Abstract

We investigate numerically and experimentally the spectral correlation between multiple modulation instability (MI) side lobes in a dispersion oscillating fiber. By leveraging the dispersive Fourier transformation, we acquire instantaneous spectra and investigate the energy correlation between individual MI sidebands through scattergrams. We found that conjugate MI side lobes are strongly correlated while other combinations experience a very low degree of correlation, revealing that parametric processes related to each side lobe pair act quasi-independently.

© 2014 Optical Society of America

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  1. V. E. Zakharov and L. A. Ostrovsky, Phys. D. 238, 540 (2009).
    [CrossRef]
  2. K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef]
  3. J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
    [CrossRef]
  4. J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers, 1st ed. (Cambridge University, 2010).
  5. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
    [CrossRef]
  6. M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices, 1st ed. (Cambridge University, 2007).
  7. G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  8. S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
    [CrossRef]
  9. F. Matera, A. Mecozzi, M. Romagnoli, and M. Settembre, Opt. Lett. 18, 1499 (1993).
    [CrossRef]
  10. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
    [CrossRef]
  11. K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
    [CrossRef]
  12. B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
    [CrossRef]
  13. T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
    [CrossRef]
  14. D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
    [CrossRef]
  15. A. Mussot and A. Kudlinski, Nat. Photonics 6, 415 (2012).
    [CrossRef]
  16. M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
    [CrossRef]
  17. A. Armaroli and F. Biancalana, Opt. Express 20, 25096 (2012).
    [CrossRef]
  18. D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
    [CrossRef]
  19. Note that here we do not plot the scattergram between first-order MI Stokes (anti-Stokes) and second-order MI anti-Stokes (Stokes) as it would be similar to the ones depicted in Figs. 2(e) and 2(f) due to the high degree of correlation between conjugate MI sidebands.

2013

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
[CrossRef]

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

2012

A. Armaroli and F. Biancalana, Opt. Express 20, 25096 (2012).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

A. Mussot and A. Kudlinski, Nat. Photonics 6, 415 (2012).
[CrossRef]

2009

V. E. Zakharov and L. A. Ostrovsky, Phys. D. 238, 540 (2009).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

2007

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

1993

1991

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

1986

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Akhmediev, N.

Armaroli, A.

Ben Salem, A.

Biancalana, F.

Bouwmans, G.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

Cavalcanti, S. B.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

Cressoni, J. C.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

da Cruz, H. R.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

Dias, F.

Droques, M.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

Dudley, J. M.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

J. M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Opt. Express 17, 21497 (2009).
[CrossRef]

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers, 1st ed. (Cambridge University, 2010).

Genty, G.

Goda, K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

Godin, T.

Gouveia-Neto, A. S.

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Herink, G.

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

Jalali, B.

D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Kibler, B.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Kudlinski, A.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

A. Mussot and A. Kudlinski, Nat. Photonics 6, 415 (2012).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Lacourt, P. A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Larger, L.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Marhic, M. E.

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices, 1st ed. (Cambridge University, 2007).

Martinelli, G.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

Matera, F.

Mecozzi, A.

Merolla, J. M.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Mussot, A.

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Opt. Lett. 37, 4832 (2012).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

A. Mussot and A. Kudlinski, Nat. Photonics 6, 415 (2012).
[CrossRef]

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, Phys. D. 238, 540 (2009).
[CrossRef]

Romagnoli, M.

Ropers, C.

D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Settembre, M.

Solli, D. R.

D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
[CrossRef]

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Stefani, A.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Sylvestre, T.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Taylor, J. R.

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers, 1st ed. (Cambridge University, 2010).

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Tsia, K. K.

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

Wetzel, B.

T. Godin, B. Wetzel, T. Sylvestre, L. Larger, A. Kudlinski, A. Mussot, A. Ben Salem, M. Zghal, G. Genty, F. Dias, and J. M. Dudley, Opt. Express 21, 18452 (2013).
[CrossRef]

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, Phys. D. 238, 540 (2009).
[CrossRef]

Zghal, M.

Nat. Photonics

D. R. Solli, G. Herink, B. Jalali, and C. Ropers, Nat. Photonics 6, 463 (2012).
[CrossRef]

A. Mussot and A. Kudlinski, Nat. Photonics 6, 415 (2012).
[CrossRef]

Nature

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 450, 1054 (2007).
[CrossRef]

Nonlinearity

D. R. Solli, C. Ropers, and B. Jalali, Nonlinearity 26, R85 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. D.

V. E. Zakharov and L. A. Ostrovsky, Phys. D. 238, 540 (2009).
[CrossRef]

Phys. Rev. A

K. Goda, D. R. Solli, K. K. Tsia, and B. Jalali, Phys. Rev. A 80, 043821 (2009).
[CrossRef]

S. B. Cavalcanti, J. C. Cressoni, H. R. da Cruz, and A. S. Gouveia-Neto, Phys. Rev. A 43, 6162 (1991).
[CrossRef]

M. Droques, A. Kudlinski, G. Bouwmans, G. Martinelli, and A. Mussot, Phys. Rev. A 87, 013813 (2013).
[CrossRef]

Phys. Rev. Lett.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef]

Sci. Rep.

B. Wetzel, A. Stefani, L. Larger, P. A. Lacourt, J. M. Merolla, T. Sylvestre, A. Kudlinski, A. Mussot, G. Genty, F. Dias, and J. M. Dudley, Sci. Rep. 2, 882 (2012).
[CrossRef]

Other

J. M. Dudley and J. R. Taylor, Supercontinuum Generation in Optical Fibers, 1st ed. (Cambridge University, 2010).

M. E. Marhic, Fiber Optical Parametric Amplifiers, Oscillators and Related Devices, 1st ed. (Cambridge University, 2007).

G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Note that here we do not plot the scattergram between first-order MI Stokes (anti-Stokes) and second-order MI anti-Stokes (Stokes) as it would be similar to the ones depicted in Figs. 2(e) and 2(f) due to the high degree of correlation between conjugate MI sidebands.

Supplementary Material (1)

» Media 1: AVI (1653 KB)     

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Figures (3)

Fig. 1.
Fig. 1.

(a) Scheme of the experimental setup. TLS, tunable laser source; MZM, Mach–Zehnder modulator; EDFA, erbium-doped fiber amplifier; TBPF, tunable bandpass filter, PC, polarization controller; CIR, circulator; DOF, dispersion oscillating fiber; DCF, dispersion-compensating fiber; FBG, fiber Bragg grating; OSA, optical spectrum analyzer; RTO, real-time oscilloscope. (b) Longitudinal evolution of the outer diameter of DOF. DOF parameters: average zero dispersion wavelength of 1577 nm, average second-order dispersion β¯2 of 8.5×104ps2/m, second-order dispersion amplitude modulation β2A of 1.8×103ps2/m, average third-order dispersion β¯3 of 5.2×105ps3/m, average fourth-order dispersion β¯4 of 1.1×107ps4/m, modulation period Z of 10 m, fiber length L of 100 m, and nonlinear coefficient γ of 5.5W1·km1.

Fig. 2.
Fig. 2.

Experimental results. (a) Spectral measurement from OSA (blue dashed–dotted line), 500 shot-to-shot realizations from RTO measurement (gray dots) and average of 500 realizations from RTO measurement (red solid line). (b) Selected single-shot spectra from RTO measurement illustrating spectral fluctuation. (c) and (d) Scattergrams between conjugate MI sideband, dotted lines with slope of 1 are shown for reference. (e) and (f) Scattergrams between distinct MI sideband.

Fig. 3.
Fig. 3.

Numerical simulations. (a) Simulated spectra of the multiple MI sidebands. (b) Selected single-shot spectra. (c) and (d) Scattergrams between conjugate MI sideband, dotted lines with slope of 1 are shown for reference. (e) and (f) Scattergrams between distinct MI sideband. A movie (Media 1) showing the scattergrams evolution along the fiber length can be seen online.

Equations (3)

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

β¯2Δω2+2γPp=2kπ/Z,
|U(L,T)|2|U˜(0,β2DCFL+(β2DCFL)2+2β3DCFLTβ3DCFL)|2,
T(ω)=β3DCFL2(ωω0)2+β2DCFL(ωω0),

Metrics