Fig. 2: Dual-microwave control comb stabilization principle.
From: Frequency microcomb stabilization via dual-microwave control
a Frequency microcomb setup for stabilization. Here EOM, Electro-optic modulator; EDFA, Erbium-doped fiber amplifier. For ξ and frep stabilization, an EOM controls the pump power and the ECDL diode current controls the pump laser frequency, through two phase-locked loops. We also note that, in place of the EOM, a polarization rotator with a PBS can also serve for intensity modulation. To increase the locking duration, we implemented slow control of the ECDL PZT (red dashed line) and the EDFA gain (yellow dashed path). The slow feedback to the EDFA gain may also alternatively be replaced by sending the feedback signal to the temperature controller on the chip holder (which controls device temperature) instead (green dashed path). This reduces loop dynamic range but also mitigates the effects of ambient temperature drift. The stability of the locked microcomb is interrogated out-of-loop by beating with an independently stabilized fiber frequency comb. b Frequency domain illustration of the demonstrated full-stabilization technique. Here the offset frequency, ξ, is linked with the primary comb line spacing, Δ, by the constitutive relation \(\xi = \Delta - \left| {\frac{\Delta }{{f_{{\mathrm{rep}}}}}} \right|f_{{\mathrm{rep}}}\). Furthermore, \(\Delta = \frac{1}{{\sqrt {\pi c\left| {\beta _2} \right|} }}\sqrt {\eta \left( {n_{\mathrm{g}}f_{\mathrm{p}} - N\frac{{n_{\mathrm{g}}^2}}{{n_0}}f_{{\mathrm{rep}}} - \frac{{\gamma cP_{{\mathrm{int}}}}}{\pi }} \right)} \) where β2 is the group velocity dispersion (GVD), \(\eta = \frac{{\beta _2}}{{\left| {\beta _2} \right|}}\) is the sign of the GVD, ng is the group index, no is the refractive index, N is the longitudinal mode number, c is the speed of light in vacuum, γ is the nonlinear coefficient, and Pint is the intracavity pump power. c Subsequent to frep stabilization, the offset frequency shows strong linear correlation with pump wavelength (blue circles) with a slope of about 4.5 MHz per picometer shift of pump. The simulated slope (plotted in orange) also shows good agreement with measured data. d Measured offset frequency as a function of applied pump power, after frep stabilization. The pump power is stepwise changed by a total of 3.4% via the EFDA gain. The offset frequency remains constant within the error bar, verifying that frep stabilization effectively eliminates the intracavity pump power fluctuation. For (c) and (d), 10 measurements are taken to determine the mean value, and the error bars are defined as the peak-to-peak deviations from the 10 measurements. Here the pump frequency is not yet stabilized, resulting in the error bars in the offset frequency measurements.
