## 2 Experimental Setup and Procedures  
The diagram in Figure 1 illustrates the setup of an erbium-doped fiber ring laser based on a TDLI filter (Kylia WT-MINT, Kylia, Paris, France) as the main protagonist. The beam is first emitted from the EDFA (EDPA-NE6000) and through the fiber connector at port 1, and then it enters the TDLI, where it travels along an interference path with a delay line route. After the beam passes through the TDLI, it is routed from the fiber connector at port 3 through the circulator to the TBF (BVF-200 CL) to filter out the unwanted wavelengths. After passing through the TBF in the initial beam path, half of the energy of the light will enter the optical spectral analyzer (OSA-Anritsu MS9740A, Anritsu, Atsugi, Japan) through the 3 dB coupler, and the other half of the energy of the light will re-enter the TDLI through the circulator and the fiber optic connector of port 3. On the other hand, this time, the interferometric path is traveled without a delay line path, and its phase is 180 degrees different from that of the interferometric path with a delay line path. The superposition of these two interferences passes through the fiber connector of port 2, and an isolator that prevents the output light at the input of the EDFA from interfering with the stability of the system is finally amplified by the EDFA. Figure 1: An experimental framework involves a multi-wavelength erbium-doped fiber ring laser with a delayed line interferometer (internal structure enlargement) as the primary component. (TDLI: tunable delay line interferometer; EDFA: erbium-doped fiber amplifier; TBF: tunable bandpass filter; OSA: optical spectral analyzer). The internal TDLI consists of two plate beam splitters, a triangular prism with a displaceable micrometer scale, and a mirror. The incident light enters port 1 and is reflected from the mirror, which is placed at an angle of 45 degrees, to a BS, which is also placed at an angle of 45 degrees. Half of the light is diverged from the BS to the forward-placed triangular prism and reflected to another BS placed at a reverse 45-degree angle; the other half of the light is diverged directly from the BS to the BS placed at a reverse 45-degree angle. The two beams of light converge together again due to the difference in optical paths, resulting in interference. This is interference with a delayed path. If the incident light enters from port 2, it does not go through the path between the mirror and the BS, which is interference without a delayed path. The distance between the mirror and the BS is intentionally designed so that the two main output interferences of the TDLI are phase-complementary and can be utilized simultaneously. It is worth mentioning that when the beam passes through the BS inside the TDLI, multiple FP interferences will occur due to the reflection inside the BS [65; 66], which forms some irregular interfering pattern embedded in the main interfering pattern at the output of the TDLI, and the spectrum is shown in Figure 2a. Since the reflected light inside the BS is relatively weak, the energy of the main interference needs to be weakened to observe the spectrum. The interferometric pattern of different FSRs shown in Figure 2a is observed from the incident light of EDFA entering the TDLI at port 1 and then reflected from the fiber connector at port 3 to the fiber connector at port 2 for OSA observation. It can be seen that the wavelengths of the peaks and troughs of the interference spectrum caused by the internal reflections of the BS are fixed regardless of the FSR of the main interference, although the powers of the peaks and troughs are modulated by the peaks and troughs of the main interference and have a difference in power. The yellow and blue lines in Figure 2b show the main interference spectra generated by the port 3 to port 2 and port 3 to port 1 paths of the TDLI, respectively.