## 4 Experimental Investigation of MTEFL Operation
The adjacent peaks in both the initial and final samples are separated by approximately 0.89 nm. Figure 9b illustrates the most significant dual-narrow-emission lines throughout the tuning process, highlighting samples \(\lambda_{1}\), \(\lambda_{3}\), \(\lambda_{12}\), and \(\lambda_{14}\). We can see that \(\lambda_{12}\) showed the highest power, with the peak power difference of each lasing line being less than 2.63 dB. The total peak power difference across all lasing lines was less than 6.10 dB, with 5.09 dB for \(\lambda_{\rm{As}}\) and \(\lambda_{\rm{Bs}}\), respectively. Furthermore, a linear relationship between the shifts in wavelength spectra and curvature was observed (see Figure 9c). The data show a linear response from 1564.56 nm to 1562.27 nm and from 1563.71 nm to 1561.40 nm, with sensitivities of \(-8.4008\) nm/m\({}^{-1}\) and \(-8.7734\) nm/m\({}^{-1}\), respectively, along with an R\({}^{2}\) value of 0.9912 and 0.99126. In state-e, a tunable dual-wavelength emission line was achieved by applying curvature to the MZI filter, resulting in a tuning range of 8.81 nm and a wavelength interval of approximately 0.22 nm, with curvature in a range from 5.3042 m\({}^{-1}\) to 6.0495 m\({}^{-1}\) (see Figure 10). The tuning process involved a total of 41 samples, labeled \(\lambda_{1}\), \(\lambda_{2}\),..., \(\lambda_{41}\). The initial \(\lambda_{1}\) (represented by the red line in Figure 10a) exhibited a dual wavelength at \(\lambda_{1A}\) = 1572.53 nm and \(\lambda_{41B}\) = 1585.69 nm, with respective SMSR values of 42.35 dB and 41.31 dB. The final dual-wavelength \(\lambda_{41}\) (depicted by the violet line in Figure 10a) was recorded at \(\lambda_{41A}\) = 1563.68 nm and \(\lambda_{41B}\) = 1576.88 nm, showing SMSR values of 29.21 dB and 42.35 dB, respectively. Figure 10b illustrates that the adjacent peaks for the initial and final wavelengths were separated by 13.16 nm and 13.21 nm. During the tuning process, it was observed that the wavelength interval between \(\lambda_{26}\) and \(\lambda_{27}\) was 1.08 nm for side A (\(\lambda^{s}\)) and 0.48 nm for side B (\(\lambda^{s}\)). The adjacent peaks for \(\lambda_{26}\) and \(\lambda_{27}\) were separated by 12.06 nm and 12.76 nm, respectively. Figure 3a shows an FSR of 9.58 nm resulting from the sensor interference pattern. This FSR is smaller than the distance between adjacent peaks. This discrepancy is due to the fact that the TCF core diameter is significantly smaller than the SMF. As a result, the ability to confine guided mode light is reduced, and the mode field diameter is considerably larger, leading to the excitation of higher-order modes and the formation of modal interference [32; 33]. As the curv  
Figure 9: Narrow-dual-emission signals (state-d). (**a**) Tuning and the potential difference between peaks and their wavelength comparisons, (**b**) most significative peaks and power comparison, (**c**) sensitivity compared to the dispersion of curvature samples. the misalignment of the core diameter and the change in the cutoff wavelength, some modes of the cladding are easily excited [34]. This condition leads to energy absorption and transitions between different modes due to fluctuations in the system. We believe that the differences in the emission spectrum of the filter modes create a variance in the wavelengths of the laser, thus creating a separation between the peaks and effectively expanding its operating range [35]. This analysis provides a thorough explanation of the continuous curvature applied to the MZI sensor and the resulting changes observed in the laser emission signals. Upon analyzing the wavelengths \(\lambda_{28}\) to \(\lambda_{41}\), it was found that the separation of adjacent peaks and their wavelength intervals fell within the initially measured tuning lines.