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A broadband chip-scale optical frequency synthesizer at 2.7 × 10−16 relative uncertainty

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Science Advances  22 Apr 2016:
Vol. 2, no. 4, e1501489
DOI: 10.1126/sciadv.1501489
  • Fig. 1 A stabilized chip-scale optical frequency comb.

    (A) Measurement setup schematic for the generation and stabilization of the chip-scale optical frequency comb. To stabilize the comb’s first degree of freedom, we phase-locked the ECDL to an optical reference (here a mode of a stabilized FFC) and then amplified it to 2 W to pump the Si3N4 microresonator. To stabilize the comb’s second degree of freedom, we monitored the Kerr comb spacing fR,KC by sending the comb to a high-speed photodetector (more than 15 GHz with a 3-dB bandwidth) and downmixing the electronic signal to the baseband with a local oscillator at fLO = 18 GHz. A fiber electro-optic modulator (EOM) controls the pump power and stabilizes the comb spacing. Δ = fR,KC − [fR,KC/fR,FFC]fR,FFC. δ, Frequency difference between the pump and the adjacent FFC line; PD, photodetector; G, grating; PH, pinhole; FPC, fiber polarization controller. (B) Example of a stabilized Kerr frequency comb spectrum, consisting of more than 400 comb lines in the telecommunication wavelength range. The horizontal (red) dashed line denotes a power level of 1 μW per comb line. Left inset: Optical micrograph of the spiral microresonator. Scale bar, 250 μm. Right inset: Clearly observed comb lines with native spacing at the cavity’s free spectral range.

  • Fig. 2 Stabilizing the pump frequency to the millihertz-level residual error and time-domain picture of the phase-locked Kerr comb.

    (A) Free-running beat note between the pump and the FFC. To obtain a sufficient SNR for reliable feedback stabilization (more than 35 dB with a 100-kHz RBW), we built a 200-pm bandwidth monochromator to filter the FFC before it was mixed with the pump. Sweep time is 10 ms. (B) RF spectrum of the stabilized beat note with a 1-kHz RBW. Control of the pump frequency was achieved by modulating the ECDL diode current with a 300-kHz bandwidth. (C) RF spectrum of the stabilized beat note with a 6-Hz RBW, showing a resolution-limited linewidth of 6 Hz. (D) Frequency counting of the stabilized beat note with a gate time of 1 s. The SD over 1000 s is 1 mHz, instrument-limited by the stability of the frequency counter. (E) Optical intensity autocorrelations of the phase-locked Kerr frequency comb at different delays, evidently showing the repetitive structures and excluding the possibility of noise correlation. Inset: RF spectrum of the free-running comb spacing with a scan range much larger than the cavity linewidth (290 MHz). The comb was tuned to enter the phase-locked state by fine control of the pump frequency.

  • Fig. 3 Stabilizing the comb spacing to the millihertz-level residual error.

    (A) RF spectrum of the stabilized comb spacing, showing a resolution-limited linewidth of 6 Hz. Control of the comb spacing was achieved by modulating the pump power via a fiber EOM. (B) SSB phase noise of the free-running (black curve) and stabilized (red curve) comb spacing. Free running, the phase noise of the comb spacing shows a f−3.5 dependence on the offset frequency in the vicinity of the carrier. Such technical noise can be removed by phase-locking the beat note to a high-performance microwave synthesizer, and the resulting close-to-carrier phase noise can reach the level of −70 dBc/Hz at 10 Hz with a f−1.5 dependence on the offset frequency (pink dashed curve), limited only by the microwave synthesizer. On the other hand, for offset frequencies above 10 kHz, the phase noise of the comb spacing is better than that of the 18-GHz local oscillator used for downmixing the electronic signal (gray dashed curve), and the measurement is thus instrument-limited. The phase noise estimated from Eq. 1 is −148 dBc/Hz at 1 MHz, and it grows with a f−2 dependence on the offset frequency. The estimated phase noise reaches −108 dBc/Hz at 10 kHz and starts to exceed the noise level of the 18-GHz local oscillator, matching the experimental observations (blue curve). Inset: Allan deviation of the comb spacing under free running (black empty squares), pump frequency stabilization (red semifilled squares), and full stabilization (blue filled squares). The fully stabilized comb spacing shows a consistent trend of Embedded Image (green dashed line) when the gate time is in the range from 0.5 to 200 s. The gray line denotes the counterlimited Allan deviation.

  • Fig. 4 Out-of-loop characterization of the fully stabilized chip-scale optical frequency comb.

    (A) To quantify the uncertainty of the stabilized chip-scale optical frequency comb, we mixed each of the comb lines from 1578.4 to 1573.6 nm (m = 1 to m = 33) and from 1570.5 to 1568.7 nm (m = 54 to m = 66) with the FFC and counted the beat frequency with a gate time of 1 s. The beat frequencies should change progressively by Δ, where Δ = fR,KC − [fR,KC/fR,FFC]fR,FFC, and the deviation from this relationship poses an upper bound on the frequency uncertainty of the chip-scale optical frequency comb. (B) Sample histograms of the frequency counting measurement on the first and second modes (m). Six hundred counts are accumulated for statistical analysis. The red lines are the Gaussian fits to the histograms. (C) Counting results on the optical frequencies of 46 comb lines. The centroid of the comb frequencies strays from the ideal with a 190-mHz peak-to-peak deviation and a 50-mHz SD. The frequency relative uncertainty of the fully stabilized chip-scale optical frequency comb is thus calculated at 2.7 × 10−16, referenced to the 188-THz optical carrier.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/4/e1501489/DC1

    I. Properties of the Si3N4 microresonator.

    II. Low-noise state of the Kerr frequency comb.

    III. Confirmation of the continuously equidistant Kerr frequency comb.

    IV. Dependence of comb spacing on pump properties.

    V. After-resonator feedback stabilization scheme and measurements.

    fig. S1. Properties of the Si3N4 microresonator.

    fig. S2. RF amplitude noise spectra of the high-noise state and the low-noise phase-locked comb state.

    fig. S3. Confirmation of the continuously equidistant Kerr frequency comb.

    fig. S4. Dependence of comb spacing on pump properties.

    fig. S5. Schematic of the alternative experimental setup for the generation and stabilization of the chip-scale optical frequency comb.

    References (3841)

  • Supplementary Materials

    This PDF file includes:

    • I. Properties of the Si3N4 microresonator.
    • II. Low-noise state of the Kerr frequency comb.
    • III. Confirmation of the continuously equidistant Kerr frequency comb.
    • IV. Dependence of comb spacing on pump properties.
    • V. After-resonator feedback stabilization scheme and measurements.
    • fig. S1. Properties of the Si3N4 microresonator.
    • fig. S2. RF amplitude noise spectra of the high-noise state and the low-noise phase-locked comb state.
    • fig. S3. Confirmation of the continuously equidistant Kerr frequency comb.
    • fig. S4. Dependence of comb spacing on pump properties.
    • fig. S5. Schematic of the alternative experimental setup for the generation and stabilization of the chip-scale optical frequency comb.
    • References (38–41)

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