High-current measurement technology is widely used in the field of industry, quality inspection, national defense, and large scientific facilities. The current up to dozens or hundreds of kA and even MA magnitude requires to be accurately measured for the process control, performance test, energy consumption reduction, and key scientific research. The fiber-optic high-current sensor based on the Faraday effect exhibits many attractive features in this field, including high accuracy, wide bandwidth, immunity to interference, excellent portability, as well as good value traceability. The flexible sensing coil of the sensor can be designed into a fiber cable that can be wrapped around the current-carrying conductor to measure current, so as to avoid breaking the current-carrying path for installation. The closed-loop signal-detecting technology can be used to recover the current to be measured, which theoretically guarantees high linearity over the wide dynamic range. However, due to the parasitic polarization cross-coupling, imperfect polarization transform, and inevitable degeneration of the circular polarization state of the light wave in the sensing optical path, the linear relation between the sensor output and the current to be measured will be deteriorated, especially when the current is high. The nonlinearity can result in measurement error and waveform distortion, which severely degrade the basic measurement accuracy of the sensor. The nonlinear error mechanism of the sensor is analyzed in detail, and parameter matching conditions realizing the linear response of the sensor to the Faraday effect are presented in this paper.

Analysis and verification for the nonlinear error mechanism and suppression method of the sensor are performed from the perspective of polarization error. First, the Jones matrix is used for describing the total light propagation path. The key polarization characteristic parameters are contained in the optical models, including the pigtail polarization crosstalk of the phase modulator, the azimuth and retardation of the quarter-wave retarder, as well as the beat length and pitch of the spun elliptical birefringent optical fiber. Then, the interference light intensity in synchronization with the modulating signal is calculated, and the nonlinear tracking relationship between the feedback phase shift and the current to be measured is deduced. The contribution of the above parameters to the nonlinear error is discussed respectively. After that, the parameter matching conditions of the retarder and the spun elliptical birefringent optical fiber are derived from the nonlinear tracking relationship, which guarantees the linearity of the sensor. The adaptability of the method to different bending radii of the sensing coil is also analyzed. Finally, the calibration device of the fiber-optic high-current sensor is built based on the equal ampere-turn method. Under the conditions of different parameters of the retarder and different bending radii of the sensing coil, the nonlinear error of the sensor is tested and compared.

Nonlinear error increases with the increase in the output pigtail polarization crosstalk of the phase modulator, and it is not related to the angular misalignment of the input pigtail (Fig. 2). For a single fiber loop, when the crosstalk is -28 dB, the variation of the scale factor is about 0.18% over the current range of 500 kA. The variation of the scale factor remains below 0.1% as long as the crosstalk does not exceed -30.6 dB. The nonlinearity increases with the increasing angular alignment error and retardation error of the quarter-wave retarder (Fig. 3). Similarly, the variation of the scale factor is about 0.1% when the deviations of the azimuth and retardation from ideal retarders are 1° and 3°, respectively. The linear birefringence in the spun elliptical birefringent sensing fiber also leads to nonlinearity (Fig. 4). With the decrease in the spun pitch of the sensing fiber, the nonlinearity can be improved. For the sensing fiber with a beat length of 10 mm, when its pitch decreases from 10 mm to 5 mm, the variation of the scale factor will reduce from 2.4% to 0.87%. When the parameters of the retarder and sensing fiber satisfy the matching conditions [Eq. (18)], the sensor output can almost linearly respond to the current to be measured. The parameter matching conditions have excellent adaptability, even when the bending radius of the sensing fiber coil reduces to 100 mm (Fig. 5). The test results show that the scale factor of the sensor, with the quarter-wave retarder satisfying the parameter matching conditions, has a variation of 0.2% with the applied current over the range of 6-500 kA, which is one order of magnitude lower than the one with the perfect quarter-wave retarder (Fig. 6). The manufacturing tolerances of the retarder and the uncertainty of the beat length to pitch ratio of the sensing fiber are two major causes of residual nonlinear error.

The polarization cross-coupling of the phase modulator causes the nonlinear error of the fiber-optic high-current sensor. It requires a focus on the angular misalignment of the output pigtail of the phase modulator. It is crucial for the high-current measurement to determine the angular alignment accuracy according to the dynamic range of the current, so as to guide the type selection and process implementation. The imperfect circular polarization state and inevitable degeneration caused by the angular misalignment and retardation error of the quarter-wave retarder and the intrinsic and bending-induced linear birefringence of the sensing fiber are primary causes of the nonlinearity. When the matching conditions are satisfied between the parameter of the retarder and the beat length to pitch ratio of the sensing fiber, the sensor has a linear response to the Faraday effect. Accordingly, the nonlinear error can be effectively suppressed. In order to improve the linearity of the sensor, it is essential to precisely determine the beat length to pitch ratio of the sensing fiber to guide the parameters design of the retarder, which will be a research direction in subsequent work.