## 2 The Fabrication and Sensing Principle of OMCI
### Sensing Mechanism  
OMCI proposed in this paper is a hybrid sensing device. There are two sensing units, one is the waist region with evanescent field transmission capability, and the other is the sensing arm of the interferometer. The OMC plays a leading role in the spectral transmission characteristics of hybrid devices, and is more sensitive to the external environment. Therefore, it is generally more effective to select OMC as the sensing unit of OMCI, and the interferometer sensing arm is only used as the light reflection and sensitizing unit. OMC characteristic can be analyzed by local coupling mode theory, that is, the total coupling of OMC is the superposition of each local coupling [1]. When the \(P_{0}\) incident power is injected into the port1, the output light intensity of the port3 and port4 is expressed as [14; 15; 16; 21]:  
\[ \begin{split} P_{3}&=P_{0}\cos^{2}(\int_{0}^{l}c( \lambda,n_{2},n_{3},z)dz)=P_{0}\cos^{2}\varphi\\ P_{4}&=P_{0}\sin^{2}(\int_{0}^{l}c(\lambda,n_{2},n_ {3},z)dz)=P_{0}\sin^{2}\varphi\end{split}  \tag{1}\]  
where \(l\) represents the coupling length, \(c(\lambda,n_{2},z)\) is the coupling coefficient in location z. For the fusing and tapering OMC, the thinner tapered transition region and uniform waist region plays a leading role in the coupling characteristics [2; 19]. Under the condition of strong coupling, the coupling coefficient \(c\) is expressed as [7; 17; 18]:  
\[c(\lambda,n_{2},n_{3},z)=\frac{3\pi\lambda}{32n_{2}r^{2}}\times\frac{1}{\left( 1+1/V\right)^{2}} \tag{2}\]  
where \(V=[(2\pi r)/\lambda](n_{2}^{2}-n_{3}^{2})^{1/2}\) is normalized frequency, \(\lambda\) is incident light wavelength, \(r\) is the radius of the microfiber at the waist region, \(n_{2}\) (1.4682 at wavelength of 1550 nm) and \(n_{3}\) (determined  
Figure 1: (**a**) The schematic diagram of the optic microfiber coupler (OMC). (**b**) Optical microfiber coupler interferometer (OMCI) is composed by connecting Faraday rotator mirrors (FRM) at port3 and port4 of OMC, respectively, the amplified spontaneous emission (ASE) broadband light source inject to port1 and monitoring the signal from port 2 by using the optical spectrum analyze. (**c**) Microscopic image of the OMC waist region. by temperature, salinity, pressure and wavelength) are the refractive indexes (RIs) of fiber cladding (silica) and external environment (sea water) respectively. For OMCI, the detection light is injected to the port1 of OMCI, after the first coupling, it will be output from the port3 and port4. The output light of the port3 and port4 will be reflected by the FRMs and reenter the OMC coupling region, and then occur coupling and superimpose interference. Assuming that the reflection efficiency of FRM is 100%, then the output light intensity at port2 can be expressed as:  
\[P_{2}=2P_{0}\cos^{2}\varphi\sin^{2}\varphi(1+\cos\phi) \tag{3}\]  
where \(\phi=2\pi n_{2}l_{a}/\lambda\) represents the phase difference indicating interference, \(l_{a}\) is the interferometer arm difference. According to Equations (1)-(3), when the environment temperature changes (\(n_{3}\) varies), or the OMC structural parameters (such as \(r\), \(l\), \(n_{3}\), etc.) are changed by the temperatures, the characteristic spectrum of OMCI will be modulated. The \"interfered\" detected light carrying environmental information will be output from the port 2 of OMC. Therefore, the ambient temperature can be monitored by monitoring the change of the OMCI reflective spectrum. If the waist region of OMCI is placed in seawater (OMC is selected as the sensing unit, the interferometer sensing arm does not participate in the sensing response), with the seawater temperature changes, the thermo-optic effect and thermal expansion effect of the optical fiber will cause the cladding RI \(n_{2}\) change to \(\Delta n_{2}\), the coupling length \(l\) change to \(\Delta l\), and the microfiber waist radius \(r\) change to \(\Delta r\). In addition, change of seawater temperature will also cause their RI \(n_{3}\) change to \(\Delta n_{3}\).