Abstract

We theoretically and experimentally study the phenomena related to self-phase modulation of Airy pulses in fibers. During nonlinear evolution, most spectral components of the Airy pulses concentrate into one or two peaks for normal and anomalous dispersion, respectively. The resulting peaks self-shift along the propagation, effectively mapping the longitudinal coordinate into the frequency domain. The frequency shift can be precisely controlled by simply acting on the spectral cubic phase structure without the need to alter the fiber length.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

2011

Y. Kaganovsky and E. Heyman, J. Opt. Soc. Am. A 28, 1243 (2011).
[CrossRef]

Y. Fattal, A. Rudnick, and D. M. Marom, Opt. Express 19, 17298 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

2010

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef]

2007

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Abdollahpour, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Agrawal, G. P.

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

Ament, C.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Bekenstein, R.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Bongiovanni, D.

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Cannan, D.

Chen, Z.

Chong, A.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

Christodoulides, D.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

Christodoulides, D. N.

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Couairon, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Courvoisier, F.

Dogariu, A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

Dudley, J. M.

Efremidis, N.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

Faccio, D.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Fattal, Y.

Froehly, L.

Furfaro, L.

Giust, R.

Heyman, E.

Hu, Y.

Huang, S.

Jacquot, M.

Kaganovsky, Y.

Kaminer, I.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Lacourt, P. A.

Li, T.

Lotti, A.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Lou, C.

Lumer, Y.

Marom, D. M.

Mathis, A.

Moloney, J. V.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Morandotti, R.

Nemirovsky, J.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

Panagiotopoulos, P.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Papazoglou, D. G.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Polynkin, P.

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

Renninger, W.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

Rudnick, A.

Salandrino, A.

Segev, M.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

I. Kaminer, Y. Lumer, M. Segev, and D. N. Christodoulides, Opt. Express 19, 23132 (2011).
[CrossRef]

Siviloglou, G.

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

Siviloglou, G. A.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

G. A. Siviloglou and D. N. Christodoulides, Opt. Lett. 32, 979 (2007).
[CrossRef]

Song, D.

Sun, Z.

Suntsov, S.

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Tzortzakis, S.

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

Wise, F. W.

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

Xu, J.

Zhang, P.

P. Zhang, Y. Hu, D. Cannan, A. Salandrino, T. Li, R. Morandotti, X. Zhang, and Z. Chen, Opt. Lett. 37, 2820 (2012).
[CrossRef]

Y. Hu, P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, Opt. Lett. 35, 2260 (2010).
[CrossRef]

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

Zhang, X.

J. Opt. Soc. Am. A

Nat. Photonics

A. Chong, W. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).

Opt. Express

Opt. Lett.

Phys. Rev. A

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, Phys. Rev. A 84, 021807(R) (2011).
[CrossRef]

Phys. Rev. Lett.

I. Kaminer, R. Bekenstein, J. Nemirovsky, and M. Segev, Phys. Rev. Lett. 108, 163901 (2012).
[CrossRef]

D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
[CrossRef]

C. Ament, P. Polynkin, and J. V. Moloney, Phys. Rev. Lett. 107, 243901 (2011).
[CrossRef]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Phys. Rev. Lett. 99, 213901 (2007).
[CrossRef]

I. Kaminer, M. Segev, and D. N. Christodoulides, Phys. Rev. Lett. 106, 213903 (2011).
[CrossRef]

Other

Y. Hu, G. Siviloglou, P. Zhang, N. Efremidis, D. Christodoulides, and Z. Chen, in Nonlinear Photonics and Novel Optical Phenomena, Z. Chen and R. Morandotti, eds. (Springer, 2012), pp. 1–46.

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

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Figures (4)

Fig. 1.
Fig. 1.

Typical spectral evolution of a Gaussian pulse propagating in an optical fiber in the presence of a mild nonlinearity for (a) anomalous and (b) normal dispersion.

Fig. 2.
Fig. 2.

Linear and nonlinear propagation of Airy pulses. (a) Evolution of the main hump in the linear case, (b) and (c) spectral components of the pulse depicted in panel (a) for anomalous (b) and normal (c) dispersion, (d) and (e) spectral distribution for anomalous (d) and normal (e) dispersion, (f) and (g) nonlinear temporal evolution corresponding to (d) and (e), respectively. Here, the dashed lines show the linear trajectories.

Fig. 3.
Fig. 3.

Experimental setup. EDFA, erbium-doped fiber amplifier and OSA, optical spectrum analyzer. The plot in the pulse shaper schematically shows the cubic phase structure wrapped between π and π where the circle indicates its center.

Fig. 4.
Fig. 4.

Experimental results (blue solid curve) and theoretical prediction (red dashed curve) of frequency shift control in (a) LEAFs and (b) DSFs. (c) and (d) plot the positions of the spectral notch and peak relative to the center of the cubic phase structure, corresponding to (a) and (b), respectively.

Equations (4)

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

φ/ξ=0.5isgn(β2)2φ/T2+iη|φ|2φ,
φ(T,ξ)=Ai[Tς2/4+α2+vm2isgn(β2)ας]×2πexp(ivm3/3)exp(αTisgn(β2)ςT/2)×exp[i2(iα+sgn(β2)ς/2)3/3ivm2(iα+sgn(β2)ς/2)],
Tp=ς2/4vm2α2.
vd=sgn(β2)μ=sgn(β2)ξ/2+vm.

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