Abstract

We examine coherence properties of small-area, intrinsically stationary statistical pulses propagating in amplifying media in the vicinity of an optical resonance. Any such medium acts as a coherent linear amplifier, amplifying and reshaping the pulse. We show that an initially nearly incoherent Gaussian Schell-model pulse becomes almost fully coherent and its state of coherence becomes nearly uniform across the temporal profile as the pulse propagates into the amplifying medium.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. W. Huang, S. A. Ponomarenko, M. Cada, and G. P. Agrawal, “Polarization changes of partially coherent pulses propagating in optical fibers,” J. Opt. Soc. Am. A 24, 3063–3068 (2007).
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  15. C. L. Ding, L. Z. Pan, and B. D. Lu, “Changes in the spectral degree of polarization of stochastic spatially and spectrally partially coherent electromagnetic pulses in dispersive media,” J. Opt. Soc. Am. B 26, 1728–1735 (2009).
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    [CrossRef]
  17. M. Brunel and S. Coëtmellec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
    [CrossRef]
  18. S. A. Ponomarenko, “Degree of phase-space separability of statistical pulses,” Opt. Express 20, 2548–2555 (2012).
    [CrossRef]
  19. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrés, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18, 14979–14991 (2010).
    [CrossRef]
  20. S. Haghgoo and S. A. Ponomarenko, “Self-similar pulses in coherent linear amplifiers,” Opt. Express 19, 9750–9758 (2011).
    [CrossRef]
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    [CrossRef]
  22. L. Mokhtarpour, G. H. Akter, and S. A. Ponomarenko, “Partially coherent self-similar pulses in resonant linear absorbers,” Opt. Express 20, 17816–17822 (2012).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (4)

2011 (3)

2010 (1)

2009 (4)

2007 (4)

2006 (1)

2004 (3)

2003 (2)

2002 (1)

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

1971 (1)

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

Agrawal, G. P.

Akter, G. H.

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975).

Andrés, P.

Bartels, R. A.

Brunel, M.

M. Brunel and S. Coëtmellec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[CrossRef]

Cada, M.

Carney, P. S.

Coëtmellec, S.

M. Brunel and S. Coëtmellec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[CrossRef]

Davis, B.

B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A 76, 043843 (2007).
[CrossRef]

Davis, B. J.

Ding, C. L.

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975).

Fernandez-Pousa, C. R.

Friberg, A. T.

Haghgoo, S.

Huang, W.

Lajunen, H.

Lamb, G. L.

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

Lancis, J.

Lavarello, R.

R. W. Schoonover, R. Lavarello, M. L. Oezle, and P. S. Carney, “Observation of generalised Wolf shifts in short pulse spectroscopy,” Appl. Phys. Lett. 98, 251107 (2011).
[CrossRef]

Lin, Q.

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

Lu, B. D.

Mandel, L.

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

Mokhtarpour, L.

Oezle, M. L.

R. W. Schoonover, R. Lavarello, M. L. Oezle, and P. S. Carney, “Observation of generalised Wolf shifts in short pulse spectroscopy,” Appl. Phys. Lett. 98, 251107 (2011).
[CrossRef]

Paakkonen, P.

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

Pan, L. Z.

Ponomarenko, S. A.

Schoonover, R. W.

Silvestre, E.

Tervo, J.

Torres-Company, V.

Turunen, J.

Vahimaa, P.

Wang, L.

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

Wolf, E.

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[CrossRef]

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

Zhu, S.

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

Appl. Phys. Lett. (1)

R. W. Schoonover, R. Lavarello, M. L. Oezle, and P. S. Carney, “Observation of generalised Wolf shifts in short pulse spectroscopy,” Appl. Phys. Lett. 98, 251107 (2011).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (2)

Opt. Commun. (3)

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

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

M. Brunel and S. Coëtmellec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun. 230, 1–5 (2004).
[CrossRef]

Opt. Express (9)

S. A. Ponomarenko, “Degree of phase-space separability of statistical pulses,” Opt. Express 20, 2548–2555 (2012).
[CrossRef]

H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrés, “Pulse-by-pulse method to characterize partially coherent pulse propagation in instantaneous nonlinear media,” Opt. Express 18, 14979–14991 (2010).
[CrossRef]

S. Haghgoo and S. A. Ponomarenko, “Self-similar pulses in coherent linear amplifiers,” Opt. Express 19, 9750–9758 (2011).
[CrossRef]

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express 11, 1894–1899 (2003).
[CrossRef]

R. W. Schoonover, B. J. Davis, and P. S. Carney, “The generalized Wolf shift for cyclostationary fields,” Opt. Express 17, 4705–4711 (2009).
[CrossRef]

P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express 14, 5007–5012 (2006).
[CrossRef]

A. T. Friberg, H. Lajunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express 15, 5160–5165 (2007).
[CrossRef]

S. A. Ponomarenko, “Complex Gaussian representation of statistical pulses,” Opt. Express 19, 17086–17091 (2011).
[CrossRef]

L. Mokhtarpour, G. H. Akter, and S. A. Ponomarenko, “Partially coherent self-similar pulses in resonant linear absorbers,” Opt. Express 20, 17816–17822 (2012).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A 76, 043843 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

G. L. Lamb, “Analytical descriptions of ultrashort optical pulse propagation in resonant medium,” Rev. Mod. Phys. 43, 99–124 (1971).
[CrossRef]

Other (3)

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1975).

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

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).

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Figures (4)

Fig. 1.
Fig. 1.

Pulse intensity profile in arbitrary units (a.u) as a function of the dimensionless propagation distance Z for two partially coherent pulses: (a) tc=5tp and (b) tc=tp/5.

Fig. 2.
Fig. 2.

Energy gain factor as a function of the dimensionless propagation distance Z for two partially coherent pulses: (a) tc=5tp and (b) tc=tp/5.

Fig. 3.
Fig. 3.

Magnitude of the complex degree of coherence of a short GSM pulse with tc=5tp for (a) Z=1 and (b) Z=5. Insets: the corresponding pulse intensity profiles.

Fig. 4.
Fig. 4.

Magnitude of the temporal degree of coherence of a short GSM pulse with tc=tp/5 for (a) Z=1 and (b) Z=5. Insets: the corresponding pulse intensity profiles.

Equations (16)

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ζΩ=iκσΔ.
τσ=(γ+iΔ)σiΩw,
τw=γ(wweq)i2(Ω*σΩσ*).
wweq=1.
ζσ=(γ+iΔ)σiΩ.
E(τ,ζ)=dωE˜0(ω)exp[iωτ+αζ2(1iωTeff)].
E˜0(ω)=dt2πE(t,0)eiωt.
Γ(τ1,τ2,ζ)=E*(τ1,ζ)E(τ2,ζ),
Γ(τ1,τ2,ζ)=dω1dω2W0(ω1,ω2)ei(ω1τ1ω2τ2)×exp{αζ[12(1iω2Teff)+12(1+iω1Teff)]}.
W0(ω1,ω2)=dt1dt2(2π)2ei(ω2t2ω1t1)Γ0(t1,t2).
Γ0(t1,t2)exp(t12+t222tp2)exp[(t1t2)22tc2],
W(Z)dTΓ(T,T,Z),
γ(T1,T2,Z)Γ(T1,T2,Z)I(T1,Z)I(T2,Z).
w0=12ϵ0cdt|E(t,0)|2=12ϵ0cπtpE02,
A0=2degdtE(t,0)=2deg2πtpE0.
w0=ϵ0c2A0216πdegtp.

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