Abstract

We develop a first-order description of spatio-temporal distortions in ultrashort pulses using normalized parameters that allow for a direct assessment of their severity, and we give intuitive pictures of pulses with different amounts of the various distortions. Also, we provide an experimental example of the use of these parameters in the case of spatial chirp monitored in real-time during the alignment of an amplified laser system.

© 2007 Optical Society of America

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  1. C. B. Schaffer, A. Brodeur, J. F. García, and E. Mazur, "Micromachining bulk glass by use of femtosecond laser pulses with nanojoule energy," Opt. Lett. 26, 93-95 (2001).
    [CrossRef]
  2. W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
    [CrossRef] [PubMed]
  3. R. L. Fork, O. E. Martinez, and J. P. Gordon, "Negative dispersion using pairs of prisms," Opt. Lett. 9, 150-152 (1984).
    [CrossRef] [PubMed]
  4. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, "Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy," Appl. Opt. 24, 1270-1282 (1985).
    [CrossRef] [PubMed]
  5. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
    [CrossRef]
  6. P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultra-short measurement," Opt. Lett. 26, 932-934 (2001).
  7. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring spatial chirp in ultrashort pulses using single-shot Frequency-Resolved Optical Gating," Opt. Express 11, 68-78 (2003).
    [CrossRef] [PubMed]
  8. S. Akturk, M. Kimmel, P. O'Shea, and R. Trebino, "Measuring pulse-front tilt in ultrashort pulses using GRENOUILLE," Opt. Express 11, 491-501 (2003).
    [CrossRef] [PubMed]
  9. C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
    [CrossRef]
  10. C. Dorrer, and I. A. Walmsley, "Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses," Opt. Lett. 27, 1947-1949 (2002).
    [CrossRef]
  11. K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, "High-precision measurement of angular dispersion in a CPA laser," Appl. Phys. B Suppl., 259-263 (2002).
    [CrossRef]
  12. M. Kempe, U. Stamm, B. Wilhelmi, and W. Rudolph, "Spatial and temporal transformation of femtosecond laser pulses by lenses and lens systems," J. Opt. Soc. Am. B 9, 1158-1165 (1992).
    [CrossRef]
  13. X. Gu, S. Akturk, and R. Trebino, "Spatial chirp in ultrafast optics," Opt. Commun. 242, 599-604 (2004).
    [CrossRef]
  14. A. G. Kostenbauder, "Ray-Pulse Matrices: A Rational Treatment for Dispersive Optical Systems," IEEE J. Quantum Electron. 26, 1148-1157 (1990).
    [CrossRef]
  15. S. Akturk, X. Gu, P. Gabolde, and R. Trebino, "The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams," Opt. Express 13, 8642-8661 (2005).
    [CrossRef] [PubMed]
  16. R. V. Hogg, and A. Craig, Introduction to Mathematical Statistics (Prentice Hall, 1994).
  17. K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
    [CrossRef]
  18. L. Cohen, Time-frequency analysis (Prentice Hall, 1995).
  19. Z. Bor, and B. Racz, "Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation," Opt. Commun. 54, 165-170 (1985).
    [CrossRef]
  20. S. Akturk, X. Gu, E. Zeek, and R. Trebino, "Pulse-front tilt caused by spatial and temporal chirp," Opt. Express 12, 4399-4410 (2004).
    [CrossRef] [PubMed]

2005

2004

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

X. Gu, S. Akturk, and R. Trebino, "Spatial chirp in ultrafast optics," Opt. Commun. 242, 599-604 (2004).
[CrossRef]

S. Akturk, X. Gu, E. Zeek, and R. Trebino, "Pulse-front tilt caused by spatial and temporal chirp," Opt. Express 12, 4399-4410 (2004).
[CrossRef] [PubMed]

2003

2002

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
[CrossRef]

C. Dorrer, and I. A. Walmsley, "Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses," Opt. Lett. 27, 1947-1949 (2002).
[CrossRef]

2001

1997

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

1992

1990

W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

A. G. Kostenbauder, "Ray-Pulse Matrices: A Rational Treatment for Dispersive Optical Systems," IEEE J. Quantum Electron. 26, 1148-1157 (1990).
[CrossRef]

1985

Z. Bor, and B. Racz, "Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation," Opt. Commun. 54, 165-170 (1985).
[CrossRef]

J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, "Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy," Appl. Opt. 24, 1270-1282 (1985).
[CrossRef] [PubMed]

1984

Akturk, S.

Bor, Z.

Z. Bor, and B. Racz, "Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation," Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Brodeur, A.

Csatári, M.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Denk, W.

W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Diels, J.-C. M.

Dorrer, C.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
[CrossRef]

C. Dorrer, and I. A. Walmsley, "Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses," Opt. Lett. 27, 1947-1949 (2002).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Fontaine, J. J.

Fork, R. L.

Gabolde, P.

García, J. F.

Gordon, J. P.

Gu, X.

Heiner, Z.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Kempe, M.

Kimmel, M.

Klebniczki, J.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

Kosik, E. M.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
[CrossRef]

Kostenbauder, A. G.

A. G. Kostenbauder, "Ray-Pulse Matrices: A Rational Treatment for Dispersive Optical Systems," IEEE J. Quantum Electron. 26, 1148-1157 (1990).
[CrossRef]

Kovács, A. P.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

Krumbuegel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Kurdi, G.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

Martinez, O. E.

Mazur, E.

McMichael, I. C.

O'Shea, P.

Osvay, K.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

Racz, B.

Z. Bor, and B. Racz, "Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation," Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Rudolph, W.

Schaffer, C. B.

Simoni, F.

Stamm, U.

Strickler, J. H.

W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Trebino, R.

Walmsley, I. A.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
[CrossRef]

C. Dorrer, and I. A. Walmsley, "Simple linear technique for the measurement of space-time coupling in ultrashort optical pulses," Opt. Lett. 27, 1947-1949 (2002).
[CrossRef]

Webb, W. W.

W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Wilhelmi, B.

Zeek, E.

Appl. Opt.

Appl. Phys. B: Lasers Opt.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, "Spatio-temporal characterization of the electric field of ultrashort pulses using two-dimensional shearing interferometry," Appl. Phys. B: Lasers Opt.  74 [Suppl.], S209-S217 (2002).
[CrossRef]

IEEE J. Quantum Electron.

A. G. Kostenbauder, "Ray-Pulse Matrices: A Rational Treatment for Dispersive Optical Systems," IEEE J. Quantum Electron. 26, 1148-1157 (1990).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Osvay, A. P. Kovács, Z. Heiner, G. Kurdi, J. Klebniczki, and M. Csatári, "Angular Dispersion and Temporal Change of Femtosecond Pulses From Misaligned Pulse Compressors," IEEE J. Sel. Top. Quantum Electron. 10, 213-220 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

X. Gu, S. Akturk, and R. Trebino, "Spatial chirp in ultrafast optics," Opt. Commun. 242, 599-604 (2004).
[CrossRef]

Z. Bor, and B. Racz, "Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation," Opt. Commun. 54, 165-170 (1985).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbuegel, and D. J. Kane, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 38, 3277-3295 (1997).
[CrossRef]

Science

W. Denk, J. H. Strickler, and W. W. Webb, "Two-Photon Laser Scanning Fluorescence Microscopy," Science 248, 73-76 (1990).
[CrossRef] [PubMed]

Other

K. Varju, A. P. Kovacs, G. Kurdi, and K. Osvay, "High-precision measurement of angular dispersion in a CPA laser," Appl. Phys. B Suppl., 259-263 (2002).
[CrossRef]

R. V. Hogg, and A. Craig, Introduction to Mathematical Statistics (Prentice Hall, 1994).

L. Cohen, Time-frequency analysis (Prentice Hall, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Profiles of an ultrashort pulse with increasing amounts of spatial chirp, and hence with increasing values of ρ . Upper row: spatio-temporal profiles. The pulses have a central wavelength of 480 nm, and 35 nm of bandwidth. Lower row: corresponding profiles of I(x,ω),from which ρ is calculated. (a) ρ = 0.00. (b) ρ = 0.30. (c) ρ = 0.60. (d) ρ = 0.90.

Fig. 2.
Fig. 2.

Apparatus used to record I(x,λ) and I(y,λ). G 1 diffraction grating (dispersing in plane);L 1 cylindrical lens (collimating in plane); G 2 diffraction grating (in Littrow, dispersing out of plane); L 2 cylindrical lens (collimating out of plane).

Fig. 3.
Fig. 3.

Typical raw experimental data obtained during real-time monitoring of a Ti:Sapphire oscillator and its external prism pulse compressor, showing the parameters ρ (top row) and ρ (bottom row) obtained after applying a threshold on the measured images. (a) Oscillator output before the external pulse compressor. (b) External pulse compressor output, misaligned in the vertical plane. (c) External pulse compressor output, adjusted in the vertical plane.

Fig. 4.
Fig. 4.

(a) Normalized temporal chirp parameter ρωt as a function of pulse broadening. Because pulse-front tilt also results in pulse broadening, this curve can also represent ρxt , as well as ρ if pulse broadening is replaced by beam magnification along x. (b) Numerical simulations of the degree of spatio-temporal uniformity μ as a function of the spatial chirp parameter ρ in the case of a Gaussian beam.

Fig. 5.
Fig. 5.

Temporal profiles of an ultrashort pulse with increasing amounts of positive temporal chirp, and hence with increasing values of ρωt . The pulses have a central wavelength of 480 nm, and 35 nm of bandwidth. (a) ρωt = 0.00 (transform limit). (b) ρωt = 0.30 (5% broadening).(c) ρωt = 0.60 (25% broadening). (d) ρωt = 0.90 (130% broadening).

Fig. 6.
Fig. 6.

Spatio-temporal profiles of an ultrashort pulse with increasing amounts of temporal and spatial chirp, and hence with increasing values of ρxt . The pulses have a central wavelength of 480 nm, and 35 nm of bandwidth. (a) ρxt = 0.00. (b) ρxt = 0.30. (c) ρxt = 0.60. (d) ρxt = 0.80.

Tables (1)

Tables Icon

Table 1. Typical values of spatial chirp measured in different ultrafast optical systems.

Equations (16)

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

ρ dxdωI ( x , ω ) Δ x Δ ω
where Δ x [ dxdωI ( x , ω ) x 2 ] 1 2
and Δ ω [ dxdωI ( x , ω ) ω 2 ] 1 2
ρ = Δ x Δ ω dx = Δ x Δ ω dx
1 < ρ < 1
ρ = ρ = ρ
e xy = 1 Δ y 2 Δ x ´ 2 = 1 Δ x 2 Δ x ´ 2 , 0 e xy < 1
μ pq x , λ I ( x , λ ) x p λ q
ρ = μ 11 μ 01 μ 10 [ μ 20 μ 10 2 ] 1 2 [ μ 02 μ 01 2 ] 1 2
ρ ωt = Δ t Δ ω inst dt = Δ ω Δ t d τ d ω
E ( ω ) = E 0 exp [ ω 2 4 Δ ω 2 + i 2 d τ d ω ω 2 ]
I W ( ω , t ) E 0 2 exp [ ω 2 2 Δ ω 2 - ( t ( d τ d ω ) ω ) 2 1 ( 2 Δ ω 2 ) ]
μ d ω 1 d ω 2 | d x E ( x , ω 1 ) E * ( x , ω 2 ) | 2 [ d x d ω | E ( x , ω ) | 2 ] 2
ρ xt dxdtI ( x , t ) xt Δ x Δ t ( pulse - front tilt )
ρ dkdωI ( k x , ω ) k x ω Δ k x Δω ( angular dispersion )
ρ kt dkdtI ( k x , t ) k x t Δ k x Δt ( angular delay )

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