Abstract

We demonstrate an experimentally simple and high-spectral-resolution version of spectral interferometry (SEA TADPOLE) that can measure complicated pulses (in time) at video rates. Additionally, SEA TADPOLE can measure spatial information about a pulse, and it is the first technique that can directly measure the spatiotemporal electric field [E(x,y,z,λ)] of a focusing ultrashort pulse. To illustrate and test SEA TADPOLE, we measured E(λ) of a shaped pulse that had a time–bandwidth product of approximately 100. To demonstrate that SEA TADPOLE can measure focusing pulses, we measured E(x,λ) at and around the focus produced by a plano–convex lens. We also measured the focus of a beam that had angular dispersion present before the lens. We have found that SEA TADPOLE can achieve better spectral resolution than an equivalent spectrometer, and here we discuss this in detail, giving both experimental and simulated examples. We also discuss the angular acceptance and spatial resolution of SEA TADPOLE when measuring the spatiotemporal field of a focusing pulse.

© 2008 Optical Society of America

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2008

L. Xu, E. Zeek, and R. Trebino, “Simulations of frequency-resolved optical gating for measuring very complex pulses,” J. Opt. Soc. B 25, A70-A80 (2008).
[CrossRef]

2007

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, “Characterization of a high efficiency, ultrashort pulse shaper incorporating a reflective 4096-element spatial light modulator,” Opt. Commun. 287, 368-376 (2007).
[CrossRef]

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses,” Opt. Express 15, 10219-10230 (2007).
[CrossRef] [PubMed]

K. Wicker and R. Heintzmann, “Interferometric resolution improvement for confocal microscopes,” Opt. Express 15, 12206-12216 (2007).
[CrossRef] [PubMed]

2006

2005

2004

2002

2001

R. Levis, G. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulse,” Science 292, 709-713 (2001).
[CrossRef] [PubMed]

R. Trebino, P. O'Shea, M. Kimmel, and X. Gu, “Measuring ultrashort laser pulses just got a lot simpler,” Opt. Photonics News 12(6), 22-25 (2001).
[CrossRef]

J. P. Geindre, P. Audebert, S. Rebibo, and J. C. Gauthier, “Single-shot spectral interferometry with chirped pulses,” Opt. Lett. 26, 1612-1614 (2001).
[CrossRef]

2000

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1790-1802 (2000).
[CrossRef]

1998

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239-242 (1998).
[CrossRef]

D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Mueller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. 23, 1046-1048 (1998).
[CrossRef]

1997

1996

1995

1993

1990

A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26, 1148-1157 (1990).
[CrossRef]

1989

1976

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703-717 (1976).

1973

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils,” Nouvelle Revue d'Optique 4, 183-196 (1973).
[CrossRef]

1955

Akturk, S.

Amir, W.

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, “Characterization of a high efficiency, ultrashort pulse shaper incorporating a reflective 4096-element spatial light modulator,” Opt. Commun. 287, 368-376 (2007).
[CrossRef]

W. Amir, T. A. Planchon, C. G. Durfee, J. A. Squier, P. Gabolde, R. Trebino, and M. Mueller, “Simultaneous visualizations of spatial and chromatic abberations by two-dimensional Fourier transform spectral interferometry,” Opt. Lett. 31, 2927-2929 (2006).
[CrossRef] [PubMed]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Audebert, P.

Barty, C. P. J.

Baumert, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Belabas, N.

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1790-1802 (2000).
[CrossRef]

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Bor, Z.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Z. Bor, “Distortion of femtosecond laser pulses in lenses,” Opt. Lett. 14, 119-121 (1989).
[CrossRef] [PubMed]

Bor, Zs.

Bowie, J. L.

Bowlan, P.

Brixner, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Buck, J. A.

J. A. Buck, Fundamentals of Optical Fibers, Pure and Applied Optics (Wiley, 2004).

Chadwick, R.

Cheriaux, G.

Coates, V. J.

Dantus, M.

DeLong, K. W.

Dorrer, C.

E. M. Kosik, A. S. Radunsky, I. Walmsley, and C. Dorrer, “Interferometric technique for measuring broadband ultrashort pulses at the sampling limit,” Opt. Lett. 30, 326-328 (2005).
[CrossRef] [PubMed]

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1790-1802 (2000).
[CrossRef]

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

Durfee, C. G.

Field, J. J.

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, “Characterization of a high efficiency, ultrashort pulse shaper incorporating a reflective 4096-element spatial light modulator,” Opt. Commun. 287, 368-376 (2007).
[CrossRef]

Fittinghoff, D. N.

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils,” Nouvelle Revue d'Optique 4, 183-196 (1973).
[CrossRef]

Fuchs, U.

Gabolde, P.

Gauthier, J. C.

Geindre, J. P.

Gerber, G.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Gorbe, M.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Gu, X.

Hausdorff, H.

Heintzmann, R.

Jansson, P. A.

P. A. Jansson, Deconvolution with Applications in Spectroscopy (Academic, 1984).

Jean-Pierre, L.

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1790-1802 (2000).
[CrossRef]

Jennings, R. T.

Joffre, M.

C. Dorrer, M. Joffre, L. Jean-Pierre, and N. Belabas, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1790-1802 (2000).
[CrossRef]

L. Lepetit, G. Cheriaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467-2474 (1995).
[CrossRef]

Kempe, M.

Kiefer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Kimmel, M.

Klenbniczki, J.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Kobayashi, T.

Kosik, E. M.

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]

Kovaecs, A. C.

Kovaecs, A. P.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Krumbügel, M. A.

Kumar, V. N.

Kurdi, G.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils,” Nouvelle Revue d'Optique 4, 183-196 (1973).
[CrossRef]

Lepetit, L.

Levis, R.

R. Levis, G. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulse,” Science 292, 709-713 (2001).
[CrossRef] [PubMed]

Lozovoy, V. V.

Marcuse, D.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703-717 (1976).

McGresham, K.

Menkir, G.

R. Levis, G. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulse,” Science 292, 709-713 (2001).
[CrossRef] [PubMed]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239-242 (1998).
[CrossRef]

D. Meshulach, D. Yelin, and Y. Silbergerg, “Real-time spatial-spectral interference measurements of ultrashort optical pulses,” J. Opt. Soc. Am. B 14, 2095-2098 (1997).
[CrossRef]

Misawa, K.

Mueller, M.

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

O'Shea, P.

Osvay, K.

A. P. Kovaecs, K. Osvay, G. Kurdi, M. Gorbe, J. Klenbniczki, and Z. Bor, “Dispersion control of a pulse stretcher-compressor system with two-dimensional spectral interferometry,” Appl. Phys. B 80, 165-170 (2005).
[CrossRef]

A. C. Kovaecs, K. Osvay, and Zs. Bor, “Group-delay measurement on laser mirrors by spectrally resolved white-light interferometry,” Opt. Lett. 20, 788-791 (1995).
[CrossRef]

Pastirk, I.

Planchon, T. A.

J. J. Field, T. A. Planchon, W. Amir, C. G. Durfee, and J. A. Squier, “Characterization of a high efficiency, ultrashort pulse shaper incorporating a reflective 4096-element spatial light modulator,” Opt. Commun. 287, 368-376 (2007).
[CrossRef]

W. Amir, T. A. Planchon, C. G. Durfee, J. A. Squier, P. Gabolde, R. Trebino, and M. Mueller, “Simultaneous visualizations of spatial and chromatic abberations by two-dimensional Fourier transform spectral interferometry,” Opt. Lett. 31, 2927-2929 (2006).
[CrossRef] [PubMed]

Rabitz, H.

R. Levis, G. Menkir, and H. Rabitz, “Selective bond dissociation and rearrangement with optimally tailored, strong-field laser pulse,” Science 292, 709-713 (2001).
[CrossRef] [PubMed]

Radunsky, A. S.

Rao, D. N.

Rebibo, S.

Rudolph, W.

Schreenath, A.

Seyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Shreenath, A. P.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, 1986).

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418, 512-514 (2002).
[CrossRef] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature 396, 239-242 (1998).
[CrossRef]

Silbergerg, Y.

Spahr, E.

Squier, J. A.

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919-922 (1998).
[CrossRef] [PubMed]

Sweetser, J. N.

Trebino, R.

L. Xu, E. Zeek, and R. Trebino, “Simulations of frequency-resolved optical gating for measuring very complex pulses,” J. Opt. Soc. B 25, A70-A80 (2008).
[CrossRef]

P. Bowlan, P. Gabolde, and R. Trebino, “Directly measuring the spatio-temporal electric field of focusing ultrashort pulses,” Opt. Express 15, 10219-10230 (2007).
[CrossRef] [PubMed]

P. Bowlan, P. Gabolde, A. Schreenath, K. McGresham, and R. Trebino, “Crossed-beam spectral interferometry: a simple, high-spectral-resolution method for completely characterizing complex ultrashort pulses in real time,” Opt. Express 14, 11892-11900 (2006).
[CrossRef] [PubMed]

W. Amir, T. A. Planchon, C. G. Durfee, J. A. Squier, P. Gabolde, R. Trebino, and M. Mueller, “Simultaneous visualizations of spatial and chromatic abberations by two-dimensional Fourier transform spectral interferometry,” Opt. Lett. 31, 2927-2929 (2006).
[CrossRef] [PubMed]

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]

X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O'Shea, A. P. Shreenath, R. Trebino, and R. S. Windeler, “Frequency-resolved optical gating and single-shot spectral measurements reveal fine structure in microstructure-fiber continuum,” Opt. Lett. 27, 1174-1176 (2002).
[CrossRef]

R. Trebino, P. O'Shea, M. Kimmel, and X. Gu, “Measuring ultrashort laser pulses just got a lot simpler,” Opt. Photonics News 12(6), 22-25 (2001).
[CrossRef]

D. N. Fittinghoff, J. A. Squier, C. P. J. Barty, J. N. Sweetser, R. Trebino, and M. Mueller, “Collinear type II second-harmonic-generation frequency-resolved optical gating for use with high-numerical-aperture objectives,” Opt. Lett. 23, 1046-1048 (1998).
[CrossRef]

D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulse,” Opt. Lett. 21, 884-886 (1996).
[CrossRef] [PubMed]

R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer, 2002).
[CrossRef]

Tuennermann, A.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse response and time frequency response of optical pupils,” Nouvelle Revue d'Optique 4, 183-196 (1973).
[CrossRef]

Walmsley, I.

Walmsley, I. A.

Wicker, K.

Windeler, R. S.

Xu, L.

Yelin, D.

Zeek, E.

Zeitner, U. D.

Appl. Opt.

Appl. Phys. B

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Figures (10)

Fig. 1
Fig. 1

SEA TADPOLE experimental setup. A reference pulse and an unknown pulse are coupled into two single-mode fibers with approximately equal lengths. At the other end of the fibers, the diverging beams are collimated using a spherical lens ( f ) . After propagating a distance f, the collimated beams cross and interfere, and a camera is placed at this point to record the interference. In the other dimension, a grating and a cylindrical lens map wavelength onto the camera’s horizontal axis ( x c ) .

Fig. 2
Fig. 2

SEA TADPOLE retrieval. The top left image is a typical interferogram, which is Fourier transformed from the λ x c to the λ k c domain where only one of the sidebands is then used. This sideband is then inverse Fourier transformed back to the λ x domain. The result is then averaged over x c , and the reference pulse is divided out in order to isolate the intensity and phase of the unknown pulse.

Fig. 3
Fig. 3

(a) SEA TADPOLE trace for a shaped pulse. (b) Retrieved spectral phase compared with the phase applied to the shaper. (c) Retrieved spectrum ( S unk ) compared with the spectrometer spectrum ( S sp ) . (d) Retrieved temporal intensity and phase.

Fig. 4
Fig. 4

E ( x , z , t ) in the focal region of a plano–convex lens. The experimental results are displayed in the top plots, and the simulations are shown in the bottom plots. Each box displays the amplitude of the electric field versus x and t at a distance z from the geometric focus. The white dots show the pulse fronts, or the maximum temporal intensity for each value of x. The color represents the instantaneous frequency, which shows that the redder colors are ahead of the bluer colors due to material dispersion.

Fig. 5
Fig. 5

E ( x , z , t ) in the focal region of the beam that had angular dispersion. The data is displayed in the same way as in Fig. 4. The angular dispersion becomes purely spatial chirp at the focus because a lens is a Fourier transformer.

Fig. 6
Fig. 6

Spectrum measured with a spectrometer (black) compared with that measured with SEA TADPOLE (gray) and the actual spectrum (white) (a) for a train of pulses, (b) for a double pulse, (c) for a sum of three double pulses with different delays, (d) for the same as (c) using shorter double pulses, (e) for a pulse with a Gaussian spectrum and a sinusoidal phase, and (f) for a very chirped Gaussian pulse. Please note that some of the curves are dashed to show that two curves are overlapping. In all cases, the color indicates the quantity.

Fig. 7
Fig. 7

Spectrum retrieved from SEA TADPOLE (lightest or green) compared with the ideal spectrum (darker or red) and the spectrum measured with a spectrometer (darkest or blue). For this simulation both the spectral response function and the unknown pulse had a width of 0.1 nm .

Fig. 8
Fig. 8

The plot on the left shows the temporal response function that we measured (dots) using an etalon and the solid curve is a fit to this data. The plot on the right shows the Fourier transform of h ( t ) , which is the spectral response function. Note that we only measured this h ( t ) on one side of the time axis because we expect it to be a symmetric function because H ( ω ) is a real function.

Fig. 9
Fig. 9

Experimental example of S unk ( λ ) versus S sp ( λ ) . For this example we used an etalon with two identical reflectors both having a reflectivity of 57%. The plot on the right shows the two spectra where the darker (blue) one is S sp ( λ ) and the lighter (green) one is S unk ( λ ) . The plot on the right shows the temporal intensity that was computed using S sp ( λ ) (darker or blue curve) and S unk ( λ ) (lighter or green curve). Because we know what these relative amplitudes should be, we can verify that the lighter (green) curve is more accurate than the darker (blue) curve.

Fig. 10
Fig. 10

Variation in the reconstructed temporal intensity with delay (simulation): The bottom plot on the left shows the temporal response function, the reference pulse and the real (light or green curve) and the reconstructed temporal intensities (dark or blue curve). The top two left plots show how the reconstructed temporal intensity becomes distorted as the unknown pulse is delayed. The plots on the right are the spectrum retrieved from SEA TADPOLE at the three different delays. For this simulation we used an unknown pulse with a Gaussian spectrum (rms bandwidth of 8.5 nm ) and a sinusoidal phase (with a frequency of 2500 fs 1 ).

Equations (7)

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S ( λ , x c ) = S ref ( λ ) + S unk ( λ ) + 2 S ref ( λ ) S unk ( λ ) cos [ 2 k x c sin θ + φ unk ( λ ) φ ref ( λ ) ] .
S ref ( λ ) + S unk ( λ ) + E unk ( λ ) E ref * ( λ ) δ ( k c + 2 2 π λ sin θ ) + E unk * ( λ ) E ref ( λ ) δ ( k c 2 2 π λ sin θ ) .
T = [ d y d x E fiber ( x , y ) E unk * ( x , y ) ] 2 .
T ( θ ) = ( 2 d w d 2 + w 2 ) 2 exp [ 2 ( π w d θ ) 2 ( w 2 + d 2 ) λ 2 ] .
T ( θ ) = exp [ ( π d θ ) 2 4 λ 2 ] .
H ( x ) = exp [ ( 2 x ) 2 d 2 ] .
2 λ π w < 2 λ π d ,

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