## 3 Results and Discussions  
The simulations of the phase variation \(\Delta\phi\) versus RI of the tested liquid medium, ranging from 1.333 to 1.343 refractive index units (RIU) for different incident angles to the surface of the KTP plate (\(\theta_{i}=40^{\circ}\)-\(50^{\circ}\)), are shown in Figure 3a. The sensitivity of the RI sensor is defined as a slope of the phase curve as shown in Figure 3b. The unit of RI measurement sensitivity is deg./RIU. The sensitivity is increased with the increased incident angle. The linearity is still good for the higher incident angles. Figure 3: **(a)** Phase change versus RI for different incident angles in a small dynamic range; **(b)** Sensitivity (deg./RIU) versus RI. Figure 2: Measurement setup for the fluidic concentration of solution in a homodyne interferometer. Figure 4a shows the phase variation versus RI in a wide dynamic range from 1.30 to 1.50 RIU. The values of sensitivity are dependent on the incident angles and RI regions as shown in Figure 4b. The higher incident angle and larger RI enhance the sensitivity. Because of the relaxed incident angle conditions, its flexibility permits adjustment of the sensitivity for measurements on different levels of concentrations. The sensitivity and linearity on the wide measuring RI range is a tradeoff at the increased incident angle. In a practical application, the nonlinear phase response needs a correction factor to recover the correct measurements. Since the probe beam is focused with a diameter of around 0.2 mm, it is still possible to induce an additional phase shift caused by the photorefractive effects in the KTP plates. At the probe power of 25 \(\mu\)W and a measurement period of 2250 s, the long-term phase variations \(\Delta\phi\) in the FBS are within one (degree) with fluidic de-ionized water (DI) at a flow rate of 30 sccm (mL/min), as shown in Figure 5a. The root mean square error (RMSE) of the measured phase data is used to express the phase stability in the measurements. The short-term stability possibly reached 0.2 (degree) during the measurement period of 100 s (200 data points), as shown in Figure 5b. The photo-induced phase variations of the KTP plate will change the initial phase values. It needs a reference injection liquid to obtain the initial phase for providing the reference baseline. The phase variations in the KTP plate are mainly dependent on the wavelengths of incident light and the input powers. The approach to reduce the photorefractive impacts can be considered to reduce the input powers by using a higher-sensitivity photodetector. Besides, the probe light with a longer wavelength (>632.8 nm) is possible to improve the phase stability. Figure 4: **(a)** Phase change versus RI for different incident angles in a wide dynamic range; **(b)** Sensitivity (deg./RIU) versus RI. Figure 5: Phase stability measurements: **(a)** long-term period and **(b)** short-term period. To study the measurement performance depending on the cell sizes, two different designs (Figure 6) are proposed to compare the phase variation profiles under the exchanged liquids between DI and salt water (SW). A quasi-linear dependence of the RI change of the salt solution's concentration (wt. %) is possible [25]. Various RIs can be adjusted by mixing with different weights of water and salt. According to the simulations in Figure 3, the phase variations are expected to have a linear dependence on the concentration. Because of the FBS's cylindrical shape, it is easy to distort the probe beam. The cylindrical lens (CL) is used to focus the transmitted beams onto the PD. There, the large cell has a 28 mm diameter and a height of 16 mm. The small one has a 14 mm diameter and a height of 16 mm. The KTP plates are the same dimensions as used in the two different cells. The length and width of the KTP plate are 8 mm, and the thickness is 1 mm. The KTP plate is placed on the center of cell. The flow rate is 30 sccm (mL/min) from the tubing pump for both cells.