Abstract

We experimentally demonstrate that an interferometric spectrogram (i.e., fringe- and frequency-resolved autocorrelation trace) with high signal-to-noise ratio can be processed by three different procedures to accurately retrieve the spectral phase profile. We also show that the data redundancy built in the interferometric spectrogram permits simultaneous retrieval of multiple spectral phase solutions, and their weighted average may give a highly robust result against the measurement noise.

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    [CrossRef]
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    [CrossRef]
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2009

2008

2007

2006

2005

2004

2002

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

1998

1996

1995

1981

H. T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[CrossRef]

Akturk, S.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Amat-Roldan, I.

Amat-Roldán, I.

Artigas, D.

Bowie, J. L.

Bowlan, P.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Cormack, I.

Cormack, I. G.

Delong, K. W.

Dorrer, C.

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Fejer, M. M.

Fittinghoff, D. N.

Gabolde, P.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Gu, X.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Gualda, E.

Hsu, C.-S.

Huang, C.-B.

Iaconis, C.

Jennings, R. T.

Jiang, Z.

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Kang, I.

Kimmel, M.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Krumbüugel, M. A.

Ladera, C. L.

Langrock, C.

Leaird, D. E.

H. Miao, D. E. Leaird, C. Langrock, M. M. Fejer, and A. M. Weiner, “Optical arbitrary waveform characterization via dual-quadrature spectral shearing interferometry,” Opt. Express 17(5), 3381–3389 (2009).
[CrossRef] [PubMed]

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Lin, S.-L.

Lin, Y.-S.

Loza-Alvarez, P.

Matsubara, E.

Miao, H.

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Parameswaran, K. R.

Sekikawa, T.

Shang, H. T.

H. T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[CrossRef]

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Steinmeyer, G.

Stibenz, G.

Sweetser, J. N.

Trebino, R.

Walmsley, I. A.

Weiner, A. M.

Yamane, K.

Yamashita, M.

Yang, S.-D.

Electron. Lett.

H. T. Shang, “Chromatic dispersion measurement by white-light interferometry on metre-length single-mode optical fibres,” Electron. Lett. 17(17), 603–605 (1981).
[CrossRef]

J. Opt. Soc. Am. B

Laser Photon. Rev.

R. Trebino, P. Bowlan, P. Gabolde, X. Gu, S. Akturk, and M. Kimmel, “Simple devices for measuring complex ultrashort pulses,” Laser Photon. Rev. 3(3), 314–342 (2009).
[CrossRef]

Nat. Photonics

Z. Jiang, C.-B. Huang, D. E. Leaird, and A. M. Weiner, “Optical arbitrary waveform processing of more than 100 spectral comb lines,” Nat. Photonics 1(8), 463–467 (2007).
[CrossRef]

Nature

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature 418(6897), 512–514 (2002).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Other

C.-S. Hsu and S.-D. Yang, “Robustness enhancement of iteration-free spectral phase retrieval by interferometric second-harmonic trace,” presented at the Conference on Lasers & Electro Optics, Baltimore, Maryland, USA, 6–11 May, 2007.

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Figures (5)

Fig. 1
Fig. 1

(a) Simulated interferometric spectrogram of a transform-limited Gaussian pulse defined in the main text, and (b) its Fourier transform with respect to delay. (For clarity, Fig. 1b is manipulated to highlight the components around κ = ± f 0 )

Fig. 2
Fig. 2

(a) Experimental setup of interferometric spectrogram measurement. DCF: dispersion compensating fiber. WDM: wavelength division multiplexer. PC: polarization controller. BS: beam splitter. MI: Michelson interferometer. PD: Photodetector. (b) Fundamental power spectra of the signal pulse measured by an optical spectrum analyzer (OSA) (solid), and fringe-corrected field autocorrelation (FA) trace (dashed), respectively.

Fig. 3
Fig. 3

(a) Experimentally measured interferometric spectrogram, and (b) its Fourier transform with respect to delay. For clarity, Fig. 3b is manipulated to highlight the components around κ = ± f 0 . (c) Spectral phase profiles, and (d) temporal intensity profiles measured by FROG (dotted), MIFA (dashed), and MEFISTO (dash-dot), respectively. The solid line in Fig. 3c represents the fundamental power spectrum measured by OSA.

Fig. 4
Fig. 4

(a) Experimentally measured interferometric spectrogram of the signal pulse broadened by a 1.9-m-long SMF. (b) Spectral phase profiles measured by FROG (dotted), MIFA (dashed), and MEFISTO (dash-dot), respectively. The solid line represents the fundamental power spectrum measured by OSA.

Fig. 5
Fig. 5

(a) Spectral phase profiles measured by MIFA using 1 (dash-dot), and 45 (solid) pairs of MIFA traces sampled from the interferometric spectrogram, respectively. The spectral phase measured by FROG at SNR = 28 (dotted) is shown as a reference. (b) rms error value versus the number of pairs of MIFA traces used for retrieving the spectral profile by Eq. (3).

Equations (4)

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I S H G ( f , τ ) I S H G ( f ) + 2 I F R O G S H G ( f , τ ) + I S H G ( f ) cos [ 2 π ( 2 f 0 + f ) τ ] + 2Re { E S H G * ( f ) E F R O G S H G ( τ , f ) [ exp ( j 2 π f 0 τ ) + exp ( j 2 π ( f 0 + f ) τ ) ] }
Ω ( f , κ i ) = Y S H G ( f , κ i ) 4 χ e f f U S H G ( f ) U ( f + f 0 κ i ) U ( κ f 0 ) , ( i = 1 , 2 ) ,
ψ M I F A ( N ) ( f ) = i = 1 N ψ M I F A , i ( 1 ) ( f ) I ( f i ) ,
ε = [ I M I F A ( t ) I F R O G ( t ) ] 2 d t / [ I F R O G ( t ) d t ] ,

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