Research ArticleAPPLIED SCIENCES AND ENGINEERING

Computational multiheterodyne spectroscopy

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Science Advances  11 Nov 2016:
Vol. 2, no. 11, e1601227
DOI: 10.1126/sciadv.1601227
  • Fig. 1 Multiheterodyne spectra of marginally stable combs.

    (A) Simplified experimental setup showing how multiheterodyne data are recorded. Two comb lasers are shined onto a detector, and the multiheterodyne beating is recorded. (B) Top: Repetition rate beatnotes of the lasers at the biases used for this demonstration, collected over 20 ms and offset with respect to 9.1 and 9.1035 GHz. Bottom: Multiheterodyne signals in the time domain. Dashed lines would indicate one dual-comb period, but no 35-MHz periodicity is present. a.u., arbitrary units. (C) Frequency domain multiheterodyne signal over an integration time of 100 μs. No peaks are spaced by 35 MHz. (D) Frequency domain multiheterodyne spectra over 1 μs at different times. Peaks spaced by 35 MHz are sometimes (but not always) present.

  • Fig. 2 Phase and timing correction.

    (A) Repetition rate fluctuations of the demodulated RF comb. (B) Offset fluctuations of the demodulated RF comb. (C) Raw, predicted, and corrected multiheterodyne signals during the instability. (D) Raw, predicted, and corrected multiheterodyne signals away from the instability.

  • Fig. 3 Corrected multiheterodyne spectra.

    (A) Raw multiheterodyne data. (B) Data following phase correction. The lines in the center of the spectrum are well-localized but the lines toward the edge are not. (C) Data following phase and timing correction. All lines are well-localized. Insets: zoomed view of three comb teeth at all three levels of correction, including a line initially buried by noise.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/11/e1601227/DC1

    Supplementary Materials and Methods

    fig. S1. Dual-comb spectroscopy in a chaotic regime.

    fig. S2. Cross-correction of multiple spectra.

    fig. S3. Incoherent sidebands in a weak dual-comb tooth.

    fig. S4. Multiheterodyne spectrum corrected by a two-line model.

    fig. S5. Correction of artificial dual-comb data.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials and Methods
    • fig. S1. Dual-comb spectroscopy in a chaotic regime.
    • fig. S2. Cross-correction of multiple spectra.
    • fig. S3. Incoherent sidebands in a weak dual-comb tooth.
    • fig. S4. Multiheterodyne spectrum corrected by a two-line model.
    • fig. S5. Correction of artificial dual-comb data.

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