Abstract

A novel (to our knowledge) kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.

© 2012 Optical Society of America

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References

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  1. M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
    [CrossRef]
  2. A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Nat. Photonics 4, 103 (2010).
    [CrossRef]
  3. D. Abdollahpour, S. Suntsov, D. G. Papazoglou, and S. Tzortzakis, Phys. Rev. Lett. 105, 253901 (2010).
    [CrossRef]
  4. M. A. Preciado and M. A. Muriel, “Método y sistema para la transmisión de pulsos ópticos a través de medios dispersivos,” Spanish patent ES 2364935 B2 (February14, 2012).
  5. O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), Chap. 4.
  6. ITU-T, Optical Fibres, Cables and Systems (ITU, 2009) Chap. 7.
  7. M. Ibsen and R. Feced, Opt. Lett. 28, 980 (2003).
    [CrossRef]
  8. A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
    [CrossRef]

2010

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

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

2003

1995

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

1979

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Abdollahpour, D.

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

Balazs, N. L.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Berry, M. V.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Chong, A.

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

Christodoulides, D. N.

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

Feced, R.

Ibsen, M.

Muriel, M. A.

M. A. Preciado and M. A. Muriel, “Método y sistema para la transmisión de pulsos ópticos a través de medios dispersivos,” Spanish patent ES 2364935 B2 (February14, 2012).

Papazoglou, D. G.

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

Preciado, M. A.

M. A. Preciado and M. A. Muriel, “Método y sistema para la transmisión de pulsos ópticos a través de medios dispersivos,” Spanish patent ES 2364935 B2 (February14, 2012).

Renninger, W. H.

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

Soares, M.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), Chap. 4.

Suntsov, S.

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

Tzortzakis, S.

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

Vallée, O.

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), Chap. 4.

Weiner, A. M.

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

Wise, F. W.

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

Am. J. Phys.

M. V. Berry and N. L. Balazs, Am. J. Phys. 47, 264 (1979).
[CrossRef]

Nat. Photonics

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

Opt. Lett.

Phys. Rev. Lett.

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

Prog. Quantum Electron.

A. M. Weiner, Prog. Quantum Electron. 19, 161 (1995).
[CrossRef]

Other

M. A. Preciado and M. A. Muriel, “Método y sistema para la transmisión de pulsos ópticos a través de medios dispersivos,” Spanish patent ES 2364935 B2 (February14, 2012).

O. Vallée and M. Soares, Airy Functions and Applications to Physics (Imperial College, 2004), Chap. 4.

ITU-T, Optical Fibres, Cables and Systems (ITU, 2009) Chap. 7.

Supplementary Material (1)

» Media 1: AVI (1698 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Spectral amplitude of the ideal infinite energy Airy rocket pulse (blue dashed curve and the finite energy pulse (blue solid curve), and spectral phase (red dotted curve) for both.

Fig. 2.
Fig. 2.

Temporal intensity of the propagation of the Airy rocket pulse designed in the example in a path of 70 km, where the corresponding total pulse energy is indicated in the right-hand side (Media 1). Four points of the path shown: (a) z=0km, (b) z=40km, (c) z=47km, and (d) z=70km.

Fig. 3.
Fig. 3.

Color map representation of the evolution of the temporal intensity of the propagated Airy rocket pulse designed in the example in a path of 70 km, as it propagates in z.

Fig. 4.
Fig. 4.

Pulse intensity peak (blue solid curve) and total pulse energy (green dotted curve).

Equations (11)

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Ar(ω)=A(ω)G(ω)=exp(ζω+jξω3),
Fprob(ω,z)=exp(ζωαz+j(ξω3β(ω)z)),
Fprop(ω,z)=exp(ζωαz)exp(jξ(ωΔω(z))3j(ϕ(z)+Δt(z)ω))=exp(ζ(ωΔω(z))+jξ(ωΔω(z))3)exp(ζΔω(z)αzj(ϕ(z)+Δt(z)ω))=Ar(ωΔω(z))exp(ζΔω(z)αzj(ϕ(z)+Δt(z)ω)),
Δω(z)=β2z/6ξ,
Δt(z)=3ξΔω(z)2+β1z,
ξω3β(ω)z=ξ(ωΔω(z))3ϕ(z)Δt(z)ω,
ζ=6ξα/β2,
Fprop(ω,z)=Ar(ωΔω(z))exp(j(ϕ(z)+Δt(z)ω)).
fprop(t,z)=ar(tΔt(z))exp(j(Δω(z)tϕ(z))),
|fprop(t,z)|2=|ar(tΔt(z))|2.
Ar,W(ω)=A(ω)G(ω)W(ω),

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