Ultra-Sensitive Fiber Refractive Index Sensor with Intensity Modulation and Self-Temperature Compensation

In this paper, a novel in-line modal interferometer for refractive index (RI) sensing is proposed and experimentally fabricated by cascading single-taper and multimode-double- cladding-multimode (MDM) fiber structure. Owing to evanescent field in taper area, the ultra-sensitive and linear intensity-responses to the varied surrounding RI are gained in both single- and double-pass structures. Moreover, the crosstalk from temperature can be effectively discriminated and compensated by means of the RI-free nature of MDM. The experimental results show that the RI sensitivities in single- and double-pass structures, respectively, reach 516.02 and 965.46 dB/RIU (RIU: refractive index unit), both with the slight wavelength shift (~0.2 nm). The temperature responses with respect to wavelength and intensity are 68.9 pm°C−1/0.103 dB°C−1 (single-pass structure) and 103 pm°C−1/0.082 dB·°C−1 (double-pass structure). So the calculated cross-sensitivity of intensity is constrained within 8.49 × 10−5 RIU/°C. In addition, our sensor presents high measurement-stability (~0.99) and low repeatability error (<4.8‰). On account of the ~620 μm size of taper, this compact sensor is cost-efficient, easy to fabricate, and very promising for the applications of biochemistry and biomedicine.

Comparatively, intensity modulation based RI sensors are more practical but it is rarely reported that they can be implemented by a cost-effective power meter [18,23]. Zhou et al. proposes an offset-core thin-core fiber (TCF) based structure and the sensitivity of −202.46 dB/RIU is obtained [24]. To enhance

Principle and Fabrication
The TMDM with a single-pass (SP) structure is illustrated in Figure 1, which includes two short-length MMFs (denoted by MMF-1 and MMF-2, respectively), a piece of tapered SMF, and a section of double-cladding fiber (DCF, SM-9/105/125-20A, Nufern, Hartford, CT, USA). In particular, the fiber-core and two fiber-claddings (inner-cladding and outer-cladding) diameters of the adopted DCF are 9, 105, and 125 µm, respectively. The matched MMFs are chosen with the fiber-core and fiber-cladding diameters of 105 and 125 µm. Therefore, the incident light from the taper area is split by MMF-1 with the ratio of κ 1 and propagates in the fiber-core and fiber-cladding. The guide mode and excited cladding modes are recoupled by MMF-2 with the ratio κ 2 . Because the phase delay (denoted by ∆φ) caused by the RI difference of the fiber-core mode and fiber-cladding mode, a stable in-line Mach-Zehnder interferometer (MZI) is formed. It is well known that its transmitted intensity can be described by I = I co + I cl + 2 I co I cl cos(∆ϕ) (1) where I co and I cl are the intensities of the fiber-core and fiber-cladding modes, respectively. ∆φ can be written as where n co , n cl , and ∆n eff are the effective RI of the fiber-core mode, the effective RI of fiber-cladding mode, and the effective RI difference of the fiber-core and fiber-cladding modes, respectively. L and λ are the DCF length and the incident light wavelength, respectively. When the condition ∆φ = (2m + 1)π, the interference dip wavelength (λ dip ) of the spectrum will be where m is an integer. Note that, the modal interference generates just between the fiber-core mode and the inner-cladding mode because of the limitation of MMF-1. In addition, the incident light will extensively leak into the cladding and air in taper area due to the evanescent field. Moreover, this loss will increase with the rise of SRI according to [32]. This means the introduced single-taper can be used as an attenuator related to SRI. extensively leak into the cladding and air in taper area due to the evanescent field. Moreover, this loss will increase with the rise of SRI according to [32]. This means the introduced single-taper can be used as an attenuator related to SRI. Here we define the loss factor as α(n) and assume κ1=κ2=κ, Equation (1) is then modified by n co co n co n co co n co I I Furthermore, the normalized fringe visibility is defined as: Equation (5) shows that, for the given κ the value of V is proportional to ) (n α and that means an RI sensing test with intensity modulation can be achieved by the proposed SP structure. In fabrication, both ends of a 45-mm long DCF are firstly spliced with two sections of MMF (MM-S105/125-22A, Nufern, Hartford, CT, USA) by a commercial fusion splicer (FSM-100P, Fujikura, Tokyo, Japan) and keep the length of MMF are about 0.4 mm by cutting to avoid the possible multimode interference. Then the formed MDM structure is respectively spliced with two pieces of SMF (Corning SMF-28) as the lead-in and lead-out fibers. Finally, an adiabatic taper locating at the middle of lead-in SMF is completed by the arc-discharge technique. In detail, the power of predischarge and main-discharge are 30 bits and 80 bits, and the corresponding discharge times are 150 and 2,200 ms, respectively. The waiting time and the speed of welding are 1,200 ms and 0.15 μm/ms, respectively. From Figure 2(a), the symmetric transitions are demonstrated with the length of ~311.3 μm and the waist-diameter is dw = 28.5 μm. Further, the cross-sectional morphology of DCF and the transmission spectrum of the SP structure (in air) are also given in Figure 2(b) and (c). Obviously, there are two fringes, respectively, located at 1,541 and 1,555 nm (denoted by dip-1 and dip-2) with the visibilities of 22.5 and 16.4 dB. In addition, the interval spacing between dip-1 and dip-2 is about 14 nm. Here we define the loss factor as α (n) and assume κ 1 = κ 2 = κ, Equation (1) is then modified by Furthermore, the normalized fringe visibility is defined as: Equation (5) shows that, for the given κ the value of V is proportional to √ α (n) and that means an RI sensing test with intensity modulation can be achieved by the proposed SP structure. In fabrication, both ends of a 45-mm long DCF are firstly spliced with two sections of MMF (MM-S105/125-22A, Nufern, Hartford, CT, USA) by a commercial fusion splicer (FSM-100P, Fujikura, Tokyo, Japan) and keep the length of MMF are about 0.4 mm by cutting to avoid the possible multimode interference. Then the formed MDM structure is respectively spliced with two pieces of SMF (Corning SMF-28) as the lead-in and lead-out fibers. Finally, an adiabatic taper locating at the middle of lead-in SMF is completed by the arc-discharge technique. In detail, the power of pre-discharge and main-discharge are 30 bits and 80 bits, and the corresponding discharge times are 150 and 2200 ms, respectively. The waiting time and the speed of welding are 1200 ms and 0.15 µm/ms, respectively. From Figure 2a, the symmetric transitions are demonstrated with the length of~311.3 µm and the waist-diameter is d w = 28.5 µm. Further, the cross-sectional morphology of DCF and the transmission spectrum of the SP structure (in air) are also given in Figure 2b,c. Obviously, there are two fringes, respectively, located at 1541 and 1555 nm (denoted by dip-1 and dip-2) with the visibilities of 22.5 and 16.4 dB. In addition, the interval spacing between dip-1 and dip-2 is about 14 nm.

Experiments and Results
The experimental setup is shown in Figure 3. The fixed sensor head is connected to a broadband source (BBS, homemade, working in 1,520-1,565 nm) and an OSA (Agilent 86142 B, resolution: 0.06 nm/0.01 dB, Palo Alto, CA, USA). We prepare glycerol solutions with different concentrations and

Experiments and Results
The experimental setup is shown in Figure 3. The fixed sensor head is connected to a broadband source (BBS, homemade, working in 1520-1565 nm) and an OSA (Agilent 86142 B, resolution: 0.06 nm/0.01 dB, Palo Alto, CA, USA). We prepare glycerol solutions with different concentrations and then perform a comprehensive RI test at room temperature of 24 ± 0.5 • C. Note that, the RI of glycerol solution is collimated using an Abbe refractometer before each test. We drip the glycerin solution on the sensor head and record the spectrum. The sensor head is thoroughly cleaned with anhydrous ethyl alcohol after each recording of the spectrum.

Experiments and Results
The experimental setup is shown in Figure 3. The fixed sensor head is connected to a broadband source (BBS, homemade, working in 1,520-1,565 nm) and an OSA (Agilent 86142 B, resolution: 0.06 nm/0.01 dB, Palo Alto, CA, USA). We prepare glycerol solutions with different concentrations and then perform a comprehensive RI test at room temperature of 24 ± 0.5 °C. Note that, the RI of glycerol solution is collimated using an Abbe refractometer before each test. We drip the glycerin solution on the sensor head and record the spectrum. The sensor head is thoroughly cleaned with anhydrous ethyl alcohol after each recording of the spectrum. Here dip-1 is selected to monitor the variation of SRI due to its larger visibility. From Figure 4(a), the intensity of dip-1 is quickly increased with the added solution concentration. By calculation the total increment reaches 12.988 dB (from -67.544 to -54.556 dB) in the range of 1.3325~1.3565 RIU. Figure  4(b) presents an intensity response of 519.71dB/RIU is obtained with high linearity. On account of 0.01-dB resolution, the detection limit of SP structure is 1.92 × 10 -5 RIU. Comparatively, dip-1 merely shifts about -0.2 nm (from 1,540.8 to 1,540.6 nm). Since the isolation of the outer cladding of the DCF makes the DCF region insensitive to the SRI, and the energy loss of the taper increases as the SRI increases, only the power in the received spectrum is affected by an RI change without the wavelength shift. In addition, the repeatability test is conducted and the solution concentration is increased (decreased) by adding the ratio of glycerol (distilled water). As shown in the insets of Figure  5, the intensity variations of fringe visibility present a high consistence for the increased and decreased concentrations of glycerol solution. In the range of 1.335-1.358, the intensity sensitivities of 520.96 and 518.47 dB/RIU with high linearity (>0.99) are gained for the rising and reducing of SRI, respectively. By calculation the repeatability error of our sensor is ~4.8‰. Here dip-1 is selected to monitor the variation of SRI due to its larger visibility. From Figure 4a, the intensity of dip-1 is quickly increased with the added solution concentration. By calculation the total increment reaches 12.988 dB (from −67.544 to −54.556 dB) in the range of 1.3325~1.3565 RIU. Figure 4b presents an intensity response of 519.71 dB/RIU is obtained with high linearity. On account of 0.01-dB resolution, the detection limit of SP structure is 1.92 × 10 −5 RIU. Comparatively, dip-1 merely shifts about −0.2 nm (from 1540.8 to 1540.6 nm). Since the isolation of the outer cladding of the DCF makes the DCF region insensitive to the SRI, and the energy loss of the taper increases as the SRI increases, only the power in the received spectrum is affected by an RI change without the wavelength shift. In addition, the repeatability test is conducted and the solution concentration is increased (decreased) by adding the ratio of glycerol (distilled water). As shown in the insets of Figure 5, the intensity variations of fringe visibility present a high consistence for the increased and decreased concentrations of glycerol solution. In the range of 1.335-1.358, the intensity sensitivities of 520.96 and 518.47 dB/RIU with high linearity (>0.99) are gained for the rising and reducing of SRI, respectively. By calculation the repeatability error of our sensor is~4.8% .

Sm+3σ
) and the proposed sensor presents a high stability. Therefore, the mean resolution of SP structure is 1.938 × 10 -5 RIU.  In order to quantify crosstalk, the temperature response is also investigated by placing the sensor head into an electric thermostat. The inset of Figure 7 shows that the fringe dip has a clear red-shift as the temperature increasing from 25 °C to 55 °C. From Figure 7, a linear relation is found and the sensitivity is ~68.9 pm/°C. Comparatively, there is a slight increase for the fringe intensity when the temperature is increased and the calculated sensitivity is ~0.103 dB/°C. So the intensity error caused by temperature cross-sensitivity is 1.98 × 10 −4 RIU/°C when non-temperature-compensation is employed.  In order to quantify crosstalk, the temperature response is also investigated by placing the sensor head into an electric thermostat. The inset of Figure 7 shows that the fringe dip has a clear red-shift Sensors 2019, 19, 3820 6 of 10 as the temperature increasing from 25 • C to 55 • C. From Figure 7, a linear relation is found and the sensitivity is~68.9 pm/ • C. Comparatively, there is a slight increase for the fringe intensity when the temperature is increased and the calculated sensitivity is~0.103 dB/ • C. So the intensity error caused by temperature cross-sensitivity is 1.98 × 10 −4 RIU/ • C when non-temperature-compensation is employed. In order to quantify crosstalk, the temperature response is also investigated by placing the sensor head into an electric thermostat. The inset of Figure 7 shows that the fringe dip has a clear red-shift as the temperature increasing from 25 °C to 55 °C. From Figure 7, a linear relation is found and the sensitivity is ~68.9 pm/°C. Comparatively, there is a slight increase for the fringe intensity when the temperature is increased and the calculated sensitivity is ~0.103 dB/°C. So the intensity error caused by temperature cross-sensitivity is 1.98 × 10 −4 RIU/°C when non-temperature-compensation is employed. Figure 7. The wavelength and intensity responses with varied temperature. Inset: transmission spectra of SP structure. Furthermore, to further enhance sensitivity, the sensing characteristics of TMDM with double-pass (DP) structure are experimentally performed. As shown in Figure 8, in DP structure, the light beams will be reflected by a well-cut end-face of DCF and pass through the taper area again. This surely  Furthermore, to further enhance sensitivity, the sensing characteristics of TMDM with double-pass (DP) structure are experimentally performed. As shown in Figure 8, in DP structure, the light beams will be reflected by a well-cut end-face of DCF and pass through the taper area again. This surely brings a twice-loss and leads a doubled sensitivity improvement. A new DP-based sample is fabricated with a shorter DCF length (~23.5mm) and a similar waist-diameter (d w = 28.8 µm) for discrimination.
Sensors 2019, 19, x FOR PEER REVIEW 7 of 11 brings a twice-loss and leads a doubled sensitivity improvement. A new DP-based sample is fabricated with a shorter DCF length (~23.5mm) and a similar waist-diameter (dw = 28.8 μm) for discrimination. The DP structure is connected with BBS and OSA by a circulator and its RI response is measured and presented in Figure 9. The inset shows that the DP structure has a much quicker intensity increase when the SRI is rising but with a ~8.5-dB reduction of visibility maybe due to the loss of the fibercore mode at the reflected end-face. In detail, the total increment is 8.455 dB in the range of 1.33~1.339 RIU and the corresponding intensity sensitivity reaches 965.46dB/RIU with a linearity of 0.989. Moreover, the maximum value of wavelength drift is merely ~0.12 nm. Thus, approximately 1.85time enhancement of detection limit (1.036 × 10 -5 RIU) is gained in the DP structure. Note that the actual sensitivity is not fully doubled possibly due to the fabricated taper difference in terms of length and waist-diameter [26]. In addition, the measurement range of the proposed sensor increases as the fringe visibility increases, and the fringe visibility is related to the waist-diameter and length of the taper. Therefore, the measurement range can be expanded by appropriately adjusting the waistdiameter and length of the taper. For comparison, the temperature response of DP structure is also measured and demonstrated in Figure 10. The inset shows a clear red-shift with the added temperature but the increased intensity is merely 0.849 dB in the range of 25~35 °C. The temperature sensitivity with respects to wavelength and intensity are 103.3 pm/°C and 0.082 dB/°C with a linearity of 0.985. So the intensity crosstalk from the temperature is further restrained within 8.49 × 10 −5 RIU/°C in the DP structure.  The DP structure is connected with BBS and OSA by a circulator and its RI response is measured and presented in Figure 9. The inset shows that the DP structure has a much quicker intensity increase when the SRI is rising but with a~8.5-dB reduction of visibility maybe due to the loss of the fiber-core mode at the reflected end-face. In detail, the total increment is 8.455 dB in the range of 1.33~1.339 RIU and the corresponding intensity sensitivity reaches 965.46dB/RIU with a linearity of 0.989. Moreover, the maximum value of wavelength drift is merely~0.12 nm. Thus, approximately 1.85-time enhancement of detection limit (1.036 × 10 −5 RIU) is gained in the DP structure. Note that the actual sensitivity is not fully doubled possibly due to the fabricated taper difference in terms of length and waist-diameter [26]. In addition, the measurement range of the proposed sensor increases as the fringe visibility increases, and the fringe visibility is related to the waist-diameter and length of the taper. Therefore, the measurement range can be expanded by appropriately adjusting the waist-diameter and length of the taper. For comparison, the temperature response of DP structure is also measured and demonstrated in Figure 10. The inset shows a clear red-shift with the added temperature but the increased intensity is merely 0.849 dB in the range of 25~35 • C. The temperature sensitivity with respects to wavelength and intensity are 103.3 pm/ • C and 0.082 dB/ • C with a linearity of 0.985. So the intensity crosstalk from the temperature is further restrained within 8.49 × 10 −5 RIU/ • C in the DP structure.
Sensors 2019, 19, 3820 7 of 10 diameter and length of the taper. For comparison, the temperature response of DP structure is also measured and demonstrated in Figure 10. The inset shows a clear red-shift with the added temperature but the increased intensity is merely 0.849 dB in the range of 25~35 °C. The temperature sensitivity with respects to wavelength and intensity are 103.3 pm/°C and 0.082 dB/°C with a linearity of 0.985. So the intensity crosstalk from the temperature is further restrained within 8.49 × 10 −5 RIU/°C in the DP structure.   Further, the variations of RI and temperature in DP structure can be discriminated by the inversion matrix method [28], which can be described as where ∆n and ∆T are the variations of RI and temperature, respectively. ∆λ and ∆I are the wavelength shift and intensity change. D = kλTkIn-kITkλn , where kλT = 0.103, kλn = 0 are wavelength sensitivities of temperature and RI in the DP structure, kIn = 965.46, kIT = 0.082 are intensity sensitivities of RI and temperature in the DP structure. Consequently, the matrix will be changed as and the measurement of RI without the crosstalk of temperature can be completed. Table 1 compares the various fiber RI sensors with our schemes (Note, the resolution of receivers in calculation are the same with 0.06 nm/0.01 dB). It is obvious that the competitive sensitivities are presented in both SP and DP structures. A near 1 × 10 3 dB/RIU is gained by the DP structure and is only slightly lower than the result reported in [30] but it has a better linearity (0.989) in the range from 1.33 to 1.339 RIU. Besides, on account of the self-temperature compensation and ultra-small size (~620 μm), our schemes have potential and are suitable to be integrated and applied in biochemical fields, such as lab-on-chip.  Further, the variations of RI and temperature in DP structure can be discriminated by the inversion matrix method [28], which can be described as where ∆n and ∆T are the variations of RI and temperature, respectively. ∆λ and ∆I are the wavelength shift and intensity change. D = k λT k In − k IT k λn , where k λT = 0.103, k λn = 0 are wavelength sensitivities of temperature and RI in the DP structure, k In = 965.46, k IT = 0.082 are intensity sensitivities of RI and temperature in the DP structure. Consequently, the matrix will be changed as and the measurement of RI without the crosstalk of temperature can be completed. Table 1 compares the various fiber RI sensors with our schemes (Note, the resolution of receivers in calculation are the same with 0.06 nm/0.01 dB). It is obvious that the competitive sensitivities are presented in both SP and DP structures. A near 1 × 10 3 dB/RIU is gained by the DP structure and is only slightly lower than the result reported in [30] but it has a better linearity (0.989) in the range from 1.33 to 1.339 RIU. Besides, on account of the self-temperature compensation and ultra-small size (~620 µm), our schemes have potential and are suitable to be integrated and applied in biochemical fields, such as lab-on-chip.

Conclusions
In conclusion, a compact RI sensor is experimentally fabricated and demonstrated by cascading the tapered SMF and multimode-double-cladding-multimode fiber structure and the performance of SP and DP based structures are measured and compared in terms of RI and temperature responses. Experimental results show that only the taper area (~620 µm) is sensitive to the varied SRI by an intensity modulation. Owing to the introduced twice-loss, the sensitivity of near 1 × 10 3 dB/RIU is gained in the DP structure with a high linearity (>0.989) and low wavelength-shift. The corresponding detection resolution is 1.036 × 10 −5 RIU and by the inversion matrix method, the measurement of RI without the crosstalk of temperature can be completed. More importantly, the proposed sensor presents a high practicality in terms of repeatability and stability. Therefore, such a compact and stable sensor with self-temperature compensation and ultrahigh linear sensitivity is very promising in high-resolution biochemical sensing.