Abstract

Angular dispersion—whether from prisms, diffraction gratings, or etalons—is well known to result in a pulse-front tilt. Focusing into a tilted etalon, in particular, generates a huge angular dispersion, which is very useful for high-resolution spectrometers and pulse shapers. Here we demonstrate experimentally that, due to the large angular dispersion (3°/nm), the pulse directly out of an etalon can have a huge pulse-front tilt—89.9°—which can cause one side of a few-millimeter-wide beam to lead the other by 1 m, that is, several nanoseconds. We propagated a 700 ps near-transform-limited pulse through the etalon and measured the resulting spatiotemporal field, confirming this result. To make this measurement, we used a high-spectral-resolution version of crossed-beam spectral interferometry, which used a high-resolution etalon spectrometer. We also performed simulations, which we found to be in good agreement with our measurements.

© 2010 Optical Society of America

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2008 (2)

2007 (1)

2006 (1)

2005 (1)

2004 (4)

S. Xiao, J. D. McKinney, and A. M. Weiner, “Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper,” IEEE Photon. Technol. Lett. 16, 1936–1938 (2004).
[CrossRef]

S. Xiao, A. M. Weiner, and C. Lin, “A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. 40, 420–426 (2004).
[CrossRef]

S. Xiao and A. Weiner, “2-D wavelength demultiplexer with potential for 1000 channels in the C-band,” Opt. Express 12, 2895–2902 (2004).
[CrossRef] [PubMed]

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]

2002 (1)

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B 74, 209–217 (2002).
[CrossRef]

2001 (1)

1997 (1)

1996 (2)

M. Shirasaki, “Large angular dispersion by a virtually imaged phased array and its application to a wavelength demultiplexer,” Opt. Lett. 21, 366–368 (1996).
[CrossRef] [PubMed]

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[CrossRef]

1995 (1)

1993 (1)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

1988 (1)

1986 (2)

O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

1981 (1)

R. Wyatt and E. E. Marinero, “Versatile single-shot background-free pulse duration measurement technique for pulses of subnanosecond to picosecond duration,” Appl. Phys. 25, 297–301 (1981).
[CrossRef]

1973 (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse responce and time frequency responce of optical pupils,” Nouv. Rev. Opt. 4, 183–196 (1973).
[CrossRef]

Akturk, S.

Audebert, P.

Bor, Z.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

G. Szabó, Z. Bor, and A. Müller, “Phase-sensitive single-pulse autocorrelator for ultrashort laser pulses,” Opt. Lett. 13, 746–748 (1988).
[CrossRef] [PubMed]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

Bowlan, P.

Dorrer, C.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B 74, 209–217 (2002).
[CrossRef]

Froehly, C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse responce and time frequency responce of optical pupils,” Nouv. Rev. Opt. 4, 183–196 (1973).
[CrossRef]

Gabolde, P.

Gauthier, J. C.

Geindre, J. P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

Gu, X.

Hazim, H. A.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

Hebling, J.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[CrossRef]

Hilbert, M.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

Huang, C. B.

Kazansky, P. G.

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2, 99–104 (2008).
[CrossRef]

Kobayashi, T.

Kosik, E. M.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B 74, 209–217 (2002).
[CrossRef]

Lacourt, A.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse responce and time frequency responce of optical pupils,” Nouv. Rev. Opt. 4, 183–196 (1973).
[CrossRef]

Leaird, D. E.

Lee, D.

Lin, C.

S. Xiao, A. M. Weiner, and C. Lin, “A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. 40, 420–426 (2004).
[CrossRef]

Marinero, E. E.

R. Wyatt and E. E. Marinero, “Versatile single-shot background-free pulse duration measurement technique for pulses of subnanosecond to picosecond duration,” Appl. Phys. 25, 297–301 (1981).
[CrossRef]

Martinez, O. E.

O. E. Martinez, “Grating and prism compressors in the case of finite beam size,” J. Opt. Soc. Am. B 3, 929–934 (1986).
[CrossRef]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

McGresham, K.

McKinney, J. D.

S. Xiao, J. D. McKinney, and A. M. Weiner, “Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper,” IEEE Photon. Technol. Lett. 16, 1936–1938 (2004).
[CrossRef]

Meshulach, D.

Misawa, K.

Müller, A.

Racz, B.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

Rebibo, S.

Schreenath, A.

Shirasaki, M.

Silbergerg, Y.

Supradeepa, V. R.

Svirko, Y. P.

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2, 99–104 (2008).
[CrossRef]

Szabo, G.

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

Szabó, G.

Trebino, R.

Vienot, J. C.

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse responce and time frequency responce of optical pupils,” Nouv. Rev. Opt. 4, 183–196 (1973).
[CrossRef]

Walmsley, I. A.

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B 74, 209–217 (2002).
[CrossRef]

Weiner, A.

Weiner, A. M.

V. R. Supradeepa, C. B. Huang, D. E. Leaird, and A. M. Weiner, “Femtosecond pulse shaping in two dimensions: Towards higher complexity optical waveforms,” Opt. Express 16, 11878–11887 (2008).
[CrossRef] [PubMed]

S. Xiao, A. M. Weiner, and C. Lin, “A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. 40, 420–426 (2004).
[CrossRef]

S. Xiao, J. D. McKinney, and A. M. Weiner, “Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper,” IEEE Photon. Technol. Lett. 16, 1936–1938 (2004).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

Wyatt, R.

R. Wyatt and E. E. Marinero, “Versatile single-shot background-free pulse duration measurement technique for pulses of subnanosecond to picosecond duration,” Appl. Phys. 25, 297–301 (1981).
[CrossRef]

Xiao, S.

S. Xiao, J. D. McKinney, and A. M. Weiner, “Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper,” IEEE Photon. Technol. Lett. 16, 1936–1938 (2004).
[CrossRef]

S. Xiao, A. M. Weiner, and C. Lin, “A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. 40, 420–426 (2004).
[CrossRef]

S. Xiao and A. Weiner, “2-D wavelength demultiplexer with potential for 1000 channels in the C-band,” Opt. Express 12, 2895–2902 (2004).
[CrossRef] [PubMed]

Yang, W.

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2, 99–104 (2008).
[CrossRef]

Yelin, D.

Zeek, E.

Appl. Phys. (1)

R. Wyatt and E. E. Marinero, “Versatile single-shot background-free pulse duration measurement technique for pulses of subnanosecond to picosecond duration,” Appl. Phys. 25, 297–301 (1981).
[CrossRef]

Appl. Phys. B (1)

C. Dorrer, E. M. Kosik, and I. A. Walmsley, “Spatio-temporal characterization of the electric field of ultrashort optical pulses using two-dimensional shearing interferometry,” Appl. Phys. B 74, 209–217 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. Xiao, A. M. Weiner, and C. Lin, “A dispersion law for virtually imaged phased-array spectral dispersers based on paraxial wave theory,” IEEE J. Quantum Electron. 40, 420–426 (2004).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Xiao, J. D. McKinney, and A. M. Weiner, “Photonic microwave arbitrary waveform generation using a virtually imaged phased-array (VIPA) direct space-to-time pulse shaper,” IEEE Photon. Technol. Lett. 16, 1936–1938 (2004).
[CrossRef]

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

Nat. Photonics (1)

W. Yang, P. G. Kazansky, and Y. P. Svirko, “Non-reciprocal ultrafast laser writing,” Nat. Photonics 2, 99–104 (2008).
[CrossRef]

Nouv. Rev. Opt. (1)

C. Froehly, A. Lacourt, and J. C. Vienot, “Time impulse responce and time frequency responce of optical pupils,” Nouv. Rev. Opt. 4, 183–196 (1973).
[CrossRef]

Opt. Commun. (1)

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59, 229–232 (1986).
[CrossRef]

Opt. Eng. (Bellingham) (1)

Z. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. (Bellingham) 32, 2501–2504 (1993).
[CrossRef]

Opt. Express (6)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28, 1759–1763 (1996).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

J. W. Goodman, Introduction to Fourier Optics (Roberts, 2005).

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Figures (5)

Fig. 1
Fig. 1

Prisms and diffraction gratings introduce angular dispersion or, if viewed in time, PFT. In prisms, the group delay is greater for rays that pass through the base of the prism than those that pass through the tip. In gratings, rays that impinge on the near edge of the grating emerge sooner and so precede those that must travel all the way to the far edge of the grating. While the reasons for the PFT are seemingly unrelated, the PFT can be shown to be due to the angular dispersion of the component.

Fig. 2
Fig. 2

Schematic of an etalon, which yields PFT because each successive delayed pulse is laterally shifted in both space and time. The particular etalon shown here had a small uncoated gap at the bottom of the entrance face for more efficient insertion of the beam.

Fig. 3
Fig. 3

Retrieving the spatio-spectral field of the unknown pulse from the interferogram. The two-dimensional interferogram (top left) was Fourier transformed along the x-dimension. In the k x -domain (top right) the data separated into three bands, where either the top or bottom band was isolated (bottom right) and then inverse-Fourier transformed back to the x-domain. The spatio-spectrum of the reference field was divided out from the resulting complex field to isolate the spatio-spectral intensity and phase of the pulse out of the etalon (bottom left). Only the intensities (indicated by color) are shown in the figure.

Fig. 4
Fig. 4

Experimental setup for measuring the spatiotemporal field of the pulse from an etalon. Top view: Along this dimension, the output of the laser was split into a reference and an unknown arm. In the unknown arm, the pulse was sent through the first etalon ( d = 5   mm ) , which introduced angular dispersion. The output of the PFT etalon was imaged onto the entrance of the etalon imaging spectrometer along the x-dimension. Also, in this dimension, the reference beam spatially overlapped and crossed at a small angle with the unknown pulse. In the etalon imaging spectrometer, the crossing beams were reimaged into the x-dimension of the camera resulting in vertical interference fringes. Along the camera’s other dimension, the beams were spectrally resolved using an etalon to introduce angular dispersion and a cylindrical lens to map angle, or color, onto vertical position.

Fig. 5
Fig. 5

Experimental (top) and theoretical (bottom) results. Although both the spatio-spectral intensity and phase were measured, we instead show the intensity in three different domains, achieved by Fourier transforming the measured field. Center: The reconstructed intensity versus λ and x. No tilt was seen, indicating that there was no detectable spatial chirp. Left: Intensity versus x and t. A large PFT is apparent. Right: Intensity versus θ and λ, where k x = k 0   sin   θ 2 π / λ   sin   θ . The tilt is due to angular dispersion.

Equations (7)

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E ̃ ̂ ( k x , ω ) = E ̃ ̂ 0 [ k x + γ ( ω ω 0 ) , ω ] ,
E ( x , t ) E 0 ( x , t + γ x ) .
PFT = k 0 β + φ ( 2 ) υ ,
E in ( x , ω , z = 0 ) = exp ( ( ω ω 0 Δ ω ) 2 ( x w 0 ) 2 i k x   sin   θ tilt + i k 0 x 2 2 f ) ,
E out ( x , ω ) = t 1 t 2 m = 0 F ( r 1 r 2 ) m E f ( x , ω , 2 d m ) ,
E f ( x , ω , 2 d m ) = I x 1 { I x { E f ( x , ω , 2 d ( m 1 ) ) } exp ( i 2 d n k 0 1 ( k x λ ) 2 ) } .
I ( x , λ ) = | E ref ( λ ) | 2 + | E unk ( x , λ ) | 2 + | E unk ( x , λ ) E ref ( λ ) | cos ( k x θ c + φ unk ( x , λ ) φ ref ( λ ) ) ,

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