Optical fiber refractive index (RI) sensors have caught widespread attention from researchers in biochemical sensing and environmental monitoring due to their high precision, high sensitivity, resistance to electromagnetic interference, corrosion resistance, low cost, and easy preparation. The commonly employed optical fiber RI sensors currently include surface plasmon resonance, local surface plasmon resonance, fiber Bragg gratings, long-period fiber Bragg gratings, fiber-optic whispering gallery mode, fiber Fabry-Perot sensors, photonic crystal fibers, D-type fibers, and tapered fibers. However, most fiber optic RI sensors are currently single-point sensors and cannot achieve multi-point detection or even distributed sensing. Based on the detection of Rayleigh backscattering spectra (RBS) in optical fiber, optical frequency domain reflectometry (OFDR) features high measurement accuracy, high sensing spatial resolution, and long measurement distance, which makes it very suitable for distributed RI sensing. Distributed RI sensing can not only obtain the RI magnitude in the solution but also locally detect the diffusion processing of the solution and test the distribution of fluids. These are all that single-point sensors or even quasi-distributed sensors cannot achieve.

Traditional distributed RI sensing based on OFDR adopts a cross-correlation demodulation algorithm, which has sound noise suppression ability and stability. However, it is difficult to achieve distributed RI measurements with a micron-level spatial resolution. Therefore, this type of distributed RI sensing based on cross-correlation demodulation is not enough to be applied to distributed biological analysis, drug design, and other fields. Unlike cross-correlation demodulation methods, OFDR based on differential relative phase demodulation realizes sensing by the relative phase change of RBS. Since the differential phase demodulation method directly measures the relative phase change caused by external RI changes, this method is more sensitive than traditional cross-correlation demodulation methods. Therefore, the differential relative phase demodulation method is expected to achieve distributed RI sensing with a micron-level spatial resolution.

We first theoretically analyze the principle of differential relative phase demodulation and the RI sensitivity characteristics. To characterize the theoretical sensitivity of the differential phase demodulation method and compare it with experimental results, we simulate the relationship between phase variation and external RI change at a taper waist of 6 μm. The simulation results are shown in Fig. 1(a), and the slope of 1483.7 rad/RIU is the theoretical sensitivity. Meanwhile, in Eq. (11), Δf is related to taper waist radius r. Therefore, the relationship between theoretical sensitivity and the diameter of the taper waist can be simulated, with the results shown in Fig. 1(b). In the experiment, the phase variations along distance in the sensing area of tapered fiber are compared when only average denoising and wavelet denoising are adopted. This reveals that only average denoising cannot achieve distributed RI sensing at the micron level. Meanwhile, with only wavelet denoising, the phase variations caused by the RI changes in the sensing region with a spatial resolution of 68 μm can be distinguished. However, due to the excessive phase noise in the subfigure of Fig. 5(b), there are still significant fluctuations in the demodulation signal of the sensing region. After average denoising (H=5) and wavelet denoising, phase fluctuation noise can be well suppressed with a sensing spatial resolution of 340 μm. The phase variations along the fiber distance under different RI can be clearly distinguished. The results are shown in Fig. 6(c). A linear fitting curve between phase variations and the external RI change at the effective sensing region is shown in Fig. 6(d) with a linear fit of 0.997. The maximum standard deviation at each RI is 0.0067 rad, and the smoothed measurement sensitivity is 1328.6 rad/RIU, which is close to the simulation results in Fig. 1(b). To compare the difference between the proposed differential phase demodulation method and the traditional cross-correlation demodulation method, we utilize cross-correlation demodulation to the data in Fig. 6. The linear fitting curve of the proposed differential phase demodulation method is better than that of the cross-correlation algorithm. Meanwhile, the standard error of the smoothed differential phase demodulation method is lower than that of the cross-correlation demodulation algorithm. More importantly, compared to the cross-correlation demodulation method, the differential phase demodulation method increases the sensing spatial resolution by 10 times, reaching the level of hundreds of micrometers.

We present distributed RI sensing by tapered fiber based on differential relative phase OFDR. The principle of the proposed method is theoretically analyzed and the sensitivity of phase variations with external RI changes are simulated. In the experiment, we achieve distributed RI sensing with a spatial resolution of 340 μm after average denoising and wavelet smoothing. The effective sensing area is 45 mm. The linear fitting between phase variations and external RI change is 0.997 and the maximum standard deviation at each RI is 0.0067 rad. The experimental RI sensitivity is 1328.6 rad/RIU, close to the simulation result of 1483.7 rad/RIU. The linear fitting and standard deviation of the differential phase method are better than those of the cross-correlation algorithm. More importantly, the sensing spatial resolution is improved by 10 times. The proposed differential relative phase method based on OFDR provides a foundation for achieving micrometer-level distributed biosensing.