Abstract

Sum-frequency generation using spectrally asymmetric type II phase matching enables significant simplifications in spectral shearing interferometry as applied for ultrashort optical pulse measurements. We present analytical and numerical models of broadband sum-frequency wave mixing essential to understand the underlying effects. We discuss spectral and temporal limits of the method together with various aspects of experimental implementation: optimization of the retrieval algorithm, calibration procedures, and extension to different spectral regions of particular interest with other crystals.

© 2007 Optical Society of America

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References

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    [CrossRef]
  2. C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186, 329-333 (2000).
    [CrossRef]
  3. P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
    [CrossRef]
  4. D. T. Reid and I. G. Cormack, "Single-shot sonogram: a real-time chirp monitor for ultrafast oscillators," Opt. Lett. 27, 658-660 (2002).
    [CrossRef]
  5. A. S. Radunsky, I. A. Walmsley, S. P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
    [CrossRef]
  6. A. S. Radunsky, E. M. Kosik, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U'Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008-1010 (2006).
    [CrossRef] [PubMed]
  7. C. Iaconis and I. A. Walmsley, "Self-referencing spectral interferometry for measuring ultrashort optical pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
    [CrossRef]
  8. A. Monmayrant, S.-P. Gorza, P. Wasylczyk, and I. Walmsley, "Beyond the fringe: SPIDER--the anatomy of ultrashort laser pulses," Photon. Int.44 (2007).
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    [CrossRef] [PubMed]
  10. E. M. Kosik, A. S. Radunsky, I. A. Walmsley, and C. Dorrer, "Interferometric technique for measuring broadband ultrashort pulses at the sampling limit," Opt. Lett. 30, 326-328 (2005).
    [CrossRef] [PubMed]
  11. A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914-1916 (2006).
    [CrossRef] [PubMed]
  12. A. P. Baronavski, H. D. Ladouceur, and J. K. Shaw, "Analysis of cross correlation, phase velocity mismatch, and group velocity mismatches in sum-frequency generation," IEEE J. Quantum Electron. 29, 580-589 (1993).
    [CrossRef]
  13. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  14. H. Wang and A. M. Weiner, "A femtosecond waveform transfer technique using type II second harmonic generation," IEEE J. Quantum Electron. 40, 937-945 (2004).
    [CrossRef]
  15. W. P. Grice, A. B. U'Ren, and I. A. Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
    [CrossRef]
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    [CrossRef]
  17. C. Dorrer, "Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram," Opt. Lett. 24, 1532-1534 (1999).
    [CrossRef]
  18. C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019-1029 (2002).
    [CrossRef]
  19. I. Z. Kozma, P. Baum, U. Schmidhammer, S. Lochbrunner, and E. Riedle, "Compact autocorrelator for the online measurement of tunable 10 femtosecond pulses," Rev. Sci. Instrum. 75, 2323-2327 (2004).
    [CrossRef]
  20. M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, "The effect of noise on ultrashort-optical-pulse measurement using SPIDER," Appl. Phys. B 70, S85-S93 (2000).
    [CrossRef]
  21. V. G. Dimitrev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer-Verlag, 1997).
  22. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, "Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses," Opt. Lett. 19, 737-739 (1994).
    [CrossRef] [PubMed]
  23. M. Hirasawa, N. Nakagawa, K. Yamamoto, R. Morita, H. Shigekawa, and M. Yamashita, "Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of low-intensity femtosecond pulses," Appl. Phys. B 74, S225-S229 (2002).
    [CrossRef]

2007

2006

2005

2004

P. Baum, S. Lochbrunner, and E. Riedle, "Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses," Opt. Lett. 29, 210-212 (2004).
[CrossRef] [PubMed]

H. Wang and A. M. Weiner, "A femtosecond waveform transfer technique using type II second harmonic generation," IEEE J. Quantum Electron. 40, 937-945 (2004).
[CrossRef]

I. Z. Kozma, P. Baum, U. Schmidhammer, S. Lochbrunner, and E. Riedle, "Compact autocorrelator for the online measurement of tunable 10 femtosecond pulses," Rev. Sci. Instrum. 75, 2323-2327 (2004).
[CrossRef]

2002

M. Hirasawa, N. Nakagawa, K. Yamamoto, R. Morita, H. Shigekawa, and M. Yamashita, "Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of low-intensity femtosecond pulses," Appl. Phys. B 74, S225-S229 (2002).
[CrossRef]

D. T. Reid and I. G. Cormack, "Single-shot sonogram: a real-time chirp monitor for ultrafast oscillators," Opt. Lett. 27, 658-660 (2002).
[CrossRef]

C. Dorrer and I. A. Walmsley, "Accuracy criterion for ultrashort pulse characterization techniques: application to spectral phase interferometry for direct electric field reconstruction," J. Opt. Soc. Am. B 19, 1019-1029 (2002).
[CrossRef]

2001

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
[CrossRef]

W. P. Grice, A. B. U'Ren, and I. A. Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
[CrossRef]

2000

C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186, 329-333 (2000).
[CrossRef]

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, "The effect of noise on ultrashort-optical-pulse measurement using SPIDER," Appl. Phys. B 70, S85-S93 (2000).
[CrossRef]

1999

C. Iaconis and I. A. Walmsley, "Self-referencing spectral interferometry for measuring ultrashort optical pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

C. Dorrer, "Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram," Opt. Lett. 24, 1532-1534 (1999).
[CrossRef]

1995

1994

1993

A. P. Baronavski, H. D. Ladouceur, and J. K. Shaw, "Analysis of cross correlation, phase velocity mismatch, and group velocity mismatches in sum-frequency generation," IEEE J. Quantum Electron. 29, 580-589 (1993).
[CrossRef]

Appl. Phys. B

M. E. Anderson, L. E. E. de Araujo, E. M. Kosik, and I. A. Walmsley, "The effect of noise on ultrashort-optical-pulse measurement using SPIDER," Appl. Phys. B 70, S85-S93 (2000).
[CrossRef]

M. Hirasawa, N. Nakagawa, K. Yamamoto, R. Morita, H. Shigekawa, and M. Yamashita, "Sensitivity improvement of spectral phase interferometry for direct electric-field reconstruction for the characterization of low-intensity femtosecond pulses," Appl. Phys. B 74, S225-S229 (2002).
[CrossRef]

IEEE J. Quantum Electron.

H. Wang and A. M. Weiner, "A femtosecond waveform transfer technique using type II second harmonic generation," IEEE J. Quantum Electron. 40, 937-945 (2004).
[CrossRef]

C. Iaconis and I. A. Walmsley, "Self-referencing spectral interferometry for measuring ultrashort optical pulses," IEEE J. Quantum Electron. 35, 501-509 (1999).
[CrossRef]

A. P. Baronavski, H. D. Ladouceur, and J. K. Shaw, "Analysis of cross correlation, phase velocity mismatch, and group velocity mismatches in sum-frequency generation," IEEE J. Quantum Electron. 29, 580-589 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

C. Radzewicz, P. Wasylczyk, and J. S. Krasinski, "A poor man's FROG," Opt. Commun. 186, 329-333 (2000).
[CrossRef]

Opt. Lett.

C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, "Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses," Opt. Lett. 19, 737-739 (1994).
[CrossRef] [PubMed]

P. Baum, S. Lochbrunner, and E. Riedle, "Zero-additional-phase SPIDER: full characterization of visible and sub-20-fs ultraviolet pulses," Opt. Lett. 29, 210-212 (2004).
[CrossRef] [PubMed]

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

A. S. Radunsky, E. M. Kosik, I. A. Walmsley, P. Wasylczyk, W. Wasilewski, A. B. U'Ren, and M. E. Anderson, "Simplified spectral phase interferometry for direct electric-field reconstruction by using a thick nonlinear crystal," Opt. Lett. 31, 1008-1010 (2006).
[CrossRef] [PubMed]

A. S. Wyatt, I. A. Walmsley, G. Stibenz, and G. Steinmeyer, "Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction," Opt. Lett. 31, 1914-1916 (2006).
[CrossRef] [PubMed]

A. S. Radunsky, I. A. Walmsley, S. P. Gorza, and P. Wasylczyk, "Compact spectral shearing interferometer for ultrashort pulse characterization," Opt. Lett. 32, 181-183 (2007).
[CrossRef]

C. Dorrer, "Implementation of spectral phase interferometry for direct electric-field reconstruction with a simultaneously recorded reference interferogram," Opt. Lett. 24, 1532-1534 (1999).
[CrossRef]

P. O'Shea, M. Kimmel, X. Gu, and R. Trebino, "Highly simplified device for ultrashort-pulse measurement," Opt. Lett. 26, 932-934 (2001).
[CrossRef]

D. T. Reid and I. G. Cormack, "Single-shot sonogram: a real-time chirp monitor for ultrafast oscillators," Opt. Lett. 27, 658-660 (2002).
[CrossRef]

Phys. Rev. A

W. P. Grice, A. B. U'Ren, and I. A. Walmsley, "Eliminating frequency and space-time correlations in multiphoton states," Phys. Rev. A 64, 063815 (2001).
[CrossRef]

Rev. Sci. Instrum.

I. Z. Kozma, P. Baum, U. Schmidhammer, S. Lochbrunner, and E. Riedle, "Compact autocorrelator for the online measurement of tunable 10 femtosecond pulses," Rev. Sci. Instrum. 75, 2323-2327 (2004).
[CrossRef]

Other

V. G. Dimitrev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, 2nd ed. (Springer-Verlag, 1997).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

A. Monmayrant, S.-P. Gorza, P. Wasylczyk, and I. Walmsley, "Beyond the fringe: SPIDER--the anatomy of ultrashort laser pulses," Photon. Int.44 (2007).

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Figures (13)

Fig. 1
Fig. 1

Absolute magnitudes of the collinear type II PMF Φ 2 of a 20 mm thick KDP crystal for two values of the propagation angle (0.5° apart), plotted as a function of frequency for ordinary ω o and extraordinary ω e input polarization components (black indicating perfect phase-matching). The SF signals are drawn on the diagonal axis, ω s = ω e + ω o , illustrating the shear between the outputs due to the specific PMF shape, which allows all the frequency content of one of the input fields to mix with a single frequency component of the other one.

Fig. 2
Fig. 2

Schematic of the ARAIGNEE device. λ 2 , half-wave plate; Q, quartz plate; MP, mutually tilted (by β) and longitudinally shifted (by d) mirror pair; PM, pick-off mirror; FM, focusing mirror; BF, blue filter; KDP, nonlinear crystal. Dotted curves depict ordinary pulses and solid curves, extraordinary pulses.

Fig. 3
Fig. 3

Upconversion in a type II nonlinear crystal. R o , e are the o- and e-polarized test pulses, respectively, and B is the sum frequency pulse. t 0 is the predelay between the two fundamental test pulses and L is the crystal thickness.

Fig. 4
Fig. 4

Evolution of the amplitude and the phase of B ( t ) , with Δ k b r o = 0 and t 0 = 4.3 T . Amplitude and phase of R o (dashed curves), amplitude and phase of B (solid curve) and amplitude of R e (dotted curve), (a) in the crystal at the location where the two fundamental pulses meet, (b) at the output of the crystal where they have walked through each other.

Fig. 5
Fig. 5

SF generation in presence of a a group velocity mismatch ( Δ k b r o = 0.15 Δ k b r e ) . Intensity and phase profiles of the SF pulse (dashed curves) and the o-fundamental pulse (solid curves) at the output of the crystal. The initial conditions are identical as for Fig. 4. The shifted and scaled output SF pulse is also shown (circles).

Fig. 6
Fig. 6

Comparison of the amplitude and the phase of the SF pulse at the output of a thick KDP crystal obtained by numerically solving the system (5) (solid curves) and derived from Eq. (21) (circles).

Fig. 7
Fig. 7

Block diagram of the phase retrieval procedure in ARAIGNEE.

Fig. 8
Fig. 8

Scaling factor s (a) and quadratic phase factor a corr (b) as a function of the central wavelength of the unknown pulse for KDP. The parameters used in (b) are: crystal thickness L = 5 mm , predelay t 0 = 317 fs .

Fig. 9
Fig. 9

Left: Spectrum of the test pulse (dotted curve) and its spectral phase retrieved by ARAIGNEE (dashed curve) and SPIDER (solid curve) for various central wavelengths. Right: Time-dependent intensity and phase measured by ARAIGNEE (circles) and SPIDER (solid curve) from the data plotted on the left.

Fig. 10
Fig. 10

(a) Spectrum of the Mira Seed laser (dotted curve) and acquired spectral phase after propagation through 9.5 mm of BK7 (dashed curve). The solid curve shows the fit to the phase that corresponds to a group delay dispersion of 440 fs 2 . (b) Spectral intensity of the test pulse (dotted curve) and sinusoidal modulation of its spectral phase reconstructed by ARAIGNEE (dotted curve) and SPIDER (solid curve).

Fig. 11
Fig. 11

(a) rms error ε of the retrieved pulse calculated from numerical simulation of the SF generation in a 20 mm thick KDP crystal as a function of the input pulse bandwidth (intensity FWHM) and central wavelength for Gaussian transform-limited input pulses. (b), (c) Temporal intensity profile (dotted curves) of the test pulse corresponding to B and C in (a) and reconstructed intensity (solid curves) and phase (dashed curves) profiles.

Fig. 12
Fig. 12

Simulated reconstruction of a double Gaussian pulse at 800 nm (dashed curve). The solid curves show the test pulse intensity and phase.

Fig. 13
Fig. 13

Simulated rms error ε of an ARAIGNEE device with a 20 mm thick BBO and KTP in the YZ plane, and a quartz plate 40 and 50 mm thick, respectively.

Tables (1)

Tables Icon

Table 1 Maximum Pulse Bandwidth ( Δ λ ) That Can Be Measured with an rms Error Less than 0.02 or 0.1

Equations (28)

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E ̃ s ( ω ) δ ( ω 1 + ω 2 ω ) E ̃ 1 ( ω 1 ) E ̃ 2 ( ω 2 ) Φ ( ω 1 , ω 2 ) d ω 1 d ω 2 = E ̃ 1 ( ω ω 2 ) E ̃ 2 ( ω 2 ) Φ ( ω ω 2 , ω 2 ) d ω 2 ,
Φ ( ω 1 , ω 2 ) = sin ( T ) T × exp ( i T ) ,
E ̃ s ( ω ) = E ̃ 1 ( ω ) E ̃ 2 ( ω ) = E ̃ 1 ( ω ω 2 ) E ̃ 2 ( ω 2 ) d ω 2 .
E ̃ s ( ω ) = [ Φ 1 ( ω ) E ̃ 1 ( ω ) ] [ Φ 2 ( ω ) E ̃ 2 ( ω ) ] .
i z R o ( t , z ) + i Δ k b r o t R o k r o 2 t t R o = Γ r o R e * B exp ( i Δ k z ) ,
i z R e ( t , z ) + i Δ k b r e t R e k r e 2 t t R e = Γ r e R o * B exp ( i Δ k z ) ,
i z B ( t , z ) k b 2 t t B = Γ b R o R e exp ( i Δ k z ) ,
z B ( t , z ) = i Γ b R o ( t Δ k b r o z ) R e ( t Δ k b r e z t 0 ) exp ( i Δ k z ) ,
B ( t , L ) = i Γ b 0 L R o ( t Δ k b r o z ) R e ( t Δ k b r e z t 0 ) exp ( i Δ k z ) d z .
R o ( t Δ k b r o z ) = 1 2 π R ̃ o ( ω ) exp ( i Δ k b r o z ω ) exp ( i ω t ) d ω ,
B ( t , L ) = i Γ b 2 π R ̃ o ( ω ) exp ( i ω t ) R e ( t Δ k b r e z t 0 ) × exp [ i ( Δ k + Δ k b r o ω ) z ] d z d ω .
B ( t , L ) = i Γ b 2 π Δ k b r e R ̃ o ( ω ) exp ( i ω t ) R e ( τ ) × exp [ i Δ k + Δ k b r o ω Δ k b r e ( t τ t 0 ) ] d τ d ω .
R e ( τ ) exp ( i Δ k + Δ k b r o ω Δ k b r e τ ) d τ = R ̃ e ( Δ k + Δ k b r o ω Δ k b r e ) ,
R ̃ e ( Δ k + Δ k b r o ω Δ k b r e ) = R ̃ e ( Δ k Δ k b r e ) Δ k b r o Δ k b r e ω R ̃ e ( Δ k Δ k b r e ) + O ( ω 2 ) ,
B ( t , L ) i Γ b 2 π Δ k b r e R ̃ e ( Δ k Δ k b r e ) exp [ i Δ k Δ k b r e ( t t 0 ) ] × R ̃ o ( ω ) exp ( i ω t ) exp [ i Δ k b r o Δ k b r e ( t t 0 ) ω ] d ω .
B ( t , L ) = i Γ b Δ k b r e R ̃ e ( Δ k Δ k b r e ) exp [ i Δ k Δ k b r e ( t t 0 ) ] R o ( t [ 1 Δ k b r o Δ k b r e ] + t 0 Δ k b r o Δ k b r e ) .
s = 1 Δ k b r o Δ k b r e .
Δ k + k r o ( ω 1 ω r o ) + k r e ( ω 2 ω r e ) k b ( ω 3 ω b ) = 0 .
Δ ω = Δ k Δ k b r e .
Δ t = t 0 Δ k b r o Δ k r o r e .
l = t 0 Δ k r e r o ,
k eff L = k r o l × 1 s 2 + k b ( L l ) .
B ̃ ( ω , L ) B ̃ 0 ( ω , L ) exp ( i 2 k eff L ( ω Δ ω ) 2 ) ,
S ̃ ( ω ) = B ̃ 1 ( ω ) + B ̃ 2 ( ω Ω ) exp ( i ω τ ) 2 = B ̃ 1 ( ω ) 2 + B ̃ 2 ( ω Ω ) 2 + 2 B ̃ 1 ( ω ) B ̃ 2 ( ω Ω ) cos [ ϕ 0 ( ω s ) ϕ 0 ( ω Ω s ) + δ ϕ ( ω ) + ω τ ] ,
δ ϕ ( ω ) = ( Δ t 1 Δ t 2 + Ω k eff L ) ω ,
ϕ corr 1 Ω δ ϕ corr ( ω ) d ω = a corr ω 2 ,
a corr = 1 2 Ω [ ( Δ k b r e 2 Δ k b r e 1 ) L + Δ t 2 Δ t 1 ] 1 2 k eff L .
ε = E in ( t ) E rec ( t ) ,

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