Ultra-dense CEO-stabilized broadband optical frequency comb generation through simple, programmable and lossless 1,000-fold frequency-spacing division

Ultra-dense broadband optical frequency combs with sub-MHz frequency spacing and stabilized carrier-envelope offset (CEO) are needed for many important applications, including high-accuracy real-time sub-Doppler spectroscopy, precise characterization of photonic devices, and greenhouse gas sounding. However, the generation of such combs remains very challenging because they require mode-locked lasers with impractically long cavities (>few hundred meters). Here we demonstrate a CEO-stabilized optical frequency comb with a programmable sub-MHz frequency spacing, obtained through simple, suitable temporal phase modulation of a 250-MHz input comb. The method preserves the energy, the bandwidth, and the CEO-stabilization of the input comb, achieving a combined (CEO and repetition-rate) integrated phase noise below $\pi /10$ , and a frequency spacing down to 250 kHz over a 5-dB bandwidth of 10 THz, i.e., corresponding to a record high 1000-fold frequency spacing reduction and more than 40 000 000 comb lines. The demonstrated method bridges the gap between presently available high-quality optical frequency combs and a host of demanding and important applications that require CEO-stabilized broadband frequency combs with sub-MHz spacings.