Fig. 4: Hybrid Kerr-electro-optic frequency comb on thin-film lithium niobate.

a Single DKS spectrum (blue, top) with a spacing \({f}_{{DKS}}\) of 410.319 GHz between comb lines and electro-optically modulated single DKS spectrum (red, bottom) with a 14-times divided spacing of 29.308 GHz. The latter spectrum is zoomed-in over 2 THz windows centered ~173, 200, 229, and 234 THz, with original DKS comb line positions overlaid. b Nonzero difference frequencies \(\Delta f\) detected as a beatnote, as the EO modulation frequency is stepped from 29.108 GHz up to 29.158 GHz in intervals of 0.01 GHz. When the modulation frequency is 29.108 GHz, a zoom-in of the beatnote over a 4 MHz window centered around 2.80791 GHz shows a narrow linewidth with 1 kHz resolution bandwidth. c Linear fit of the difference frequencies \(\Delta f\) to the modulation frequencies (\({f}_{{RF}}\)) in b. The absolute value of the slope is \(N=14\), the number of EO sidebands required to completely divide the single DKS spacing. d Spectrogram of \(\Delta f\) when \({f}_{{RF}}\) is fixed at 29.158 GHz. Left panel shows the progression of \(\Delta f\) when it is unlocked, phase locked to a microwave reference oscillator, and unlocked again. Right panel shows the progression of \(\Delta f\) when it is phase locked to a microwave reference oscillator that is fixed frequency, sinusoidally modulated in frequency, and fixed frequency again