Farey tree locking of terahertz quantum cascade laser frequency combs

Guibin Liu; Xuhong Ma; Kang Zhou; Binbin Liu; Lulu Zheng; Xianglong Bi; Shumin Wu; Yanming Lu; Ziping Li; Wenjian Wan; Zhenzhen Zhang; Junsong Peng; Ya Zhang; Heping Zeng; Hua Li

doi:10.1038/s41377-025-01819-9

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Farey tree locking of terahertz quantum cascade laser frequency combs

Original Articles

- Farey tree locking of terahertz quantum cascade laser frequency combs
- Farey tree locking of terahertz quantum cascade laser frequency combs
- LSA 2025年14卷第4期页码：1156-1168
- Affiliations：
  
  1.State Key Laboratory of Materials for Integrated Circuits and Key Laboratory of Terahertz Solid State Technology, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050, China
  2.Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
  3.Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, China
  4.State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200241, China
  5.Institute of Engineering, Tokyo University of Agriculture and Technology, Koganei-shi 184-8588 Tokyo, Japan
- Author bio：
  
  Heping Zeng (hpzeng@phy.ecnu.edu.cn)
  Hua Li (hua.li@mail.sim.ac.cn)
- Funds：
- DOI：10.1038/s41377-025-01819-9
  中图分类号：
- 收稿日期：2024-07-21，
  
  修回日期：2025-02-12，
  
  录用日期：2025-03-08，
  
  网络出版日期：2025-03-31，
  
  纸质出版日期：2025-04-30
- Accepted：
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Farey tree locking of terahertz quantum cascade laser frequency combs[J]. LSA, 2025,14(4):1156-1168.

Liu, G. B. et al. Farey tree locking of terahertz quantum cascade laser frequency combs. Light: Science & Applications, 14, 1156-1168 (2025).
Farey tree locking of terahertz quantum cascade laser frequency combs[J]. LSA, 2025,14(4):1156-1168. DOI： 10.1038/s41377-025-01819-9.

Liu, G. B. et al. Farey tree locking of terahertz quantum cascade laser frequency combs. Light: Science & Applications, 14, 1156-1168 (2025). DOI： 10.1038/s41377-025-01819-9.

摘要

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.

关键词

Keywords

references

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