Farey tree locking of terahertz semiconductor laser frequency combs

TL;DR

This paper introduces a novel Farey tree locking technique for terahertz quantum cascade laser frequency combs, achieving stable, low phase noise operation without complex external locking systems, thus advancing compact terahertz sources.

Contribution

The study presents the first implementation of Farey tree locking in terahertz QCL frequency combs, demonstrating improved phase noise reduction and predictable frequency locking based on Farey hierarchy.

Findings

Farey tree locking stabilizes terahertz QCL combs.

Phase noise of dual-comb spectral lines is significantly reduced.

Frequency locking aligns with Farey fraction hierarchy.

Abstract

Frequency combs show various applications in molecular fingerprinting, imaging, communications, and so on. In the terahertz frequency range, semiconductor-based quantum cascade lasers (QCLs) are ideal platforms for realizing the frequency comb operation. Although self-started frequency comb operation can be obtained in free-running terahertz QCLs due to the four-wave mixing locking effects, resonant/off-resonant microwave injection, phase locking, and femtosecond laser based locking techniques have been widely used to broaden and stabilize terahertz QCL combs. These active locking methods indeed show significant effects on the frequency stabilization of terahertz QCL combs, but they simultaneously have drawbacks, such as introducing large phase noise and requiring complex optical coupling and/or electrical circuits. Here, we demonstrate Farey tree locking of terahertz QCL frequency combs under microwave injection. The frequency competition between the Farey fraction frequency and the cavity round-trip frequency results in the frequency locking of terahertz QCL combs, and the Farey fraction frequencies can be accurately anticipated based on the downward trend of the Farey tree hierarchy. Furthermore, dual-comb experimental results show that the phase noise of the dual-comb spectral lines is significantly reduced by employing the Farey tree locking method. These results pave the way to deploying compact and low phase noise terahertz frequency comb sources.