Mechanical Control of a Microrod-Resonator Optical Frequency Comb

We report on the stabilization of a microresonator-based optical frequency comb (microcomb) by way of mechanical actuation. These experiments use novel ${\mathrm{CO}}_2$-laser-machined microrod resonators, which are introduced here and feature optical $Q\gtrsim 5\times {10}^8$, less than 1 minute processing time, and tunable geometry. Residual fluctuations of our 32.6 GHz microcomb line spacing reach a stability level of $5\times {10}^{-15}$ for 1 s averaging, thereby highlighting the potential of microcombs to support modern optical-frequency standards. Furthermore, measurements of the line spacing with respect to an independent frequency reference reveal stabilization of different spectral slices of the comb with a $<0.5\mathrm{\text{−}}\mathrm{mHz}$ variation among 140 comb lines spanning 4.5 THz. Together, these results demonstrate an important step in the development of microcombs, namely, that they can be fabricated and precisely controlled with simple and accessible techniques.

Popular Summary

Measuring optical frequencies with a precision up to 20 digits after the decimal point sounds like a prohibitively difficult task. But that is exactly what has been achieved by optical-frequency combs, which are composed of many thousands of phase-locked laser teeth all separated by an equal frequency spacing. The more-established frequency combs are all based on tabletop, mode-locked lasers. While this approach has been successful, an alternative that is much smaller in size and lower in power consumption but with similar measurement precision could leverage precision metrology in new fields of research, particularly outside the laboratory. Such an alternative has recently emerged in the form of optical-microcavity-based frequency combs, or “microcombs.” In this experimental paper, we report two important advances in the development of microcombs.

In microcombs, the comb generation relies on a nonlinear optical effect in a microcavity—parametric oscillation—which can create 1000 or more new colors of light from a single monochromatic laser. We have made two new and significant steps forward in developing microcombs. First, we have developed a new microcavity fabrication method that employs laser machining to produce an ultrahigh-quality-factor device in less than one minute. This important technical simplification over the existing fabrication techniques will allow rapid exploration and optimization of microcomb physics. Second, based on the realization that high-sensitivity control of the optical modes of the cavity can be achieved through applying mechanical strain to the cavity, we have achieved line-spacing stabilization of the optical spectrum of our microcomb in the wavelength span from 1510 nm to 1620 nm with a precision of $5\times {10}^{-15}$. This degree of stabilization demonstrates the potential of this new frequency-comb platform to support modern frequency references beyond the level associated with the best traditional technology.

Our mechanical technique can be applied to any microcavity geometry, and it offers the performance needed to support today’s best optical clocks. We foresee further developments that increase the frequency span by leveraging the ultrafast optical waveform generated from the superposition of phase-locked comb modes. This will make possible all-optical stabilization of microcombs for applications that rely on ultraprecise frequency and timing measurements.

Figure 1

Fabrication of fused-quartz microrod resonators by use of ${\mathrm{CO}}_2$-laser machining. (a) A rotating fused-quartz rod is illuminated with a focused ${\mathrm{CO}}_2$ laser that selectively removes material. By applying the laser at different positions along the rod’s axis, a microresonator is produced. (b) Image of a microrod with $Q=5\times {10}^8$, 2-mm diameter, and approximately $100\mathrm{\text{−}}\mu \mathrm{m}$ mode cross-sectional diameter. (c) Fabrication of resonators with variable diameter. Starting at top left and counting clockwise, the resonator diameters are 0.58 mm, 0.36 mm, 0.71 mm, 1.2 mm, 1.5 mm, and 1.0 mm. (d) Optical spectrum from the device in (b), which has a modulated envelope characteristic of parametric combs [14, 18, 36]. The span of this comb is sufficient to access the D1 and D2 transitions of atomic Rb, following second-harmonic generation.

Figure 2

Mechanical control mechanism for microresonator combs. (a) Control apparatus. A PZT compresses the microrod resonator to adjust its mode frequencies. (b, c) Response of optical resonance (b) and microcomb line spacing (c) with PZT drive frequency. (d) A three-hour record of the microcomb line spacing ($\Delta \nu$) under free-running and stabilized conditions. The line-spacing lock point $f_s$ is 32.5671 GHz.

Figure 3

Microcomb line-spacing stability. (a) Schematic of our systems for microcomb generation and line-spacing stabilization (green box), and “out-of-loop” analysis (gray box). The entire optical path is in fiber, including a programmable optical filter used to study the line-spacing stability for portions of the comb (Fig. 4). Commercial frequency synthesizers create references $f_{1,2}$ that are used for baseband conversion, and signals $S_{1,2}$ are measured. The generation and analysis systems have independent maser references. (b) Line-spacing Allan deviation versus averaging time for (triangles) stabilized residual, (points) stabilized absolute, and (open circles) free running. The gray line shows the Allan deviation of reference $f_2$.

Figure 4

Line-spacing equidistance and stability for different spectral slices of the comb. (a) Microcomb optical spectrum about the pump laser frequency ${\nu }_0$ prior to filtering. (b) Measurements of the frequency difference ($\Delta {\nu }_1-\Delta {\nu }_2$) between the whole comb and a spectral slice. The horizontal bars indicate the frequency range of each measurement, which is highlighted by the shaded region for one point. (c) For different spectral slices, the points show the 1-s Allan deviation of $\Delta {\nu }_2$ measured against maser 2, and the triangles characterize residual fluctuations between $\Delta {\nu }_1$ and $\Delta {\nu }_2$ measured against maser 1. For the open circle and open triangle data points, only a 0.3-THz range about ${\nu }_0$ is blocked.

Figure 5

Spectrum of line-spacing fluctuations $S_{\Delta {\nu }_1}$. The black (i) and green (ii) lines show the free-running and stabilized line-spacing spectral density, respectively. The broad resonance at 600 kHz in the green line coincides with a mechanical resonance of the fused-quartz rod, which we speculate is weakly excited via the PZT. The red (iii) line indicates the contribution from reference $f_1$. The gray (iv) and blue (v) lines show the predicted contributions from pump frequency and intensity noise, respectively.