With the continuous upgrade of the power system, requirements for the accuracy and stability of current detection are increasing. As a new type of current detection technology, the fiber-optic current sensor (FOCS) has the advantages of strong anti-interference ability, high measurement accuracy, and high security. Therefore, FOCS is of concern for more and more researchers and has been widely used^[1–4].

The quarter-wave plate (QWP), as a significant element of FOCS, has been studied by many researchers^[5–7]. It is generally fabricated with high-birefringence optical fibers by many methods, most of which require high precision. Reference [8] proposed a method for manufacturing a QWP by bending instead of selecting the accurate length and electronically controlling its phase shift between polarization modes. A new type of variable spin rate high-birefringence fiber was fabricated in Ref. [9], which could provide better stable temperature dependence. What is more, a method of fabricating an all-fiber wave plate by helically winding spun highly birefringent fiber was proposed, which was less sensitive to external disturbance and offered stable polarization transformation in Refs. [10,11]. In addition to proposing numerous fabrication methods of QWPs, researchers also focused on influencing factors. It has been confirmed that the phase retardation angle of the wave plate varies with temperature^[12]. In Ref. [13], the fiber wave plates were made of specific fiber whose beat length was related to temperature and wavelength, so the working wavelength was another factor. Moreover, it was also found that the QWP and sensitive spun fiber were most affected by temperature in Ref. [14], which would affect the measurement of FOCS.

According to the research results, QWPs are mainly influenced by temperatures, so many novel optical fibers have been fabricated to address this problem in recent years. A polarization-transforming fiber was fabricated in Ref. [15], whose dependence on temperature and wavelength was many times smaller than that of traditional polarization-maintaining fiber (PMF) QWPs in some cases. Reference [16] proposed a QWP fabricated with a novel polarization-maintaining photonic crystal fiber, which was verified as less sensitive to temperature. What is more, Ref. [17] designed a combination of different PMFs to eliminate the temperature sensitivity of PMF wave plates. It can be concluded that the conventional all-fiber QWPs usually change with the fluctuation of the ambient temperature, which reduces the measurement accuracy of FOCSs. Therefore, all-fiber QWPs with low cost, low loss, and temperature insensitivity are needed. In addition, there is little research on the function of all-fiber QWPs in lasers.

In this paper, a novel high-birefringence fiber, Tb:YAG crystal-derived silica fiber (TYDSF), was fabricated and then utilized to manufacture an all-fiber QWP device. We compared the performance of three kinds of all-fiber QWPs, including TYDSF, PANDA-type PMF, and elliptical-core PMF, by observing their output polarization state in the temperature range of $-5°\mathrm{C}$ to 200°C. Additionally, the device was also used in a high-power laser system to restrain the nonlinear effects of the system.

When linearly polarized light passes through a PMF, it will be decomposed into light components that propagate along the fast and slow axes, respectively. As a result of the different refractive index of the fast and slow axes, light undergoes a phase difference, which increases with the propagation distance during the transmission. Therefore, the concept of beat length ($L_{\text{beat}}$) is introduced, that is, the periodic distance when the phase difference increases to $2\pi$. The whole changing process of the state of polarization (SOP) within a single beat length is shown in Fig. 1. The beat length can be calculated by^[18]$$L_{\text{beat}}=\frac{\lambda }{B},$$(1)where $\lambda$ is the working wavelength and $B$ represents the birefringence of the optical fiber.

From Fig. 1, it can be seen that the output light will become circularly polarized light when the polarization direction of the fast axis or slow axis is 45°^[19]. In theory, QWPs can be made as long as the phase retardance is odd times of $\pi /2$. Therefore, the intercepted length $L_{1/4}$ of QWP can be expressed as $$L_{1/4}=\frac{2k+1}{4}{L}_{\text{beat}},$$(2)where $k$ is an integer. Although the length that matches Eq. (2) is acceptable, it is best to take $k=0$, which is called zero-order QWP. The longer the intercepted length is, the more easily the QWP is affected by external environmental factors, which leads to the decline in performance. Thus, better performance of the wave plate requires shorter $L_{1/4}$; that is to say, a quarter of the beat length is the most ideal intercepted length for QWPs.

There are two main conventional manufacturing methods of all-fiber QWPs, including the fusion method^[20] and the twisting method^[21]. The twisting method is that the sensing fiber spliced with PMF is twisted 45°, and then an arc discharge is used at a quarter of the beat length from the fusion point until the torsional stress is released. In this way, a QWP can be formed between the first fusion point and the second discharge point, but the discharge time and intensity need to be controlled, which makes the fabricating process complicated. In the fusion method, a quarter of the beat length of the PMF is directly intercepted, and the fast axis of the front PMF is aligned at a 45° angle with respect to that of the rear PMF. The fabricating process seems easier, but it is difficult to accurately control the fusion angle of 45° with the axis, which leads to a certain axis angle error. Moreover, the beat length of the PMF is generally on the millimeter scale, so it is difficult to accurately intercept a quarter of beat length.

By comprehensively comparing the two conventional methods mentioned above, we selected the improved fusion method on the basis of the original method as the main fabrication method, as shown in Fig. 2. At first, the wave plate fiber is spliced with the spun fiber, whose output end is linked with the SOP observation equipment. Then, the wave plate fiber is cut into a quarter of its beat length. The improved fusion method is not to set a 45° angle in the fiber fusion splicer for automatically splicing, but to rotate the fiber until the output SOP reaches the optimal circular polarization state with ellipticity close to 45° and then fuse the optical fibers together. This method can achieve high accuracy and manufacture QWPs with better quality.

TYDSF was fabricated by the ${\mathrm{CO}}_2$ laser-heating drawing technique. Its core diameter was 11.32 µm, and its cladding diameter was 125.20 µm. Additionally, its loss was less than 0.15 dB/cm, ranging from 600 to 1500 nm. Since the improved fusion method is chosen to fabricate an all-fiber QWP device, it is necessary to confirm the beat length of the fiber. A microscope birefringence measurement instrument^[22] was used to measure the beat lengths of TYDSF, PANDA-type PMF, and elliptical-core PMF. The measurement system diagram is shown in Fig. 3(a).

We intercepted a TYDSF of 10 mm, a PANDA-type PMF of 5 mm, and an elliptical-core PMF of 6 mm as three samples, and then put them into a polarizing microscope to observe their retardance. The detailed observations and related calculations are shown in Fig. 3(b). According to the measured retardance, the birefringence $B$ of TYDSF can be calculated by the equation $B=R/L$, where $R$ is the retardance and $L$ is the length, so its value was $2.99\times {10}^{-5}$. Similarly, the birefringence of PANDA-type PMF and elliptical-core PMF was $4.55\times {10}^{-4}$ and $2.73\times {10}^{-4}$. Thus, we can obtain the beat length of TYDSF at 1310 nm ($L_{\text{beat}}=44\mathrm{mm}$).

The most commonly used fibers for all-fiber QWPs are high-birefringence fibers, namely, PMFs, with a birefringence coefficient $B$ of approximately ${10}^{-4}$. However, higher birefringence means shorter beat length, which requires higher intercepting accuracy requirements for preparation. Most PMFs have a beat length on the millimeter scale, so an error of 1 mm will cause serious deviation in the output SOP of QWP. According to the experimental results, TYDSF has a beat length on the centimeter scale, so the required length of manufacturing all-fiber QWPs is 11 mm, which means easier cutting requirements, higher yield, and lower transmission loss.

Since the beat length of fibers was confirmed through the experiment, it was easy to calculate how long the fiber was needed for QWPs. Three types of QWP samples had been manufactured with TYDSF, PANDA-type PMF, and elliptical-core PMF according to Eq. (2). We used PMF as the input side and low-birefringence fiber (LBF) as the output side. Here, TYDSF QWP was taken as an example to show the fabrication process. First, the output side was fusion with TYDSF, and subsequently it was intercepted to the precise length of 11 mm. To acquire high-performance QWP, the input side was kept stationary, and then TYDSF was rotated until the output SOP approached the maximum ellipticity observed by the polarization analyzer (PA). In this way, another two QWP samples were fabricated at 1310 nm, as shown in Fig. 4. Since a quarter of the beat length of the PMF was too short to be intercepted, five-fourths of the beat length was instead selected for preparation. Therefore, we took a 5 mm PANDA-type PMF and a 6 mm elliptical-core PMF to fabricate samples.

In order to test the performance of the TYDSF QWP sample, a system was set up to measure its output SOP at 1310 nm, as shown in Fig. 5(a), where CL, P1, Q, P2, and L refer to collimating lens, the first polarizer, QWP, the second polarizer, and lens, respectively. These five components formed the polarization control part to obtain better quality linearly polarized light and to control the different input angles of linearly polarized light. P2 was rotated until PA showed the maximum ellipticity and degree of polarization (DOP) of the output SOP. The output ellipticity variation was monitored in PA, where a Poincaré sphere was used to demonstrate SOP. We placed the TYDSF QWP sample flat and straight, and then caused slight vibration on it. Figure 5(b) shows the variation tendency within 4 min. It can be seen that the output ellipticity of this QWP sample was 44.27°, and the fluctuation range was very small, at 1310 nm. That is to say, the TYDSF QWP sample had good resistance to the environmental destabilization.

In practical applications, all-fiber QWPs generally face many environmental influencing factors, among which temperature is a significant one. Therefore, an experiment was designed to test the temperature sensitivity of QWPs. In the following experiment, the temperature changed with time while the SOP measurement was monitored.

The schematic diagram of experimental devices is shown in Fig. 6, and the experimental conditions are set as follows. The temperature range of the temperature control chamber (TCC) was set between $-5°\mathrm{C}$ and 200°C. The working temperature rose by 10°C every 3 min, and lasted for 2 min. When the temperature was rising, the polarization extinction ratio (PER) and ellipticity of the output light were concurrently measured and recorded by the power meter (PM) and PA, respectively. As shown in Fig. 6, the temperature sensitivity testing system was measured at 1310 nm, and then we took the TYDSF QWP sample into TCC. In Fig. 6(a), a PER measurement system of the output light is shown, where the output power is recorded when the polarizer P is rotated. The output SOP is observed through the photodetector linked with PA depicted in Fig. 6(b). The PER can be calculated by the equation ${\mathrm{PER}=P}_{\max }/P_{\min }$, where $P_{\max }$ and $P_{\min }$ represent the maximum and minimum output power, respectively.

Figure 7 shows the experimental results of the output SOP of the TYDSF QWP sample with temperature, where the black curve refers to PER and the red curve refers to ellipticity. At a room temperature of 25°C, its PER was 0.29 dB and its ellipticity was 44.26° at 1310 nm. When the temperature decreased to $-5°\mathrm{C}$ or rose to 155°C, the fluctuations of PER and ellipticity were very small and their values were, respectively, less than 0.40 dB and more than 43.0°. When the working temperature exceeded 155°C, the variation trend of SOP began to fluctuate slightly, but its PER was still less than 0.80 dB, and its ellipticity was more than 42.0°. Obviously, the TYDSF QWP sample can maintain a relatively good circular polarization state in a temperature range of $-5°\mathrm{C}$ to 200°C. This phenomenon may result from the fact that the crystal-derived fiber has good thermal insensitivity.

The performance of another two all-fiber QWP samples made of PANDA-type PMF and elliptical-core PMF can be tested in the range of $-5°\mathrm{C}$ to 200°C with the measurement system shown in Fig. 6, and then these two samples were compared with the TYDSF QWP sample at 1310 nm. In Fig. 8, the ellipticity of the three samples fabricated with TYDSF, PANDA-type PMF, and elliptical-core PMF at 25°C was, respectively, 44.26°, 43.25°, and 43.25°. However, when the temperature dropped to $-5°\mathrm{C}$, their values were 43.84°, 33.87°, and 41.12°. Moreover, when the temperature rose to 200°C, their values become 42.02°, 5.47°, and 34.90°. It is obvious that the ability of the PANDA-type PMF QWP sample to maintain a circular polarization state was the worst when the working temperature changes, and the TYDSF QWP sample was the best among these samples. Since the beat length of PANDA-type PMFs was greatly affected by temperature and was on the millimeter scale, a small change in temperature may lead to an obvious change in beat length. Therefore, the blue curve in Fig. 8 has a turning point at 175°C, which proves the drastic change of beat length with temperature. The elliptical-core PMF, which is commonly used as the wave plate fiber in FOCSs, is less sensitive to the temperature variation, but it cannot maintain a circular polarization state within a wider temperature range. Accordingly, we believe that TYDSF is more suitable to manufacture an all-fiber QWP device because it is insensitive to temperature variation.

The coating of the partial fiber in the TYDSF QWP sample was removed during the fabrication process, so it needs to be fixed in the protection device to ensure practicality.

First of all, the bare section was put into the silica capillary and glue dropped at both ends of the capillary. Then, it was covered by the fiber-optic heat shrink tubing. Finally, stainless steel casing pipe covered the device completed in the above step. The PER of the initial TYDSF QWP sample was 0.49 dB, while that of the finished packaged sample was 0.85 dB. The packaged sample can be protected from external influencing factors and have a longer lifespan in practical applications. It was then used as an element of a high-power laser system (offered by Laser Fusion Research Center, China Academy of Engineering Physics, Mianyang, China), as shown in Fig. 9. The output power of the pre-amplifier 2 was 20 W, followed by the QWP. In the high-power laser system, this device was not affected by high temperature and can still convert linearly polarized light into good circularly polarized light. By manipulating the polarization, the nonlinear effects, such as stimulated Brillouin scattering effect, stimulated Raman scattering effect, and thermally induced mode instability, can be suppressed to some extent, which can facilitate the further power scaling of high-power laser systems with near diffraction-limited beam quality^[23,24]. More detailed experimental data need to be further studied and will be reported elsewhere in the future.

In this paper, we fabricated what we believe to be a novel high-birefringence TYDSF by the ${\mathrm{CO}}_2$ laser-heating drawing technique. Through the microscope birefringence measurement instrument, its linear birefringence was measured as approximately $2.99\times {10}^{-5}$. TYDSF was then used to manufacture an all-fiber QWP device with a length of 11 mm by the improved fusion method at 1310 nm. A temperature sensitivity testing system was set up to measure the output SOP of QWP samples in a full temperature range of $-5°\mathrm{C}$ to 200°C. The PER of the TYDSF QWP sample was 0.29 dB, and its ellipticity was 44.26° at 25°C. Additionally, its PER was always less than 0.80 dB, and its ellipticity was more than 42.0° during the period when the working temperature dropped to $-5°\mathrm{C}$ or rose to 200°C. Compared with conventional QWP samples fabricated with PANDA-type PMF and elliptical-core PMF, the SOP of the TYDSF QWP sample was the least sensitive to temperature. Finally, the TYDSF QWP sample was packaged with three procedures and was used as an element of a high-power laser system. Obviously, it performed better in maintaining a circular polarization state at higher temperatures, which may be useful in high-power laser systems, medical treatment, and FOCSs.