## 4 Experimental Investigation of MTEFL Operation  
This section analyzes the tuning and switching process of the multi-wavelength thin-core erbium-doped fiber laser (MTEFL) emission lines. The analysis aims to provide a comprehensive explanation of the continuous curvature applied to the MZI sensor and the subsequent changes observed in the laser emissions. In Figure 6a, we illustrate the initial tuning process of an MTEFL. This figure displays the first and last lasing lines obtained within a wavelength range of 1556.63 nm to 1564.25 nm from 89 tuning samples for state-a. The tuning process spanned a wavelength range of 7.62 nm, corresponding to a curvature range from 2.3452 m\({}^{-1}\) to 4.9323 m\({}^{-1}\). Figure 6b shows that the initial signal (\(\lambda_{1}\) = 1556.63 nm) had an SMSR of 40.04 dB, while the final lasing signal emission for a single line (\(\lambda_{89}\) = 1564.25 nm) had an SMSR of 36.04 dB. The linewidths of 3 dB were 0.02 nm for \(\lambda_{1}\) and 0.03 nm for \(\lambda_{89}\), with a wavelength interval of approximately 0.08 nm. The SMSR difference between the first (\(\lambda_{1}\)) and the last (\(\lambda_{89}\)) emission lines is 4 dB. To further understand this variation, we focus on a more significant single-line emission, as depicted in Figure 6c. For this single tuning emission at wavelength \(\lambda_{1}\), the SMSR was 40.04 dB, which increased to 49.80 dB at \(\lambda_{46}\), before dropping to 36.04 dB at \(\lambda_{89}\). The corresponding signal-to-noise ratios (SNRs) for these wavelengths were \(\lambda_{\text{SNRI}}\) = 1562.46 nm, \(\lambda_{\text{SNR46}}\) = 1566.69 nm, and \(\lambda_{\text{SNR89}}\) = 1558.29 nm, with SNR values of 16.64 dB, 7.17 dB, and 18.74 dB, respectively. The laser SNR is defined as the ratio of the laser peak power to the adjacent ASE level monitored from the output laser [29]. The variation in SMSR during the tuning process is due to the increment in the curvature applied to the filter. This change in curvature may lead to insertion loss during tuning, which induces variations in propagation through both the core and cladding modes. As a result, these changes affect the gain and lead to variations in the gain spectrum [12]. The average peak output power obtained from 89 tuning samples was measured to be \(-\)14.76 dBm. We observed a maximum power fluctuation of 2.19 dB across the total emission tuning lines, which is below the threshold of 3.0 dB. The variation observed in the SMSR and SNR is not  
Figure 5: MTEFL emission tuning and switching cases generated for single (state-a), quadruple (state-b), triple (state-c), narrow-double (state-d), and double (state-e) lasing signals. substantial enough to affect the peak output power. To assess the response of the MZI filter to curvature, we analyzed all 89 samples taken while tuning a single lasing emission line, as shown in Figure 6d. Our study encompasses a curvature range of 2.3452 m\({}^{-1}\) to 4.9323 m\({}^{-1}\), from which we derived a sensitivity of 2.67 nm/m\({}^{-1}\), with an R\({}^{2}\) value of 0.9982. The relationship between curvature and wavelength shift was established through the use of a polynomial fit adjustment, which yielded the equation \(y=1555.7397-1.0064x+0.5571x^{2}\). This equation accurately represents the aforementioned relationship. The curvature was incremented to 4.9537 m\({}^{-1}\), leading to a wavelength switch that resulted in the division of a single lasing signal into quadruple-emission lines (state-b), as shown in Figure 7a. These lines were identified as \(\lambda_{1}=1557.99\) nm, \(\lambda_{2}=1558.89\) nm, \(\lambda_{3}=1564.02\) nm, and \(\lambda_{4}=1564.78\) nm. The spectral power distribution of these lines was measured, revealing SMSR values of 29.07 dB, 31.98 dB, 39.96 dB, and 34.11 dB for each emission line. Additionally, the 3 dB line widths were determined to be 0.03 nm, 0.05 nm, 0.04 nm, and 0.05 nm, respectively. The adjacent peaks were separated by distances of 0.90 nm, 5.13 nm, and 0.78 nm.