Abstract

We consider partially coherent plane-wave pulses with non-uniform correlation distributions and study their propagation in linear second-order dispersive media. Particular models for coherence functions are introduced both in time and frequency domains. It is shown that the maximum peak of the pulse energy can be accelerating or decelerating and also self-focusing effects are possible due to coherence-induced propagation effects.

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References

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    [CrossRef]
  4. H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012

2011

2010

2009

K. Saastamoinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A80, 053804 (2009).
[CrossRef]

2007

2006

2005

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andres, “Space-time analogy for partially coherent plane-wave-type pulses,” Opt. Lett.30, 2973–2975 (2005).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

2003

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
[CrossRef]

2002

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 1995).

Akter, G. H.

Andres, P.

Cai, Y.

Ding, C.

Friberg, A. T.

Gori, F.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products7th ed. (Academic Press, 2007).

Korotkova, O.

Lajunen, H.

Lancis, J.

Lin, Q.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).

Minguez-Vega, G.

Mokhtarpour, L.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Pan, L.

Ponomarenko, S. A.

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products7th ed. (Academic Press, 2007).

Saastamoinen, K.

K. Saastamoinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A80, 053804 (2009).
[CrossRef]

Saastamoinen, T.

Santarsiero, M.

Silvestre, E.

Tervo, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

Tong, Z.

Torres-Company, V.

Turunen, J.

K. Saastamoinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A80, 053804 (2009).
[CrossRef]

P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express14, 5007–5012 (2006).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Vahimaa, P.

K. Saastamoinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A80, 053804 (2009).
[CrossRef]

P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express14, 5007–5012 (2006).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Wang, L. G.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
[CrossRef]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).

Wyrowski, F.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Zhang, Y.

Zhu, S. Y.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

Q. Lin, L. G. Wang, and S. Y. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
[CrossRef]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, “Spectrally partially coherent pulse trains in dispersive media,” Opt. Commun.255, 12–22 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

K. Saastamoinen, J. Turunen, P. Vahimaa, and A. T. Friberg, “Spectrally partially coherent propagation-invariant fields,” Phys. Rev. A80, 053804 (2009).
[CrossRef]

Other

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products7th ed. (Academic Press, 2007).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 1995).

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Figures (3)

Fig. 1
Fig. 1

(a) The mutual coherence function Γ(t1, t2) and (b) the degree of coherence γ(t1, t2) given by Eq. (6) with T0 = 15 ps, Tc = 10 ps and tc = −10 ps. (c) The corresponding cross-spectral density W(ω1, ω2) and (d) degree of spectral coherence μ(ω1, ω2) calculated numerically by Eq.(2).

Fig. 2
Fig. 2

(a) Evolution of the intensity distribution I(t) of pulses given at z = 0 by Eq. (6) with T0 = 15 ps, Tc = 10 ps and tc = −10 ps in a medium with β2 = 50 ps2/km. (b) Pulse shapes at selected propagation distances. The time coordinate is measured in the reference frame moving at the group velocity of the pulse.

Fig. 3
Fig. 3

(a) Evolution of the intensity distribution I(t) of pulses given at z = 0 by Eq. (9) with Ω0 = 0.3 THz*rad, Ωc = 0.3 THz*rad and ωc = −0.2 THz*rad in a medium with β2 = 50 ps2/km. (b) Pulse shapes at selected propagation distances. The time coordinate is measured in the reference frame moving at the group velocity of the pulse.

Equations (9)

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Γ ( t 1 , t 2 ) = p ( v ) V * ( t 1 , v ) V ( t 2 , v ) d v ,
W ( ω 1 , ω 2 ) = 1 ( 2 π ) 2 Γ ( t 1 , t 2 ) exp [ i ( ω 1 t 1 ω 2 t 2 ) ] d t 1 d t 2 ,
W ( ω 1 , ω 2 ) = 1 ( 2 π ) 2 p ( v ) V ˜ * ( ω 1 , v ) V ˜ ( ω 2 , v ) d v .
p ( v ) = ( π a ) 1 exp ( v 2 / a 2 )
V 0 ( t , v ) = exp ( t 2 2 T 0 2 ) exp [ i κ v ( t t c ) 2 ] ,
Γ 0 ( t 1 , t 2 ) = exp ( t 1 2 + t 2 2 2 T 0 2 ) exp { [ ( t 2 t c ) 2 ( t 1 t c ) 2 ] 2 T c 4 } ,
V ˜ 0 ( ω , v ) = [ π A ( v ) ] 1 / 2 exp [ ( ω + 2 κ v t c ) 2 / A ( v ) i κ v t c 2 ] ,
V ˜ 0 ( ω , v ) = exp ( ω 2 2 Ω 0 2 ) exp [ i b v ( ω ω c ) 2 ] ,
W 0 ( ω 1 , ω 2 ) = exp ( ω 1 2 + ω 2 2 2 Ω 0 2 ) exp { [ ( ω 2 ω c ) 2 ( ω 1 ω c ) 2 ] 2 Ω c 4 } ,

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