## 2 Experimental Section  
The schematic of our multi-harmonic optical comb is shown in Figure 1. The watt-level frequency division-by-three singly resonant optical parametric oscillator (SRO) cavity is a bow-tie ring cavity consisting of two curved mirrors (M1 and M2) with a 100 mm radius of curvature, a flat mirror (M3), and an output coupler (M4). The OPO crystal is a 5 mol % MgO-doped PPLN crystal (from HC Photonics) with a length of 40 mm. The total cavity length is 500 mm. The pump, signal, and idler waves are designed to correspond to the 3 rd harmonic wave, the 2 nd harmonic wave, and the fundamental wave of a multi-harmonic optical comb. M1 and M2 have reflectance of \(<\)2%, \(>\)99.9%, and \(<\)5% at the pump, signal and idler wavelengths, respectively. M3 has reflectance of \(>\)99.9% at the signal wavelength. Output coupler mirror M4 has a 0.6% output coupling at the signal wavelength. Figure 1: Multi-harmonic optical comb based on a frequency division-by-three singly resonant optical parametric oscillator. The optical parametric oscillator generates the fundamental wave (idler), the 2 nd harmonic wave (signal), and the 3 rd harmonic wave (pump) of the multi-harmonic optical comb. The 4 th harmonic to 6 th harmonic are generated by intracavity second harmonic generation (SHG), external cavity single-pass sum frequency generation (SFG), and external cavity single-pass SHG, respectively. The idler (the fundamental wave) SHG and a small portion of the 2 nd harmonic wave are combined to produce an error signal for frequency control by tweaking the cavity length that is based on a home-made phase detection circuit, a commercial high-speed proportional integrating (PI) controller (New Focus LB1005) and a high voltage PZT driver (Physik Instruments E-501.621) shown inside the dashed box. The two end faces of the MgO:PPLN crystal are optically polished and antireflection-coated with \(<\)1%, \(<\)0.2%, and \(<\)5% reflectance at pump, signal, and idler wavelengths. The OPO crystal has a period of 30.8 \(\upmu\)m and generates radiation at 1596-nm (signal) and at 3192-nm (idler) at 92.8 \({}^{\circ}\)C when pumped at 1064 nm. The pump laser is a cw linearly polarized, single-frequency Yb-doped fiber laser amplifier which is seeded by a single-mode mW-level DFB diode laser that has \(<\)0.1 MHz linewidth at 1064 nm from IPG Photonics. The pump laser is capable of producing \(\sim\)15-W power with TEM\({}_{00}\) mode and a M\({}^{2}<1.05\). The cavity is designed to resonate at the signal wave that has a focusing parameter \(\xi\) = L/b of 1 (L is the crystal length and b is the confocal parameter). The pump beam is focused to a beam waist radius of 60 \(\upmu\)m to mode-match to the cavity mode of the signal beam. The pump and idler exit the cavity from M2 and the signal output is at M4. The pump and idler are separated by a dichroic mirror for their power measurements. The idler wave is immediately focused into a 25 mm long MgO:PPLN crystal of period 34.25 \(\upmu\)m for SHG of the idler to produce a beat signal with the signal wave. The purpose of the beat signal is to lock the length of the SRO cavity. This beat signal which is detected by a fast photodiode (EOT ET-3010) is sent to a cavity stabilization feedback circuit shown enclosed in the dash box in Figure 1. Locking the cavity length in turn fixes the wavelength of the signal to one of the cavity modes. A 250-\(\upmu\)m thick intracavity fused silica etalon is inserted between M2 and M3 to maintain single-longitudinal-mode operation at high pump power. The 4 th harmonic to 6 th harmonic waves can be generated by either intracavity or external cavity configurations. Intracavity frequency conversion could provide higher conversion efficiency, but the dynamic of the SRO cavity becomes more complicated and the cavity mirrors' coatings are more susceptible to damage. So only the 4 th harmonic comb component is generated by intracavity SHG from the 2 nd harmonic wave (SRO signal wave).