# Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems
## 4 Comparative Analysis and Technical Difficulties
### Comparative Analysis of Linewidth Measurement Techniques
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Structures** & **Methods** & **Linewidth** & **Output Power** & **Wavelength** & **Time** \\ \hline DFB Laser & High resolution & 8.7 MHz & — & 1550 nm & 2005 [122] \\ \hline VCSEL laser & spectral analyzer & — & 1.95 mW & 1550 nm & 2007 [117] \\ \hline \multirow{2}{*}{Quantum cascade laser} & Near-infrared frequency comb & \multirow{2}{*}{230 Hz} & \multirow{2}{*}{2 mW} & \multirow{2}{*}{780 nm} & \multirow{2}{*}{2012 [119]} \\ \cline{1-1} \cline{5-5} Brillouin fiber laser & Voigt fitting & 40 Hz & 3 mW & — & 2015 [49] \\ \hline \multirow{2}{*}{Mid-infrared quantum laser} & Optical feedback interferometry & \multirow{2}{*}{280 kHz} & — & \multirow{2}{*}{—} & \multirow{2}{*}{2016 [120]} \\ \cline{1-1} \cline{5-5}  & & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of other measurement techniques. Finally, it is also necessary to consider the impact of the measuring time and the linewidth of the tested/reference light source. The measuring time is reflected in the frequency/phase noise analysis based on the \(\beta\) isolation line algorithm, which obtains the linewidth by integrating the power spectral density of the low-frequency modulation region, and the testing time directly determines the lower limit of the integration bandwidth [128; 129; 130]. It is necessary to consider the linewidth of the measured/reference light source in the heterodyne beat frequency method. One approach is to require the linewidth of the reference light to be approximately equal to the linewidth of the measured light and the linewidth of the beat spectrum to be twice the linewidth of the measured light. Another approach is to ensure that the linewidth of the reference light is much smaller than the linewidth of the measured light, while the spectral linewidth is approximately equal to the linewidth of the measured light [131]. Both of these problems are difficult to satisfy, which limits the use of the heterodyne beat frequency method. New characterization techniques for narrow-linewidth lasers have emerged in recent years, opening a new chapter for the characterization of narrow linewidth. The second-order Stokes wave based on SBS as a reference light source has become a trending research topic. Its principle has been successfully applied in fiber delay self-heterodyne and F-P interferometers, with a maximum resolution of 300 Hz, achieving sub-Hz-level linewidth characterization. Voigt fitting, the \(\beta\) isolation modulation algorithm, and three-wavelength interferometry measurement techniques can be used to calculate the linewidth by measuring the frequency noise [132] and phase noise of lasers, which can be applied to any type of laser. Real-time oscillations of long fibers and lasers can generate \(1/f\) noise in delayed self-heterodyne measurement systems. Voigt contour fitting can effectively filter out linewidth broadening caused by \(1/f\) noise, while the \(\beta\) isolation modulation algorithm can also separate white noise and \(1/f\) noise; therefore, the distribution characteristics of the laser under the influence of noise can be fully observed.