Abstract

A general analytical formula has been found to describe the evolution of the pulse width of the femtosecond pulses in a Gaussian beam after passing an angular disperser without the assumption of well collimation. This formula is experimentally verified by measuring the pulse width with an autocorrelator based on two-photon absorption. It is found that the effect of the spectral lateral walk-off and group delay dispersion on the pulse-width evolution, and its dependence on the distance traveled, are substantially different when the beam has not been well collimated than from when it has been collimated. These differences result from the decaying nature of the angular dispersion of the Gaussian beam sent across a distance.

© 2007 Optical Society of America

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References

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2005 (1)

2004 (3)

X. Gu, S. Akturk, and R. Trebino, Opt. Express 242, 599 (2004).

S. Akturk, X. Gu, E. Zeek, and R. Trebino, Opt. Express 12, 4399 (2004).
[CrossRef] [PubMed]

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

2003 (2)

2002 (1)

1993 (1)

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

1986 (2)

Akturk, S.

Benkö, Z.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Bor, Z.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Csatári, M.

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 2.

Gabolde, P.

Gu, X.

Hazim, H. A.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Heiner, Z.

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Horváth, Z. L.

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Kimmel, M.

Klebniczki, J.

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

Kovács, A. P.

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

K. Varjú, A. P. Kovács, K. Osvay, and G. Kurdi, Opt. Lett. 27, 2034 (2002).
[CrossRef]

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Kurdi, G.

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

K. Varjú, A. P. Kovács, K. Osvay, and G. Kurdi, Opt. Lett. 27, 2034 (2002).
[CrossRef]

Martinez, O. E.

O'Shea, P.

Osvay, K.

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 2.

Trebino, R.

Varjú, K.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

Zeek, E.

IEEE J. Sel. Top. Quantum Electron. (1)

A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, IEEE J. Sel. Top. Quantum Electron. 10, 213 (2004).
[CrossRef]

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

Opt. Commun. (1)

O. E. Martinez, Opt. Commun. 59, 229 (1986).
[CrossRef]

Opt. Eng. (1)

Z. L. Horváth, Z. Benkö, A. P. Kovács, H. A. Hazim, and Z. Bor, Opt. Eng. 32, 2491 (1993).
[CrossRef]

Opt. Express (5)

Opt. Lett. (1)

Other (2)

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, 1996), Chap. 2.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1980).

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Figures (4)

Fig. 1
Fig. 1

Scheme of a Gaussian beam passing through the prism. The Z axis is defined as the direction of central frequency, Z ω is the direction of the ω component of the spectra, ε is the angle from Z to Z ω , and ε is the angle between the phase fronts. BW, beam waist; d, distance between BW and the disperser.

Fig. 2
Fig. 2

Effect of spectral lateral walk-off, U and u, as a function of the propagation distance.

Fig. 3
Fig. 3

Effect of GDD, V and v, as a function of the propagation distance.

Fig. 4
Fig. 4

Measured (symbols) and calculated (curves) values of the pulse width as a function of distance away from the prism at an angle of incidence of 50° and 55°, respectively.

Equations (5)

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Δ θ ( γ , ω ) = α Δ γ + β Δ ω = θ γ Δ γ + θ ω Δ ω ,
a ( x , z , ω ) = b exp [ τ 0 2 8 ln 2 ( ω ω 0 ) 2 ] × exp ( i k x 2 2 z ) exp [ i k z q ( d ) 2 q ( d + α 2 z ) ( x 2 z 2 + β 2 ω 2 + 2 x β ω z ) ] ,
τ τ 0 = [ ( 1 + U ) + V 2 1 + U ] 1 2 ,
U = 2 ln 2 z R 2 ( d + α 2 z ) 2 + z R 2 ( 2 α β z w 0 τ 0 ) 2 ,
V = ( 4 ln 2 ) τ 0 2 [ k β 2 z ( d + α 2 z ) d + z R 2 ( d + α 2 z ) 2 + z R 2 ] ,

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