# Linewidth Measurement of a Narrow-Linewidth Laser: Principles, Methods, and Systems
## 3 Research Progress
### Delayed Self-Hondyne Method  
In 1998, [PERSON] et al. reported a modified self-homodyne setup with a phase modulator and electrical upconversion [31], which amplifies the photocurrent signal at the detection end using a low-noise amplifier and mixes it with a 200 MHz intrinsic oscillator in a dual balanced mixer. A 460 kHz linewidth measurement was achieved using only 71.7 m of short-delay optical fiber. This structure is rarely used for direct linewidth measurements due to system stability limitations. It is often used for linewidth measurement of optical frequency discriminator (OFD) structures, calculating linewidth based on noise spectra.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Principles** & **Advantages** & **Disadvantages** & **References** \\ \hline Heterodyne & Beat frequency & — & \begin{tabular}{c} Strict requirements for \\ reference light sources \\ \end{tabular} & [26; 27] \\ \hline Delayed & Mach–Zehnder & Avoiding dependence on & Zero-frequency signal affect & [28; 29] \\ self-homodyne & configuration & reference laser & the beat frequency & [28; 29] \\ \hline MZI delayed & Decoherent coupling & \begin{tabular}{c} Avoiding interference from \\ zero frequency \\ \end{tabular} & \begin{tabular}{c} Long fiber length can \\ introduce \(1/f\) noise \\ \end{tabular} & [30; 31; 32; 33] \\ \hline MI delayed & Decoherent coupling & \begin{tabular}{c} Reduce fiber by half for \\ same optical path \\ \end{tabular} & \begin{tabular}{c} Long fiber length can \\ introduce \(1/f\) noise \\ \end{tabular} & [40] \\ \hline Loop delayed & Gain compensation & \begin{tabular}{c} Can measure wide range of \\ laser bands \\ \end{tabular} & \begin{tabular}{c} Unable to eliminate the impact \\ of \(1/f\) noise \\ \end{tabular} & [41; 42] \\ \hline \begin{tabular}{c} Second order \\ Stokes wave \\ \end{tabular} & Beat frequency & \begin{tabular}{c} High measurement \\ accuracy \\ \end{tabular} & Sensitive to system parameters & [53; 54] \\ \hline \begin{tabular}{c} Frequency \\ discrimination \\ \end{tabular} & FM-AM & \begin{tabular}{c} Avoiding interference from \\ zero frequency \\ \end{tabular} & \begin{tabular}{c} Frequency range is limited and \\ precise control is required \\ \end{tabular} & [71; 72] \\ \hline Optical coherent & Coherent mixing & \
\begin{tabular}{c} Directly measure \\ instantaneous \\ phase change \\ \end{tabular} &
\begin{tabular}{c} Complex structure and \\ high cost \\ \end{tabular} & [73; 74; 75] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of linewidth characterization methods.  
In 2019, [PERSON] et al. measured the output of a narrow-linewidth Brillouin laser integrated on a Si\({}_{3}\)N\({}_{4}\) waveguide platform using a delayed self-homodyne structure [88], achieving an ultra-narrow-linewidth measurement of 0.7 Hz.  
In 2021, [PERSON] et al. constructed a delayed self-homodyne device in the visible light band for linewidth measurement with a 269 Hz visible-light photon integrated Brillouin laser [89].  
The method avoids the stringent performance requirements of the reference light source compared with the heterodyne method. However, environmental noise from factors such as temperature changes and air vibrations near the zero-frequency limits the stability and resolution of the system, and the system has strict requirements for environmental stability.