## Abstract

In this paper, we demonstrate a novel all-fiber current sensor using ordinary silica fiber. The sensor employs a fiber solenoid as a current sensor head, which improves the current sensitivity by allowing optical signals to traverse the sensor head repeatedly. Theory and experiment prove that the improvement in sensitivity increases periodically with the number of repetitions of optical signals circulating round the loop.

© 2012 OSA

## 1. Introduction

Optical current sensors (OCSs) have been a topic of research since the 1970s because of their immunity to electromagnetic interference (EMI), safety, and low weight in comparison with traditional current sensors [1]. Among the OCSs, all-fiber current sensors are mainly based on the Faraday magneto-optic effect and are particularly attractive because they have better optical integration than other OCSs such as bulk-glass current sensors or space coupling optical current sensors [2, 3]. In other words, an all-fiber current sensor consisting of passive fiber components has a relatively simple construction and can be fabricated and maintained easily [4]. However, one disadvantage of the all-fiber current sensor is its low current sensitivity. Compared with the sensor media of bulk-glass current sensors, the conventional silica fiber has a very low Verdet constant, and thus, a very long fiber is necessary to achieve a comparable sensitivity. However, a long fiber increases both the size and the birefringence of the system, the latter of which reduces the actual sensitivity below that predicted by theory [1]. Another method of enhancing the sensitivity is the use of a doped fiber, which possesses a high Verdet constant, such as a terbium-doped fiber or europium-doped fiber [5]. However, the use of a doped fiber increases cost as well as the temperature sensitivity because the Verdet constant is highly dependent on temperature [6].

As a well-developed optical architecture, the fiber loop has enormous application in many areas, such as laser, sensor and optical communication [7–10]. The main advantages of designs using the fiber loop architecture include high flexibility, low cost, and good extensibility [7–10]. These characteristics can also be implemented in the optical current sensor. For example, an experiment using a fiber loop resonator to enhance sensitivity on optical current sensor has been reported since the 1980s [11].

In this paper, we demonstrate an all-fiber current sensor based on the fiber loop architecture to improve current sensitivity. A fiber solenoid is employed as the current sensor head of a fiber loop. The optical signal can traverse the sensor head repeatedly so that the Faraday rotation angle is increased and the current sensitivity is enhanced correspondingly. This design exploits the advantages of the fiber loop and makes a minimally sized conventional silica fiber current sensor possible. Furthermore, it has a series of current sensitivities to satisfy various requirements. Experiments reveal that the sensitivity increases in an oscillatory, non-linear manner with increasing circulation of the optical signal through the fiber solenoid. A Jones matrix of the sensor is presented in section 2 to explain this phenomenon and the experiments to prove the theoretical model are described in section 3.

## 2. Configuration and principle

In conventional fiber current sensors, the optical signal travels across the sensor head just once [1], whereas in a reflective fiber current sensor, it travels twice the distance because of the presence of a reflecting mirror, which reduces the linear birefringence [12]. However, conventional silica fiber has a very low Verdet constant [13]; for example, the typical values are 4.68 μrad/A at 633nm, 1.38 μrad/A at 1064 nm and 0.804 μrad/A at 1550nm [13, 14]. In order to obtain a higher current sensitivity, a longer fiber is necessary for the aforementioned structures; however, this also increases the size and birefringence of the sensor and reduces the actual sensitivity [1].

Figure 1
shows the configuration of an all-fiber current sensor based on the fiber loop architecture. Two fiber couplers and a fiber solenoid constitute a fiber loop structure. Optical pulses that pass through a polarizer are coupled into the fiber loop and circulate inside the structure for many round trips before the light is completely attenuated. The ring-down time and the maximal number of round trips are determined by the coupling ratio of the couplers and the attenuation coefficient of the fiber loop. In each round trip a small fraction of the light is coupled into a polarizing beam splitter (PBS) by the coupler *B*. The orthogonally polarized beams output from the PBS can be coupled into one channel by the coupler *C*, and a photo-detectors *D* measures the final results.

A Jones matrix *T _{H}* can be used to describe the propagation of light through the fiber loop for a single round trip [15]. The final Jones matrix of the system can be derived as:

*K*is the number of round trips, $\phi =\sqrt{{\delta}^{2}+{\theta}^{2}}$, and the phase shifts

*δ*and

*θ*are imposed by the linear and circular birefringence respectively [12]. When the Jones vector of the input pulse is $\left[\begin{array}{l}0\\ 1\end{array}\right]$, the degree of polarization of the output pulse is

*P*caused by the electric current. The expression is given by

*ε*is the phase shift caused by unwanted circular birefringence, Ω is the rotational angle induced by the current, ${\theta}^{2}={\left(\epsilon +2\Omega \right)}^{2}$, ${\phi}^{2}={\delta}^{2}+{\epsilon}^{2}$ and ${\varphi}^{2}={\delta}^{2}+{\left(\epsilon +2\Omega \right)}^{2}$. With the assumption that $\delta >>2\Omega $ and $\epsilon >>2\Omega $ (because the sensor is made of conventional silica fiber), Eq. (3) can be transformed into:where,

*γ*is a correction factor, and is expressed as

*P*is approximately proportional to the rotational angle Ω and exhibits a periodic fluctuating growth with

*K*. The current sensitivity

*S*, which represents the susceptibility of the degree of polarization variation Δ

*P*to the current intensity changes, can be defined aswhere,

*N*is the number of turns of the fiber solenoid and

_{S}*V*is the Verdet constant of the fiber. This value obviously varies with the number of round trips

*K*in a periodic manner; thus, determining an appropriate

*K*to measure a given current is a key process. The relationship between

*S*and

*K*can be obtained via the derivative of

*S*with respect to

*K*. The maximal and minimal sensitivities and the corresponding conditions of

*K*are

*N*is a natural number. Considering the range of

*P*from −1 to 1, the maximum measurable current can be deduced as:

*K*,

*φ*and

*ε*, and becomes positive (negative) when Δ

*P*increases (decreases) with the growth of current

*I*. It should be noted that the maximum current is inversely proportional to the current sensitivity. Thus, the selection of

*K*should take into account both the range of the current and the current sensitivity.

## 3. Experiment and discussion

The experimental layout, shown in Fig. 1, comprises a 1550 nm pulsed laser diode (LD, *Connet Co., Ltd., model MS3400-1550, average output power* 3.8 mW, *peak power* 10 W, *pulse width* 15 ns, *output frequency* 1Mhz), a polarizer, three 2 × 1 fiber couplers (*FUSOTEK Co., Ltd.*), a fiber solenoid, a PBS (*GIGALIGHT Co., Ltd., model PBS-1 × 2-1550*), one detector and a system for digital signal processing. The fiber solenoid section adopts a standard single-mode fiber and has a diameter of 50 mm. Two sensor heads with 50 and 150 turns are fabricated for comparison. The phase shifts imparted to the system by the linear birefringence are *δ* = 1.649 rad/m and *δ* = 2.044 rad/m for 50 turns and 150 turns respectively, and the corresponding phase shifts imparted to the system by the circular birefringence are *ε* = 2.399 rad/m and *ε* = 1.700 rad/m respectively. The splitting ratio of coupler *A* is 5:95 and the ratio of *B* is 1:99. Light from the LD travels through the 5% leg of the coupler *A* and couples into the fiber loop structure. In each round trip a small fraction of the light is coupled into the 1% leg of coupler B. The length of delay fiber is 10 meter. The signals from the coupler *C* are detected by a *Thorlabs DET01CFC* InGaAs photo-detector and displayed by a *Tektronix TDS3054B 500* digital oscilloscope. The range of the direct current in the experiment is 0 – 500 A.

Figure 2
shows the intensity variations with respect to the detected optical pulses when 0, 125 and 250 A currents pass through a 150-turn solenoid, respectively. The time scale in Fig. 2 is 200 ns. Adjacent pairs of peaks are the orthogonally polarized beams output from the PBS. The waveform’s round trip number *K* is from 0 to 7 in the left part of Fig. 2 and is from 8 to 15 in the right part of Fig. 2. It clearly shows that the intensity variations of adjacent pairs of peaks increase with the round trip number *K* in an oscillatory manner.

The variation in the degree of polarization change with *K* can be obtained from the oscilloscope data, and the results are shown in Fig. 3
. Waveform (a) is the result for 50 turns of fiber and waveform (b) for 150 turns of fiber. The dotted line in Fig. 3 denotes the normalized light intensity. Clearly, the relationship between Δ*P* and *K* is also an oscillation. The phenomenon agrees with that predicted in Eq. (4). Although the variation of the polarization state rapidly increases with *K*, the intensity of the optical signal is also exponentially attenuated with *K*. Thus, the attenuation of light should be taken into account in the selection of *K*. For example, if 1/e of initial light intensity was set as a base line, the number *K* should be smaller than 8 in the experiment.

Figure 4
shows a comparison of the experimental and theoretical results of the relationship between Δ*P and K*. It can be seen from Fig. 4 that the experimental results can be predicted accurately by the theoretical model following Eq. (4), and the difference between those results increases with *K* and *I* because of the growth of the correction factor *γ* expressed in Eq. (5).

The relationship between the variation in the degree of polarization and the current intensity is shown in Fig. 5
. The experimental results are very close to the theoretical data. It illustrates an approximate linear dependence of Δ*P* on *I* when *K* < 10. A nonlinear relation distinctly occurs when *K* >10, and the nonlinearity increases with increasing *I*. The phenomenon is also can be explained by the increase in the correction factor *γ*.

Finally, Fig. 6
shows the relationship between the current sensitivity *S* and *K*. The sensitivity periodically increases with *K*, and the phenomenon is in agreement with Eq. (6). It can be seen from Fig. 6 that the peaks of the curves have a high current sensitivity; for example, for the 50-turn sensor, the sensitivity when *K* = 5 is about four times larger than a single pass sensor (*K* = 1), and the ratio value is about ten times when *K* = 10; for 150 turns, the sensitivity is about five times when *K* = 5 and eleven times when *K* = 10. The difference between experimental and theoretical results in Fig. 6 also periodically increases with *K* because the sine of *K* is included in the correction factor *γ* expressed in Eq. (5). The fiber current sensor based on the fiber loop architecture can enhance the system’s current sensitivity effectively; however, as the current sensitivity is inversely proportional to the maximum measurable current as shown by Eq. (8), the selection of *K* is dependent on the intended application.

## 4. Conclusion

In conclusion, we have demonstrated a novel all-fiber current sensor based on the fiber loop architecture. The design effectively improves the current sensitivity by increasing the number of round trips of the optical signal. Both theory and experiment prove that the improvement in sensitivity increases periodically with the number of round trips *K* and an appropriate *K* can be selected to measure a specific current range. This allowed us to build an ordinary silica fiber current sensor, which has advantages including low cost, small size, high flexibility, and high sensitivity.

## Acknowledgments

This work was supported by the Natural Science Foundation of Fujian Province of China (No: 2010J01325), and Fujian Province Department of Education Foundation of China (No: JA11271 and No: JA10077).

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