Coherence control of spectrally multiplied frequency combs using an integrated multi-mode DBR laser

Optical frequency combs (OFCs) have been identified as a key building block for many applications ranging from spectroscopy to optical communications. In these applications, the fixed phase relation between the individual spectral components of the comb is a crucial aspect of frequency combs. Recently multi-wavelength lasers that are in essence multimode lasers have shown a promising capability to enable frequency comb multiplication over a broad range of frequency offsets surpassing 1 THz. Despite the robust phase coherence within each comb's lines, there remains a notable lack of phase coherence among distinct sub-combs. In this work, we show that the injecting of an adapted frequency comb, i.e., a narrowband comb comprising five lines and an extra tone separated by a certain frequency offset from the central line of the comb, facilitates cascaded phase locking between three adjacent sub-combs. The interaction between the regenerated comb and the multiplied comb induced by the extra tone initiates a modulation at their beating frequency. By fine-tuning the frequency of the extra tone, we can adjust the position of the resulting beating, and eventually achieve a cascaded phase locking for the third mode. We envision that cascaded phase-locking can advantageously be extended to additional modes leading to cover higher frequency offsets up to a few THz.