Abstract

We propose a noniterative data inversion process for the phase retrieval by omega oscillating filtering method that could measure both isolated attosecond pulses and periodic optical arbitrary waveform (OAW). The built-in phase modulation depth recovery not only prevents the need of independent calibration (a critical advantage in the extreme ultraviolet regime) but provides a self-consistency check for the data integrity. Our experiments successfully retrieved OAW with 100% duty cycle in the near infrared regime.

© 2013 Optical Society of America

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References

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2012 (2)

2010 (2)

S. T. Cundiff and A. M. Weiner, Nat. Photonics 4, 760 (2010).
[CrossRef]

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

2009 (3)

2008 (2)

C.-B. Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M. Weiner, Laser Photon. Rev. 2, 227 (2008).
[CrossRef]

C. Dorrer and I. Kang, J. Opt. Soc. Am. B 25, A1 (2008).
[CrossRef]

2007 (1)

1998 (1)

1995 (1)

1993 (1)

Caraquitena, J.

C.-B. Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M. Weiner, Laser Photon. Rev. 2, 227 (2008).
[CrossRef]

Chang, Z.

K. Zhao, Q. Zhang, M. Chini, Y. Wu, X. Wang, and Z. Chang, Opt. Lett. 37, 3891 (2012).
[CrossRef]

Z. Chang, Fundamentals of Attosecond Optics (CRC Press, 2011), pp. 405–408.

Chen, C.-C.

Chini, M.

Cundiff, S. T.

S. T. Cundiff and A. M. Weiner, Nat. Photonics 4, 760 (2010).
[CrossRef]

Delong, K. W.

Dorrer, C.

Fejer, M. M.

Fittinghoff, D. N.

Fontaine, N. K.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

Heritage, J. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

Hsieh, I.-C.

Hsu, C.-S.

Huang, C.-B.

C.-C. Chen, I.-C. Hsieh, S.-D. Yang, and C.-B. Huang, Opt. Express 20, 27062 (2012).
[CrossRef]

C.-B. Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M. Weiner, Laser Photon. Rev. 2, 227 (2008).
[CrossRef]

Iaconis, C.

Jiang, Z.

C.-B. Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M. Weiner, Laser Photon. Rev. 2, 227 (2008).
[CrossRef]

Kane, D. J.

Kang, I.

Ladera, C. L.

Langrock, C.

Leaird, D. E.

Lin, S.-L.

Lin, Y.-S.

Miao, H. X.

Scott, R. P.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

Soares, F. M.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

Supradeepa, V. R.

Trebino, R.

Walmsley, I. A.

Wang, X.

Weiner, A. M.

S. T. Cundiff and A. M. Weiner, Nat. Photonics 4, 760 (2010).
[CrossRef]

V. R. Supradeepa, D. E. Leaird, and A. M. Weiner, Opt. Express 17, 25 (2009).
[CrossRef]

H. X. Miao, D. E. Leaird, C. Langrock, M. M. Fejer, and A. M. Weiner, Opt. Express 17, 3381 (2009).
[CrossRef]

C.-B. Huang, Z. Jiang, D. E. Leaird, J. Caraquitena, and A. M. Weiner, Laser Photon. Rev. 2, 227 (2008).
[CrossRef]

Wu, Y.

Yang, S.-D.

Yoo, S. J. B.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

Zhang, Q.

Zhao, K.

Zhou, L.

N. K. Fontaine, R. P. Scott, L. Zhou, F. M. Soares, J. P. Heritage, and S. J. B. Yoo, Nat. Photonics 4, 248 (2010).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic of noniterative PROOF method. (b) The power spectrum (shaded), the assumed (solid), and retrieved (open circles) spectral phases. (c) rms phase error versus phase modulation depth at SNR values of infinity (circles), 100 (squares), and 10 (crosses), respectively. All the figures are obtained by simulation with the frequency comb shown in (b) and Φ=0.1rad.

Fig. 2.
Fig. 2.

(a) Experimental setup. PM1 and PM2, phase modulator; PA, power amplifier; OSA, optical spectrum analyzer. (b) Power spectrum (shaded) and the spectral phase retrieved by PROOF (open circles) of the PMCW comb. (c) The IA functions of the ideal transform-limited (TL) pulse (dashed) and the phase-compensated pulse (solid), respectively. The inset shows the temporal intensities of the TL (solid) and uncompensated (dotted) pulses, corresponding to duty cycles of 13% and 100%, respectively.

Fig. 3.
Fig. 3.

(a) and (b) Measurement of ψ1(ω). (a) Power spectrum (shaded). The applied (solid) and retrieved (circles) spectral phases. (b) Simulated (dashed) and experimentally measured (solid) IA functions. The inset shows the temporal intensity. (c), (d) Counterparts of (a), (b) for the measurement of ψ2(ω).

Equations (3)

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a(t,τ)a(tτ)×ejϕ(t)a(tτ)×[1+jϕ(t)]=a(tτ)×[1+j0.5Φ(ejωmodt+ejωmodt)],
b×I0(ω)=U2(ω)+0.25Φ[U2(ωωmod)+U2(ω+ωmod)].
b×I+1(ω)=j0.5Φ×U(ω)×{U(ω+ωmod)ej[ψ(ω)ψ(ω+ωmod)]U(ωωmod)ej[ψ(ωωmod)ψ(ω)]}.

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