Abstract

Two mechanisms can cause similar broadening of pulses in a pulse train: variable temporal/spectral phase in a train of identical pulses (a deterministic mechanism) and partial correlations between different frequency components of the pulses (a stochastic mechanism). We discuss methods to distinguish between these two fundamentally different mechanisms. We show that their roles can be separated, at least for an important class of fields known as Gaussian Schell-model pulses, using time-resolved intensity measurements of pulses passing through Michelson’s interferometer.

© 2010 Optical Society of America

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References

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    [CrossRef]
  9. F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
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  10. Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
    [CrossRef]
  11. P. Vahimaa and J. Turunen, Opt. Express 14, 5007 (2006).
    [CrossRef] [PubMed]
  12. We replace the lower integration limits (zero) with −∞ in Eq. (3) in carrying out the integrations, thus assuming that Ω⪡ω0.

2009

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

2007

2006

2005

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

2004

2003

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

2002

2000

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

1997

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Bertolotti, M.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Boitier, F.

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

Coen, S.

Dudley, J. M.

Fabre, C.

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

Ferrari, A.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Friberg, A. T.

V. Torres-Company, H. Lajunen, and A. T. Friberg, J. Opt. Soc. Am. B 24, 1441 (2007).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Gorard, A.

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

Gu, X.

Haus, H. A.

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

Lajunen, H.

V. Torres-Company, H. Lajunen, and A. T. Friberg, J. Opt. Soc. Am. B 24, 1441 (2007).
[CrossRef]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

Lin, Q.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Nicholson, J. W.

O'Shea, P.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Rosenthal, E.

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

Sereda, L.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Shreenath, A. P.

Tervo, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

Torres-Company, V.

Trebino, R.

Turunen, J.

P. Vahimaa and J. Turunen, Opt. Express 14, 5007 (2006).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Vahimaa, P.

P. Vahimaa and J. Turunen, Opt. Express 14, 5007 (2006).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Wang, L.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Windeler, R. S.

Wyrowski, F.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Xu, L.

Yan, M. F.

Zeek, E.

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

H. A. Haus, IEEE J. Sel. Top. Quantum Electron. 6, 1173 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Phys.

F. Boitier, A. Gorard, E. Rosenthal, and C. Fabre, Nat. Phys. 5, 267 (2009).
[CrossRef]

Opt. Commun.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Pure Appl. Opt.

M. Bertolotti, L. Sereda, and A. Ferrari, Pure Appl. Opt. 6, 153 (1997).
[CrossRef]

Other

We replace the lower integration limits (zero) with −∞ in Eq. (3) in carrying out the integrations, thus assuming that Ω⪡ω0.

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Figures (3)

Fig. 1
Fig. 1

Michelson’s interferometer illuminated by a coherent pulse U 0 ( ω ) produces the output U ( ω ) given by Eq. (5): s is the source, BS is a beam splitter, R and S are adjustable mirrors with deflections z R and z S from zero-path-difference positions (dashed lines), and D is a fast intensity detector.

Fig. 2
Fig. 2

Total time-dependent intensity from Eq. (10) and its three components: the signals from the reference ( R ) and signal ( S ) mirrors and the interference term. The input pulse parameters are 2 π c / ω 0 = 800   nm , κ = 2 , Ω = 44.2   THz , and Ω g = 29.5   THz , which correspond to 15 and 10 nm in the wavelength scale. The displacement between mirrors R and S is Δ z = 15 μ m , the pulse duration is T = 70   fs , and the coherence time is T g = 47   fs .

Fig. 3
Fig. 3

Interference term in Eq. (10) with the same pulse parameters as in Fig. 2, but with values of κ ranging from 0 to 3. Chirping affects the pulse duration and coherence time according to Eq. (11). The pulse durations for different values of κ are 53, 58, 70, and 86 fs, and coherence times are 35, 38, 47, and 57 fs, respectively.

Equations (12)

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W ( ω 1 , ω 2 ) = S ( ω 1 ) S ( ω 2 ) μ ( ω 1 , ω 2 ) ,
W ( ω 1 , ω 2 ) = U ( ω 1 ) U ( ω 2 ) G ( ω 1 ω 2 ) ,
Γ ( t 1 , t 2 ) = 0 W ( ω 1 , ω 2 ) exp [ i ( ω 1 t 1 ω 2 t 2 ) ] d ω 1 d ω 2 .
U 0 ( ω ) = S 0 ( ω ) exp [ i ϕ ( ω ) ] ,
U ( ω ) = U 0 ( ω ) [ exp ( i 2 z R ω / c ) + r   exp ( i 2 z S ω / c ) ] ,
S 0 ( ω ) = S 0   exp [ ( ω ω 0 ) 2 Ω 2 ] ,
ϕ ( ω ) = κ 2 Ω 2 ( ω ω 0 ) 2 ,
G ( ω 1 ω 2 ) = G 0   exp [ ( ω 1 ω 2 ) 2 2 Ω g 2 ] .
S ( ω ) = S 0 G 0   exp [ ( ω ω 0 ) 2 / Ω 2 ] [ 1 + | r | 2 + 2 | r | cos ( 2 Δ z ω / c + α ) ] ,
I ( t ) / I 0 = exp [ ( t t R ) 2 T 2 ] + | r | 2   exp [ ( t t S ) 2 T 2 ] + 2 | r | exp [ ( t t R ) 2 + ( t t S ) 2 2 T 2 ] exp ( τ 2 2 T g 2 ) cos { ω 0 τ + α + κ 2 T 2 [ ( t t S ) 2 ( t t R ) 2 ] } ,
T 2 = 1 + κ 2 Ω 2 + 2 Ω g 2 ,     T g = T Ω g Ω ,
F / F 0 = I ( t ) d t 2 π 0 S ( ω ) d ω = 1 + | r | 2 + 2 | r | exp [ ( Ω τ 2 ) 2 ] cos ( ω 0 τ + α ) ,

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