Abstract

We theoretically describe several classes of ultrashort partially coherent pulses that maintain their shape on propagation in coherent linear absorbers near optical resonance.

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References

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  1. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
    [CrossRef]
  2. M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B12, 341–347 (1995).
    [CrossRef]
  3. L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
    [CrossRef]
  4. P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, “Partially coherent Gaussian pulses,” Opt. Commun.204, 53–58 (2002).
    [CrossRef]
  5. H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express11, 1894–1899 (2003).
    [CrossRef] [PubMed]
  6. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett.29, 394–396 (2004).
    [CrossRef] [PubMed]
  7. B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A76, 043843 (2007).
    [CrossRef]
  8. P. Vahimaa and J. Turunen, “Independent-elementary-pulse representation for non-stationary fields,” Opt. Express14, 5007–5012 (2006).
    [CrossRef] [PubMed]
  9. A. T. Friberg, H. Lahunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express15, 5160–5165 (2007).
    [CrossRef] [PubMed]
  10. S. A. Ponomarenko, “Complex Gaussian representation of statistical pulses,” Opt. Express19, 17086–17091 (2011).
    [CrossRef] [PubMed]
  11. Q. Lin, L. Wang, and S. Zhu, “Partially coherent light pulse and its propagation,” Opt. Commun.219, 65–70 (2003).
    [CrossRef]
  12. M. Brunel and S. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun.230, 1–5 (2004).
    [CrossRef]
  13. E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).
  14. S. A. Ponomarenko, “Degree of phase-space separability of statistical pulses,” Opt. Express20, 2548–2555 (2012).
    [CrossRef] [PubMed]
  15. 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. Express18, 14979–14991 (2011).
    [CrossRef]
  16. S. Haghgoo and S. A. Ponomarenko, “Self-similar pulses in coherent linear amplifiers,” Opt. Express19, 9750–9758 (2011).
    [CrossRef] [PubMed]
  17. S. Haghgoo and S. A. Ponomarenko, “Shape-invariant pulses in resonant linear absorbers,” Opt. Lett.37, 1328–1330 (2012).
    [CrossRef] [PubMed]
  18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).
  19. H. Lajunen, J. Tervo, and P. Vahimaa, “Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses,” J. Opt. Soc. Am. A21, 2117–2123 (2004).
    [CrossRef]
  20. P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).
  21. M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, 1972).

2012 (2)

2011 (3)

2007 (2)

2006 (1)

2004 (3)

2003 (2)

2002 (1)

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

1998 (1)

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
[CrossRef]

1995 (1)

Abramowitz, M.

M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, 1972).

Agrawal, G. P.

Andrés, P.

Bertolotti, M.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
[CrossRef]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B12, 341–347 (1995).
[CrossRef]

Brunel, M.

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

Coëtlemec, S.

M. Brunel and S. Coëtlemec, “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. A76, 043843 (2007).
[CrossRef]

Eberly, J. H.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

Ferrari, A.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
[CrossRef]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B12, 341–347 (1995).
[CrossRef]

Friberg, A. T.

A. T. Friberg, H. Lahunen, and V. Torres-Company, “Spectral elementary-coherence-function representation for partially coherent light pulses,” Opt. Express15, 5160–5165 (2007).
[CrossRef] [PubMed]

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

Haghgoo, S.

Lahunen, H.

Lajunen, H.

Lancis, J.

Lin, Q.

Q. Lin, L. Wang, and S. 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, 1995).

Milonni, P. W.

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

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]

Ponomarenko, S. A.

Sereda, L.

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
[CrossRef]

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B12, 341–347 (1995).
[CrossRef]

Silvestre, E.

Stegan, I. A.

M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, 1972).

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.

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, “Energy spectrum of a nonstationary ensemble of pulses,” Opt. Lett.29, 394–396 (2004).
[CrossRef] [PubMed]

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

E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).

Wyrowski, F.

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, “Spectral coherence properties of temporarily modulated stationary light sources,” Opt. Express11, 1894–1899 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, 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]

J. Opt. Soc. Am. A (1)

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

M. Bertolotti, A. Ferrari, and L. Sereda, “Coherence properties of nonstationary polychromatic light sources,” J. Opt. Soc. Am. B12, 341–347 (1995).
[CrossRef]

L. Sereda, M. Bertolotti, and A. Ferrari, “Coherence properties of nonstationary light wave fields,” J. Opt. Soc. Am. B15, 695–705 (1998).
[CrossRef]

Opt. Commun. (3)

P. Pääkkönen, 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. Coëtlemec, “Fractional-order Fourier formulation of the propagation of partially coherent light pulses,” Opt. Commun.230, 1–5 (2004).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Phys. Rev. A (1)

B. Davis, “Measurable coherence theory for statistically periodic fields,” Phys. Rev. A76, 043843 (2007).
[CrossRef]

Other (5)

E. Wolf, Introduction to the Theory of Coherence and Polarization (Cambridge University Press, 2007).

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

P. W. Milonni and J. H. Eberly, Lasers (Wiley, 1985).

M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, 1972).

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

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Figures (6)

Fig. 1
Fig. 1

Spectral amplitude of the pulse with the power-law modal weight distribution in arbitrary units. The parameters are (a) λ = 0.1, Z0 = 5; (b) λ = 0.3, Z0 = 3, and (c) λ = 10, Z0 = 0.1.

Fig. 2
Fig. 2

Modulus of the spectral degree of coherence. The parameters are (a) λ = 0.1, Z0 = 5 and (b) λ = 10, Z0 = 0.1.

Fig. 3
Fig. 3

Modulus of the spectral degree of coherence as a function of Ω1 for a fixed Ω2: (a) Ω2 = −15, (b) Ω2 = 0.

Fig. 4
Fig. 4

Spectral amplitude of the pulse with λnλ2n/(n!)2 in arbitrary units. The parameters are (a) λ = 0.9, Z0 = 0.1; (b) λ = 0.9, Z0 = 15; (c) λ = 2, Z0 = 0.1, and (d) λ = 2, Z0 = 15.

Fig. 5
Fig. 5

Modulus of the spectral degree of coherence. The parameters are (a) λ = 0.9, Z0 = 15 and (b) λ = 2, Z0 = 15.

Fig. 6
Fig. 6

Modulus of the spectral degree of coherence as a function of Ω1 for a fixed Ω2: (a) Ω2 = −15, (b) Ω2 = 0.

Equations (12)

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

˜ s ( ω , ζ ) ( α ζ 0 / 2 ) s ( 1 i ω T ) s + 1 exp [ α ( ζ + ζ 0 ) 2 ( 1 i ω T ) ] .
˜ n ( Ω , Z ) ( Z 0 / 2 ) n ( 1 i Ω ) n + 1 exp [ Z + Z 0 2 ( 1 i Ω ) ] .
˜ ( Ω , Z ) = n = 0 C n ˜ n ( Ω , Z ) .
C n * C m = λ n δ m n ,
W ( Ω 1 , Ω 2 , Z ) = ˜ * ( Ω 1 , Z ) ˜ ( Ω 2 , Z ) .
W ( Ω 1 , Ω 2 , Z ) = n = 0 λ n ˜ n * ( Ω 1 , Z ) ˜ n ( Ω 2 , Z ) .
λ n = 𝒜 λ 2 n ,
S ( Ω , Z ) = 𝒜 ( 1 λ 2 Z 0 2 / 4 ) + Ω 2 exp [ Z + Z 0 1 + Ω 2 ] .
μ ( Ω 1 , Ω 2 , Z ) = W ( Ω 1 , Ω 2 , Z ) S ( Ω 1 , Z ) S ( Ω 2 , Z ) .
λ n = λ 2 n ( n ! ) 2 ,
I 0 ( x ) = n = 0 ( x / 2 ) 2 n ( n ! ) 2 ,
S ( Ω , Z ) = 1 + Ω 2 I 0 ( λ Z 0 1 + Ω 2 ) exp [ Z + Z 0 1 + Ω 2 ] .

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