Abstract

We investigate the accuracy of the femtosecond pulse-retrieval technique called phase and intensity from correlation and spectrum only (PICASO). Different versions of this technique that make use of balanced and unbalanced intensity and interferometric correlations are compared with respect to the rms phase and the intensity error. The effect of measurement noise on the phase and amplitude retrieval is studied, and the results are compared with other retrieval methods.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  11. A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
    [CrossRef]
  12. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1995).
  13. J. W. Nicholson, F. G. Omenetto, D. J. Funk, and A. J. Taylor, “Evolving FROGs: phase retrieval from frequency-resolved optical gating measurements by use of genetic algorithms,” Opt. Lett. 24, 490–492 (1999).
    [CrossRef]
  14. D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, “Noise sensitivity in frequency-resolved optical-gating measurements of ultrashort pulses,” J. Opt. Soc. Am. B 12, 1955–1967 (1995).
    [CrossRef]
  15. E. M. Kosik, M. E. Anderson, L. E. E. de Araujo, and I. A. Walmsley, “The effects of noise on ultrashort optical pulse measurement using spider,” in Ultrafast Phenomena, Vol. 43 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 21–23.
  16. J. H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse retrieval from intensity autocorrelation and power spectrum,” in Conference on Lasers and Electro-Optics, 2001 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), p. 204.

2000 (1)

1999 (4)

1998 (2)

1997 (1)

1995 (1)

1993 (1)

1989 (1)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

1985 (1)

Bernstein, A.

DeLong, K. W.

Diels, J.-C.

Fittinghoff, D. N.

Fontaine, J. J.

Funk, D. J.

Gaeta, A. L.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Iaconis, C.

Ippen, E. P.

Jasapara, J.

Kane, D. J.

Kung, P.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Ladera, C. L.

Langlois, P.

Lester, L. F.

McMichael, I. C.

Mero, M.

Mogi, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Moll, K. D.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Nicholson, J. W.

Omenetto, F. G.

Peatross, J.

Razeghi, M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Rudolph, W.

Rundquist, A.

Sheik-Bahae, M.

Simoni, F.

Streltsov, A. M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Taylor, A. J.

Trebino, R.

Walker, D.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

Walmsley, I. A.

Yamada, H.

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker, and M. Razeghi, “Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode,” Appl. Phys. Lett. 75, 3778–3780 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Naganuma, K. Mogi, and H. Yamada, “General method for ultrashort light pulse chirp measurement,” IEEE J. Quantum Electron. 25, 1225–1233 (1989).
[CrossRef]

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

Opt. Lett. (7)

Other (4)

A. Baltuska, A. Pugzlys, M. Pshenichnikov, and D. A. Wiersma, “Rapid amplitude-phase reconstruction of femtosecond pulses from intensity autocorrelation and spectrum,” in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 264–265.

E. M. Kosik, M. E. Anderson, L. E. E. de Araujo, and I. A. Walmsley, “The effects of noise on ultrashort optical pulse measurement using spider,” in Ultrafast Phenomena, Vol. 43 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 21–23.

J. H. Chung and A. M. Weiner, “Ambiguity of ultrashort pulse retrieval from intensity autocorrelation and power spectrum,” in Conference on Lasers and Electro-Optics, 2001 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2001), p. 204.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1995).

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Figures (11)

Fig. 1
Fig. 1

Variations on the PICASO setup: (a) balanced correlations, (b) unbalanced correlations, and (c) dual correlations.

Fig. 2
Fig. 2

PICASO figure of merit Δ(ϕ2, ϕ3) for (a) a balanced second-order correlation and (b) a second-order correlation unbalanced by a 2-mm glass plate. The 30-fs target pulse has a Gaussian spectrum with second-order (ϕ2=100 fs2) and third-order (ϕ3=1000 fs2) spectral phase.

Fig. 3
Fig. 3

Δ(ϕ2, ϕ3) for the pulse of Fig. 2 for second-harmonic FROG.

Fig. 4
Fig. 4

PICASO figure of merit Δ(ϕ2, ϕ3) for third-order correlations: (a) an amplitude-unbalanced third-order correlation, (b) an amplitude- and phase-unbalanced third-order correlation, and (c) dual, amplitude-unbalanced third-order correlations.

Fig. 5
Fig. 5

Two of the test pulses used in the intensity and phase rms error calculations: (a) a pulse with an asymmetric spectrum and second- and third-order spectral phase; (b) a more complex pulse with phase and intensity substructure.

Fig. 6
Fig. 6

(a) Target (balanced) second-order interferometric correlation with 3% additive and multiplicative noise. (b) Target intensity and phase (solid curves) and retrieved intensity and phase (dashed curve) from correlation in (a). (c) Noisy interferometric correlation after preprocessing. (d) Intensity and phase retrieved from correlation in (c).

Fig. 7
Fig. 7

Rms intensity (solid squares) and phase (open circles) errors as a function of noise fraction for test pulse 1. The correlations and spectrum were subjected to both additive and multiplicative noise.

Fig. 8
Fig. 8

(a) Target (solid curve) and retrieved (dashed curve) amplitude-unbalanced third-order correlation for test pulse 2 with 3% additive and multiplicative noise fraction. (b) Target (solid curves) and retrieved (dashed curves) intensity and phase.

Fig. 9
Fig. 9

(a) Rms intensity error and (b) phase error as a function of both additive and multiplicative noise fraction for test pulse 2. FROG calculations used additive noise only; SPIDER used both additive and multiplicative noise. Data for FROG are from Ref. 14, and data for SPIDER are from Ref. 15.

Fig. 10
Fig. 10

Intensity and phase rms errors for different PICASO versions with 3% additive and multiplicative noise fraction: (a) test pulse 1 and (b) test pulse 2.

Fig. 11
Fig. 11

Intensity and phase errors for interferometric and intensity correlations for a 5-fs pulse with 3% noise fraction.

Equations (17)

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Δ=1Ni=1N[Am(τi)-Ar(τi)]21/2.
A(τ)=1+2A0(τ)+2 Re[A1(τ)exp(-iω0τ)]+Re[A2(τ)exp(-2iω0τ)],
A0(τ)=-I1(t)I2(t-τ)dt,
A1(τ)=-[I1(t)+I2(t-τ)]E1(t)E2*(t-τ)dt,
A2(τ)=-E12(t)E2*2(t-τ)dt,
B(τ)=1+9B0(τ)+3 Re[B1(τ)exp(-iω0τ)]+3 Re[B2(τ)exp(-2iω0τ)]+Re[B3(τ)exp(-3iω0τ)],
B0(τ)=-[I12(t)I2(t-τ)+I1(t)I22(t-τ)]dt,
B1(τ)=-{[I12(t)+I22(t-τ)]E1(t)E2*(t-τ)+3I1(t)I2(t-τ)E1(t)E2*(t-τ)}dt,
B2(τ)=-[I1(t)+I2(t-τ)]E12(t)E2*2(t-τ)dt,
B3(τ)=-E13(t)E2*3(t-τ)dt.
B0(τ)=-[α2I2(t)I(t-τ)+α4I2(t-τ)I(t)]dt.
Φ(ω)=i=2nϕi(ω-ω0)i.
Φ(ω)=ϕe(ω)+ϕo(ω).
εI=1Ni=1N[It(τi)-Ir(τi)]21/2,
εϕ=1Ni=1NIt2(τi)[ϕt(τi)-ϕr(τi)]21/21Ni=1NIt2(τi)1/2.
Am(τi)=[1+ξm(f)]Am(τi)+fξa(n)n,
S(ωi)=[1+ξm(f)]S(ωi)+fξa(n)n,

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