A Refractive Index Sensitive Liquid Level Monitoring Sensor Based on Multimode Interference

According to the beam propagation method, a fiber refractive index-sensitive multimode interference (MMI) structure fabricated by splicing a self-made silica glass rod between two single mode fibers (SMF–NCF (no core fiber)–SMF structure) is proposed for liquid level monitoring. Theoretical and experimental investigation was carried out meticulously using a 4.5 cm and a 9.5 cm long silica glass rod. It is proved that the simple and economical sensor with the shorter length has high sensitivity, satisfactory repeatability, and favorable stability. The sensitivity climbs with the increase in refractive index of the measured liquid, which is 204 pm/mm for pure water, 265.8 pm/mm for 10% glycerin solution, and 352.5 pm/mm for 25% glycerin solution. The proposed sensor can be standardized in certain application circumstances to achieve accurate liquid level monitoring.

For practical application, the fiber-dependent liquid level monitoring sensor plays a significant role in laboratory and engineering conditions, especially in the fuel and petroleum industry, biomedicine, and chemical processing [32,33]. Up to now, a number of techniques associated with liquid level monitoring have been reported. For instance, sensors based on fiber gratings [34], plastic optical fibers [35], interferometers [36], and the local refractive index curved modulation effect [37] have been proposed for this purpose. However, many of them require complicated procedures or structures, or expensive cost to achieve high sensitivity. Therefore, a simple and economical means to realize real-time liquid level monitoring is worth expecting.
In this work, a fiber multimode interference (MMI) structure fabricated by splicing a self-made silica glass rod between two single mode fibers (SMFs) has been proposed to monitor liquid level variation, whose formation is simple and costless. After rigorous theoretical analysis and experimental verification, the sensor is proved to have high sensitivity, satisfactory linearity, and repeatability, which can be standardized in certain circumstances to realize fast and high-accuracy measurement, and can be further applied in the engineering, chemistry, and biology fields.

Fabrication and Principle
The designed liquid level sensor is fabricated by splicing a length of self-made silica glass rod between two SMFs, as shown in Figure 1a. The cross-section of the silica glass rod is presented in Figure 1b, whose diameter is about 125 μm. During light transmission, the input light initially enters into the lead-in SMF (left) and transmits as the fundamental mode. The silica glass rod can be regarded as a no core fiber, and the light is spliced into multiple high-order modes at the left fusion point. After transmitting through the rod, light in numerous directions converges at the right fusion point to a core fundamental mode and forms an interference spectrum at the end of the lead-out SMF.
Differing from other multimode fibers, the no core fiber itself acts as a fiber core, and the surrounding environment plays the role of cladding. If the sensor is immersed into liquid, the external refractive index of the rod section will be determined by the liquid refractive index and the air refractive index, and the immersing depth would play an extremely important role. When the liquid level changes, the external refractive index of the sensing part alters correspondingly, which means the cladding refractive index and mode coupling changes, resulting in a shift of the interference spectrum. Based on it, a liquid level monitoring sensor is put forward, as shown in Figure  1c. The intensity of the interference spectrum (I) can be expressed as the following formula [38]: where and are the intensity of any two-order mode involved in the interference, is the phase difference between the two modes, and and are their effective refractive indices, respectively. L is the length of the silica glass rod and is the free space wavelength of the input light. From this formula, we can see clearly that I is under the direct influence of L, which impacts the mode distribution and interference. Therefore, by observing the variation of the spectrum intensity, liquid level change can be monitored.

Numerical Analysis
The transmission properties of the MMI are simulated based on the beam propagation method (BPM). The core refractive index of the SMFs is 1.45, the cladding refractive index 1.445, and the length 1 cm. The length of the silica glass rod is selected to be 4.5 or 9.5 cm, and its refractive index is assumed to be 1.45. The liquid refractive index (nliquid) is set to be 1.33, and the immersing depth grows from 1 to 1.4 cm with a step size of 2 mm. During the numerical simulation, the material dispersion induced by silica Sellmeier coefficients was not taken into consideration due to its limited influence. Figure 2 demonstrates the simulated transmission property of MMI using a 9.5 cm long silica glass rod. In Figure 2a, it is clear that light is, at first, confined to the core of the lead-in SMF. After entering into the silica glass rod, various modes are excited and couple with each other to fluctuate regularly between the maximum and minimum. In other words, with the different length of the no core fiber, the distribution of the optical field will periodically reproduce, which is the self-imaging effect [39,40]. Finally, the light returns to the lead-out SMF, and due to the different mode coupling condition, the light intensity varies slightly at different wavelengths, which produces an interference spectrum. Figure 2b presents the output light intensity at different free space wavelengths and the evolution of the interference spectrum when the immersing depth rises by 4 mm. We can see that with the increase in liquid level, the interference spectrum tends to red shift and the sensitivity mounts to 300 pm/mm.   Figure 2, it can be seen that a shorter MMI structure brings about less interference peaks but the sensitivity is enhanced to 400 pm/mm. This is because the increased length enlarges the loss, resulting in a rising number of loss peaks in the transmission spectrum, which is adverse to the sensing sensitivity. In addition, to simulate different liquid detection environments, we adjust the liquid refractive index to 1.36 and 1.39 and analyze, respectively, the sensitivities, as shown in Figure 4. There is no doubt that the sensitivity climbs with the increase in the liquid refractive index, and 400 pm/mm for nliquid = 1.333, 500 pm/mm for nliquid = 1.36, and 800 pm/mm for nliquid = 1.39. This is because the larger the liquid refractive index, the more significant the contrast with the air, and in turn, the more sensitive the mode coupling is to the liquid/air interface, which finally leads to a higher sensitivity to liquid level monitoring.

Experimental Results and Discussion
The experimental setup is shown in Figure 5. Light was emitted by an ASE (amplified spontaneous emission) light source passed through the designed MMI-based sensor, which was immersed in the measured liquid. The output light was collected by an optical spectrum analyzer (OSA: Yokogawa AQ6375B) to monitor the interference spectrum. For fabrication of the MMI-based sensor, we firstly used a wire stripper to remove the coating layer of the single mode fiber, and used a cutting knife (CT-50, Fujikura) to make the fiber tip flat. After selecting an appropriate length of silica rod according to the liquid level, an optical fiber fusion machine (S179c, Furukawa) was used for the connection of the fiber rod and single mode fibers. During the fusion process, a built-in program (single mode-multimode, SM-MM) was used, and each fiber was cleaned with alcohol before fusion.  Figure 6 presents the respective sensing properties when using different NCF lengths (4.5 and 9.5 cm) during the measurement of pure water (nliquid = 1.333). We can see that the longer NCF is superior to the shorter one in terms of visibility of the fringe pattern and the number of the interference peaks, and as the liquid level went up, the interference spectrum moved towards the longer wavelength. According to Equations (1) and (2), the intensity of interference spectrum depends on the intensity of the existing modes and their phase difference. With the increasing liquid level, the effective refractive index difference decreases, bringing about a decrease in phase difference ( ) and a spectral shift to the right. The spatial frequency information of the interference spectrum of the MMI structures with different silica glass rod lengths was obtained using Fast Fourier Transform (FFT), as shown in Figure  7a. In comparison, the longer MMI structure has more peaks in frequency domain space, which means it has more cladding modes to interfere and an increasing number of interference peaks and dips. The respective sensitivity of the MMI-based sensor using different silica glass rod lengths is shown in Figure 7b. We can see clearly that the sensor using the shorter MMI length (4.5 cm) has a sensitivity twice higher than that of the other one (9.5 cm), which is 204 pm/mm for the former and 106 pm/mm for the latter. Thus, the increasing number of interference peaks and the larger modulation depth of the longer MMI length were not conductive to improving sensitivity. This conclusion is consistent with the theoretical simulation result. The 4.5 cm long MMI was selected for the following discussion.  Figure 8a gives information about the sensitivities of two varying interference dips, namely, Dip A and Dip B in Figure 6b. It can be seen that the sensitivity of Dip A is 204 pm/mm, and that of Dip B is 158 pm/mm. This sensitivity disparity of the dips in the experiment resulted from the existence of a surface evanescent field induced by various higher order modes. The external environment refractive index would affect the higher order modes to numerous extents, and the loss of these modes is different. When modes interfere with each other, dips will be formed and affected by the diverse interference conditions. Therefore, when the external environment changes, different dips would have different sensitivities. The ideal simulation fails to take these complexities into consideration. Because the sensing sensitivity decreases with the blue shift of the dip position, thus Dip A is chosen for sensitivity calibration of the liquid level monitoring sensor. Repeatability of this sensor is verified, as shown in Figure 8b. It is clear that during the rising up and falling down of the liquid level, the sensitivity only exhibits a slight fluctuation, which is 204 and 196 pm/mm (Dip A@ 4.5 cm length), respectively. Consequently, the designed sensor is experimentally proved to have satisfactory repeatability.  Figure 9 illustrates the stability of the sensor, and a 10 cm high liquid level test was repeated five times. The mean wavelength of the interference spectrum Dip A is 1589.34 nm, and the standard deviation is 0.055, which shows a fine stability. Furthermore, for the response time of the sensor, spectrum changes were observed by OSA after adjusting the liquid level. After a few scanning cycles, the response time is measured to be about five to six seconds when the liquid level increases. This value rises a little bit as the liquid level drops, since when the liquid level decreases, there is some residual liquid on the surface of the sensor and it takes more time for the liquid to fall back. Apart from the liquid level detection of pure water, the designed sensor was also used to measure a glycerin solution with a volume fraction of 10% and 25% to test its sensing property. Figure  10 illustrates the respective sensitivities, which is 204 pm/mm for pure water, 265.8 pm/mm for the 10% glycerin solution, and 352.5 pm/mm for the 25% glycerin solution. The refractive index of the glycerin solution is larger than that of pure water, and its value climbs with the increase in glycerin volume fraction [41], as does the sensitivity of the MMI-based sensor. As a matter of fact, as long as the test liquid has a refractive index lower than that of the fiber, the proposed sensor can exhibit a good performance in detecting its liquid level change. If the refractive index of the liquid surpasses that of the fiber MMI structure, light would leak to the liquid based on optical transmission theory, leading to a detection failure. As is evidenced by all the figures released above, the goodness of fit (R 2 ) concerning each linear fit line is larger than 0.97, which means the sensor has satisfactory linearity and accuracy. In this experiment, we used a shorter MMI structure to achieve higher sensitivity, but this did not mean the shorter the better. A shorter length would naturally limit the sensing range, which would mutually restrict the sensitivity and the measuring range. Therefore, in field applications, the MMI length needs to be adjusted according to the actual environment. Meanwhile, surface cleaning of the sensor should be taken into consideration to avoid measuring errors. Table 1 presents a comparison of the designed sensor and other liquid level sensors reported previously, which highlights the advantages such as high sensitivity and wide measuring range aside from its easy fabrication.

Conclusions
In summary, a refractive index-sensitive liquid level monitoring sensor was proposed based on a fiber MMI, and theoretical and experimental investigation was carried out in detail in this work. The influence of the NCF length and liquid refractive index on the sensing sensitivity was analyzed with discretion. By comparing the performance of sensors made by different silica glass rod lengths (4.5 and 9.5 cm), it is proved that the sensor with the shorter length had high sensitivity, satisfactory repeatability, and favorable stability. The sensitivity of the proposed sensor climbed with the increase in refractive index of the measured liquid, which was 204pm/mm for pure water, 265.8 pm/mm for 10% glycerin solution, and 352.5 pm/mm for 25% glycerin solution. The theoretical analysis was consistent with the experimental results. The proposed sensor can be standardized in certain application circumstances to achieve fast and accurate liquid level monitoring, which can be applied in the engineering, chemistry, and biology fields.