# Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems
## 1 Introduction  
The research and application of advanced laser technology have been highly valued with the rapid development of optical communications, quantum technology, artificial intelligence, and other fields. Narrow-linewidth lasers have become key devices in fields such as long-distance optical space communications, ultra-high-speed fiber-optic communications, high-sensitivity optical sensing, and quantum precision measurement [1; 2; 3; 4] due to their high monochromaticity, high coherence, low noise, high stability, and dynamic single-mode characteristics. In satellite laser communications, the longest link between the satellite and the ground is approximately 80,000 km, and the coherent laser transmission rate between satellites can reach 10 Gb/s. An ultra-narrow spectral linewidth and extremely high coherence based on narrow-linewidth lasers can achieve ultra-high-speed and large-capacity data transmission in space optical communications [5; 6]. In terms of precision measurement, such as for atomic clocks, atomic magnetometers and LiDAR, laser heterodyne interferometry measurement systems have more stringent performance requirements for lasers [7; 8; 9; 10]. A narrow-linewidth laser characterizes physical quantities such as the time reference, gravity, and magnetic field by pumping atoms and manipulating quantum states [11; 12; 13; 14]. In the field of ultra-high-speed optical communication, different coherent modulation systems require different minimum laser linewidths. For example, 4-PSK with a coherent detection function requires a linewidth of \(\leq\)100 kHz [15; 16; 17; 18], whilecurrently in 40 Gbps optical communications, the highest-sensitivity high-order 8-QAM, 16-QAM, and 64-QAM signals require a minimum linewidth of 1.2 kHz [19; 20]. Linewidth and noise characteristics are important performance indicators for measuring narrow-linewidth lasers. The linewidth restricts the information transmission capacity and optical detection sensitivity in laser communications, while noise affects the transmission quality of laser communications. The applications of narrow-linewidth lasers have become increasingly diverse after decades of development, and the requirements for linewidth characterization technology have become increasingly stringent. The continued development of narrow-linewidth lasers has enabled the linewidth to advance from MHz level to kHz or even Hz level [21; 22] while also promoting the advancement of linewidth characterization methods.  
The manuscript introduces typical linewidth characterization methods for narrow-linewidth lasers. The characterization methods are classified into two categories based on the principle of linewidth measurement: the beat frequency power spectrum and the phase noise spectrum. The two methods use Voigt contour fitting and phase noise analysis, and the \(\beta\) isolation line equation characterizes the laser linewidth. The limiting factors and error sources of the measurement methods are discussed and combined with the current development status of linewidth characterization technology based on the performance parameters and testing conditions of different lasers. In response to the technical difficulties of phase noise jitter and spectrum broadening caused by 1/\(f\) noise introduced by long-fiber self-heterodynes, this manuscript discusses the iterative algorithm and self-coherent detection method based on short-delay fiber coherent envelope spectra, which improves the range and accuracy of linewidth measurements. Finally, future research directions for linewidth measurement technology are discussed and summarized.