crossref]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
[Crossref] [PubMed]

Wadsworth, W. J.

Wang, X.

Wong, G. K. L.

Wong, K. K. Y.

Yang, F. S.

IEEE J. Quantum. Electron (1)

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum. Electron 18(7), 1062–1072 (1982).
[Crossref]

J. Lightwave Technol. (1)

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

Opt. Commun. (1)

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]

Opt. Express (2)

Opt. Fiber Tech. (1)

C. Finot, F. Feng, Y. Chembo, and S. Wabnitz, “Gain sideband splitting in dispersion oscillating fibers,” Opt. Fiber Tech. 20(5), 513–519 (2014).
[Crossref]

Opt. Lett. (7)

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, A. Mussot, A. Armaroli, and F. Biancalana, “Fourth-order dispersion mediated modulation instability in dispersion oscillating fibers,” Opt. Lett. 38(17), 3464–3467 (2013).
[Crossref] [PubMed]

X. Wang, D. Bigourd, A. Kudlinski, K. K. Y. Wong, M. Douay, L. Bigot, A. Lerouge, Y. Quiquempois, and A. Mussot, “Correlation between multiple modulation instability side lobes in dispersion oscillating fiber,” Opt. Lett. 39(7), 1881–1884 (2014).
[Crossref] [PubMed]

S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulational instability in optical fibers,” Opt. Lett. 16(13), 986–988 (1991).
[Crossref] [PubMed]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, “Experimental demonstration of modulation instability in an optical fiber with a periodic dispersion landscape,” Opt. Lett. 37(23), 4832–4834 (2012).
[Crossref] [PubMed]

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

F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, “Sideband instability induced by periodic power variation in long-distance fiber links,” Opt. Lett. 18(18), 1499–1501 (1993).
[Crossref] [PubMed]

N. J. Smith and N. J. Doran, “Modulational instabilities in fibers with periodic dispersion management,” Opt. Lett. 21(8), 570–572 (1996).
[Crossref] [PubMed]

Phys. Lett. A (1)

F. K. Abdullaev, S. A. Darmanyan, A. Kobyakov, and F. Lederer, “Modulational instability in optical fibers with variable dispersion,” Phys. Lett. A 220(4–5), 213–218 (1996).
[Crossref]

Phys. Rev. A (2)

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, “Dynamics of the modulation instability spectrum in optical fibers with oscillating dispersion,” Phys. Rev. A 87(1), 013813 (2013).
[Crossref]

A. Armaroli and F. Biancalana, “Vector modulational instability induced by parametric resonance in periodically tapered highly birefringent optical fibers,” Phys. Rev. A 87(6), 063848 (2013).
[Crossref]

Other (1)

G. Agrawal, Nonlinear Fiber Optics, 5. (Academic, 2013).

Supplementary Material (1)

» Media 1: MP4 (1656 KB)     

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Figures (3)

Fig. 1
Fig. 1 (a) Typical amplitude modulated dispersion profile. (b) Corresponding gain spectrum simulated according to the NLS equation. The red circles represent the positions and maximum gain values of the sidelobes predicted by the analytical model. Each sidelobe is identified by its [k k′] label. (c) Longitudinal evolution of the gain of the first sidelobe calculated using the analytical model. A movie ( Media 1) showing the evolution of the gain spectrum along the fiber length can be seen online. L = 150 m, Z1 = 5 m, Z2 = 50 m, Pp = 15 W, γ = 7.5 W−1·km−1, β ¯ 2 = 1 ps 2 / km, β 2 A = 0.8 ps 2 / km.
Fig. 2
Fig. 2 (a) Gain spectrum in amplitude modulated fibers as a function of the Z1/Z2 ratio (Z1 is fixed and equal to 7.5 m, Z2 varies from ∞ to Z1). The dotted lines represent the predicted positions of the sidelobes maximum. Cross-sections of this figure along with sections of the corresponding dispersion profiles are presented for different ratios: (f,g) simply oscillating fiber (Z1/Z2 = 0), (d,e) amplitude modulated fiber (Z1/Z2 = 0.2) and (b,c) modulation and oscillation periods are equal (Z1/Z2 = 1). Same parameters as in Fig. 1.
Fig. 3
Fig. 3 (a) Experimental setup for the observation of modulation instability. External diameter and dispersion profile of (b) the reference oscillating fiber (c) the amplitude modulated fiber (dispersion scale is calculated for λp = 1057.5 nm). (d) Transverse profile of the PCF. (e) Experimental spectra out of the reference fiber (blue dotted line) and the amplitude modulated fiber (solid red line). The red arrows point out the predicted positions of the first two sidelobes in the amplitude modulated fiber. Inset is the full-span spectrum in the reference fiber exhibiting multiple sidelobes. Pp = 15 W, γ = 7.5 W−1· km−1, β ¯ 2 = 1.2 ps 2 / km.

Equations (7)

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d P s ( Ω , z ) d z = 2 γ P p P s ( Ω , z ) P i ( Ω , z ) sin [ θ ( Ω , z ) ]
d P i ( Ω , z ) d z = 2 γ P p P s ( Ω , z ) P i ( Ω , z ) sin [ θ ( Ω , z ) ]
d θ ( Ω , z ) d z = β 2 ( z ) Ω 2 + 2 γ P p { 1 + cos [ θ ( Ω , z ) ] }
β 2 ( z ) = β ¯ 2 + β 2 A sin ( 2 π z Z 1 ) cos ( 2 π z Z 2 )
G S ( Ω , z ) = P s ( Ω , z ) P s ( Ω , 0 ) = 1 4 ( 1 ρ ) + 1 4 ( 1 + ρ + 2 ρ ) exp [ 0 z g ( Ω , θ , z ) d z ]
g ( Ω , z ) = 2 γ P p q = + q = + J q ( β 2 A Ω 2 2 Λ s ) J q ( β 2 A Ω 2 2 Λ d ) sin [ ( Ω 2 β ¯ 2 + 2 γ P p q Λ s q Λ d ) z + θ ( 0 ) ]
β ¯ 2 Ω k k 2 + 2 γ P p = k Λ s + k Λ d

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