Phase locking of terahertz semiconductor dual-comb laser sources

Dual-comb sources with equally spaced and low phase noise frequency lines are of great importance for high resolution spectroscopy and metrology. In the terahertz frequency regime, the electrically pumped semiconductor quantum cascade lasers (QCLs), demonstrating high output power, good far-field beam quality, and wide frequency coverage, are suitable candidates for frequency comb and dual-comb operations. Although free-running terahertz QCLs are able to work as frequency comb and dual-comb sources, the phase noises originated from the carrier and repetition frequencies' instabilities are relatively high, which strongly hinder the high precision applications. For a single laser frequency comb, the repetition frequency can be locked using a microwave injection locking and the carrier frequency can be locked to a highly stable source. Although these techniques can be, in principle, applied to a dual-comb laser source, the complexity of simultaneous locking of four frequencies (two repetition frequencies and two carrier frequencies) makes it difficult to be implemented friendly. Here, we propose a method to lock a terahertz QCL dual-comb source by phase locking one of the dual-comb lines to a RF synthesizer. Without a need of locking of carrier offset and repetition frequencies of the two lasers, the technique can force one of the lasers to follow the "tone" of the other one. Although only one dual-comb line is locked, the phase noise of other dual-comb lines can be significantly reduced. Furthermore, we demonstrate that the dual-comb signal with the phase locked loop can generate periodic time pulses in a 2 $\mu$s time scale, which further indicates that the free running terahertz QCL comb can produce pulsed type waveforms without any active or passive mode locking techniques.