## 3 Sensing Characteristics and Demodulation
### Analysis of Sensing Characteristics
Moreover, it is contradictory between the number of detectable parameters and the dynamic range of monitored parameters, which needs to be comprehensively considered in the design of the sensor [17]. From the aforementioned analysis, it can be seen that the OMC waist region diameter has a greater affect on the sensor sensitivity. Therefore, the number of characteristic wavelengths can be determined by adjusting the length L, and the sensing characteristics of the device can be adjusted by changing the waist region radius \(r\). Figure 2: (**a**) The numerical results of output spectra of OMCI with temperatures under different microfiber waist radius of 1, 3, and 5 \(\upmu\)m. (**b**) Analysis results of temperature sensing response characteristics of OMCI under different microfiber waist radius \(r\). The two arm difference of OMCI used in the above analysis is zero, so the OMC is mainly used as sensing unit to analyze the influence of OMC structure on the sensing characteristics of the combined device. In addition, the interferometer itself also has the sensing function. In view of this, this paper selects different interferometer arm differences to analyze the spectral transmission and temperature sensing characteristics of OMCI. First, select the structural parameters of OMC as \(r=2\)\(\mu\)m, \(L=2\) mm, When the interferometer arm lengths \(l_{a}\) are 1, 3, and 5 mm respectively, the output spectra under different temperatures are shown in Figure 4. The intensity envelope characteristics of the OMCI output spectra are mainly determined by the coupling filtering characteristics of the OMC, and the interference fringe characteristics within the envelope are determined by the interferometer arm difference. The temperature sensing function can be realized by tracking the wavelength corresponding to the extreme point of the envelope (the dip or peak characteristic wavelength that are mentioned above). Figure 4: (**a**) Output spectra with OMCI arm difference \(la=1\) mm. (**b**) The detail of output spectra in (**a**). (**c**) Output spectra at OMCI arm difference \(la=3\) mm. (**d**) Output spectra at OMCI arm difference \(la=5\) mm. Figure 3: (**a**) The numerical results of output spectra of OMCI with temperatures under OMC uniform waist length of 1, 3, and 5 mm. (**b**) Analysis results of temperature sensing response characteristics of OMCI under different uniform waist length L.  
Moreover, it can be seen from Figure 4 that the larger the interferometer arm difference, the shorter the distance d of the typical interference peaks in the envelope. d is only related to the optical path difference between the two arms of the interferometer (d = \(\lambda 1^{\circ}\lambda 2/2/n_{1}/l_{a}\), where \(n_{1}\) is the RI of the fiber core, and \(\lambda 1\), \(\lambda 2\) are the wavelength corresponding to the typical interference peak). When the ambient temperature changes, the two arms of the interferometer will also be affected by the thermo-optic effect and thermal expansion effect. Then the core RI \(n_{1}\) changes to \(\Delta n_{1}\), and the arm difference \(l_{a}\) changes to \(\Delta l_{a}\), which change the phase of the interference signal, that is, the interference peak spacing d changes. Therefore, in theory, temperature sensing can also be achieved by tracking the interference peak spacing in the envelope. The temperature sensitivity corresponding to the change of the interferometric peak spacing can be expressed as:  
\[\left\{ \begin{array}{l}S_{T-\Delta d}=\frac{dd}{dT}=\frac{\partial d}{ \partial\phi}\cdot(\frac{\partial\phi}{dn_{1}}\cdot\frac{dn_{1}}{dT}+\frac{ \partial\phi}{dl_{a}}\cdot\frac{dl_{a}}{dT})\\ dl_{a}=dT\times C_{\text{fec}}\times(L_{2}-L_{1})=dT\times C_{\text{fec}}\times l _{a}\\ dn_{1}=dT\times C_{\text{foc}}\times n_{1}\end{array} \right.