# Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems
## 4 Comparative Analysis and Technical Difficulties  
### Comparative Analysis of Linewidth Measurement Techniques  
The delayed self-heterodyne is the most widely used and mature linewidth measurement technology, from the MZI structure to the MI structure and cyclic self-heterodyne structure, as well as second-order Stokes waves based on Brillouin scattering. Researchers have gradually optimized the spectrum acquisition, signal analysis, data processing, and testing conditions of the delayed self-heterodyne, effectively improving the measurement range and resolution of linewidth characterization. The most basic devices for linewidth measurement are optical fibers and photodetectors. The characteristics of the devices and the noise they introduce (such as 1/_f_ noise and white noise) significantly restrict the accuracy, range, and precision of linewidth measurements [122; 123]. First, the delay time \(\tau_{0}\) approaches the coherence time \(\tau_{c}\) when the length of the delay is insufficient. The exponential function factor in the power spectrum oscillates at both ends of the peak. The beat frequency power spectrum is no longer a standard Lorentz line shape, and a delta function spike appears at the center frequency. The measured signal and reference signal gradually achieve decoherence as the length of the delay fiber increases, and the beat frequency power spectrum approximates the standard Lorentz line shape. The power spectrum will become a Voigt contour line with Gaussian-like components due to the 1/_f_ noise of the laser signal itself when \(\tau_{0}\) is much greater than \(\tau_{c}\)[124]. The coherent beat frequency used for linewidth measurement is mainly contributed by the white noise Lorentz line shape, while the 1/_f_ noise Gaussian line shape introduces additional spectral line broadening [125]. The frequency spectrum of the external difference signal is corrected to obtain an accurate linewidth by fitting Voigt contour. Second, linewidth measurements are also limited by devices such as PDs, AOMs and ESAs. PDs introduce thermal noise and shot noise [126; 127]; the former is present in almost all transmission media and electronic devices, cannot be eliminated and is not affected by frequency shifts. The latter is related to the emission power and detection bandwidth, which originate from the random fluctuations of charge carriers generated when radiation waves contact a photodetector. The detection bandwidth should be reduced to reduce the impact of shot noise when receiving the complete photoelectric current spectrum. An AOM can lead to issues such as insertion loss and an unstable polarization state, and the complexity of the measurement system increases. We should comprehensively consider the advantages and disadvantages of the AOM and choose whether to shift the frequency for different testing environments. The impact of the spectrum analyzer on the linewidth measurement mainly lies in two aspects: the resolution and the scanning time. All points on the spectrum cannot be accurately calculated simultaneously when the resolution of the spectrum analyzer is too low. The time required to scan the entire RF spectrum is not faster than 1 ms in practical situations, which prevents time dependence research on the linewidth. The linewidth should be measured repeatedly, and the average and standard deviation should be calculated to obtain a more accurate linewidth.