## 2 Structural Principle, Detection Mechanism, and Performance Indicators
### Structural Principle of Optical Waveguide Refractive Index Sensing
#### 2.1.2 Refractive Index Sensing Principle of MZI Structure  
The interferometer structure can be divided into several types, such as the MZI, Fabry-Perot interferometer (FPI), and Young interferometer (YI). The MZI is the most commonly used and can be divided into symmetrical and asymmetrical MZI structure considering the symmetry of their two arms.  
Furthermore, the MZI structure shown in Figure 2 includes an input waveguide, an output waveguide, a Y-shaped beam splitter, a Y-shaped coupler, and the sensing and reference arms located between the two Y-shaped junctions, which are constructed by a straight waveguide [17]. In the symmetric MZI, the laser is coupled to the input waveguide, which splits at the Y-junction to form two interferometer arms. The arms recombine at the next Y-junction to form the output waveguide, which then goes through the recombination at the Y-coupler. The sizes of the two arms are the same, and a sensing window with a bare core layer on the sensing arm is used to detect the object under test. It is worth noting that the reference arm is not in contact with the object under test; hence, the phase difference of the wave function in the two arms changes the output optical power. In addition, the characteristic parameters (such as the refractive index) of the material of the object under test on the sensing arm can be obtained. In the asymmetric MZI, the two arms are in contact with the object under test simultaneously; however, the two arm sizes are different; thus, the phase difference of the input light field during transmission causes a change in the output light power to provide a sensing detection.  
MZI sensors typically consist of a laser, light detection unit, sensing arm with an evanescent field sensing window, and reference arm. The light from the laser is coupled to  
Figure 2: MZIs sensor structure diagram.  
the input waveguide and divided into two similar beams at the beam splitter; these two beams travel a certain distance before re-combining at the coupler. Based on the theory of evanescent field sensing, the effective refractive index of the mode transmitted in the sensing arm is altered by the changes in its environment. As a result, phase modulation occurs through the interference of the two arms and generates a phase difference to enable detection. The phase difference \(\Delta\varphi\) can be expressed as follows:  
\[\Delta\varphi=\frac{2\pi}{\lambda}\Delta n_{eff}L, \tag{3}\]  
where \(L\) denotes the sensing window length of the sensing arm. The concentration of the substance under test can be determined by measuring the interference intensity at the output waveguide.  
At present, several novel waveguide structures, such as slot, plasmonic, subwavelength grating slot, metal cladding, and composite waveguides, have been studied. These waveguides have improved the device sensitivity to a certain extent. However, they also increase the complexity of the waveguide design and difficulty of the device fabrication compared to conventional waveguides [18]. The materials used in the waveguide structures include silicon-based optical waveguide materials, chalcogenide compounds, lithium niobate compounds, and polymers [19].