Method for measurement of fusion-splicing-induced reflection in a photonic bandgap fiber-optical gyro

Xiaobin Xu; Zhihao Zhang; Zuchen Zhang; Jing Jin; Ningfang Song

doi:10.3788/COL201513.030601

Photonic crystal fibers (PCFs) are characterized by a periodic arrangement of air holes around a core^[1,2]. A photonic bandgap fiber (PBF) is a kind of air-core PCF, and it has attracted a great deal of interest owing to its unique optical properties^[3,4]. A PBF makes the light propagate in air which is much more stable than ${SiO}_{2}$ in a conventional fiber, so it becomes a radically new method to solve the problems of environmental adaptability in a fiber-optical gyroscope (FOG). A FOG composed of a PBF coil is generally called a photonic bandgap fiber optical gyroscope (PBFOG), and a PBFOG has a greatly reduced sensitivity to the Kerr, irradiation, temperature transient, and Faraday effects compared to a conventional FOG^[5,6].

Reflection occurs at an interface between two media exhibiting different refractive indices^[7]. In a PBFOG, the pigtails of an integrated optic chip (IOC) or the succeeding Lyot depolarizers are conventional fibers which have a Ge-doped ${SiO}_{2}$ core, but the coil is made up of a PBF having an air core, as illustrated in Fig. 1. The strong reflection inevitably happens at both fusion splices between the PBF coil and the tail fibers of the IOC (or depolarizers)^[8]. However, the reflectance is not always 4% as per the Fresnel law, because the endface of the fiber is not an ideal mirror face due to the damage of high temperature or imperfect cutting in the process of fusion splicing, as illustrated in Fig. 2. In fact, the reflectance may not even be a constant for each time of fusion splicing, because random fluctuation always exists for the fusion parameters such as power and cutting angle. In a PBFOG, the secondary waves reflected back to the detector can cause noise, even bias error if they are able to interfere when the length of the IOC tail fibers is not proper^[7,9]. Therefore, it is extremely important to precisely measure the reflection at these two fusion splicing points, such that we can make an inline examination of the fusion splicing quality to control the reflection to an accepted level in time; the PBFOG performance can be evaluated with the measuring result of the reflection. In fact, reflection also exists in a conventional FOG, but it originates from the interfaces between the endfaces of the IOC and its tail fibers. A reflection of this kind is very small ( $< - 60 dB$ ), because the endfaces of both the IOC and its tail fibers are intentionally polished to some proper oblique angles to avoid the reflection^[7,9]. Finally, the problems concerning the reflection can always be neglected in a conventional FOG, but it is a big problem in PBFOG. The traditional measuring methods, including optical time-domain reflectometer (OTDR) and optical continuous wave reflectometer (OCWR), are not feasible in this context due to the fact that it is a closed optical circuit in the sensing coil of the PBFOG^[10]. In this Letter, we promote a simple method to implement inline measurement of the reflection at the splicing points between the PBF coil and the IOC tail fibers during the process of fusion splicing, without any alteration to the optical configuration of the PBFOG except replacement of the light source.

Figure 1.Cross sections; (a) PBF; (b) conventional polarization-maintained fiber^[11].

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Figure 2.Cross section of the fusion splicing point between the PBF and the conventional Panda fiber.

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A scheme of measuring the reflection at fusion splicing points between the PBF coil and the pigtails of IOC is shown in Fig. 3^[9]. The light outputs from the IOC pigtails with the power $P_{A}$ and $P_{B}$ (the subscripts A and B, throughout the paper, refer to Points A and B), and the corresponding secondary waves ( $W_{A}$ and $W_{B}$ ), originate due to reflection at the interfaces. $W_{A}$ and $W_{B}$ go backward to the detector through the IOC and the coupler, respectively producing an intensity of $V_{A}$ (mV) and $V_{B}$ (mV) after photoelectronic conversion at the detector. The reflectance $R$ , at Points A and B, is defined in this Letter as $R_{A} = V_{A} / (K_{PIN} E_{PIN} L_{A} P_{A})$ and $R_{B} = V_{B} / (K_{PIN} E_{PIN} L_{B} P_{B})$ , respectively, where $K_{PIN}$ and $E_{PIN}$ are, respectively, the transimpedance and conversion efficiency of the detector which is always composed of a PIN photodiode and a field-effect transistor (FET); $L_{A}$ and $L_{B}$ are, respectively, the loss of the optical path from Points A and B to the detector. Those parameters are readily and accurately obtained except $V_{A}$ and $V_{B}$ , because $V_{A}$ and $V_{B}$ are not readily distinguished from the intensity produced by the clockwise (CW) and counter clockwise (CCW) primary waves ( $W_{CW}$ and $W_{CCW}$ , Fig. 3) in a complete FOG. Therefore, $V_{A}$ and $V_{B}$ are actually our targets of measurement, which are crucial for the evaluation of fusion splicing quality and reflection-induced noise in a PBFOG.

Figure 3.Scheme of the measurement of fusion-splicing-induced reflection in a PBFOG.

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The bear end of the coupler is intentionally cut to be a mirror face to produce another reflection-induced secondary wave $W_{C}$ (the subscript C, throughout the paper, refers to Point C). $W_{C}$ also goes backward to the detector through the coupler and produces an intensity of $V_{C}$ (mV) at the detector. This artificial secondary wave provides some additional information and plays an important role in the process of measurement. A laser source with proper coherence length is employed to guarantee the interference among $W_{A}$ , $W_{B}$ , and $W_{C}$ at the detector, but it must avoid the interference between the primary waves ( $W_{CW}$ and $W_{CCW}$ ) and the secondary waves ( $W_{A}$ , $W_{B}$ , and $W_{C}$ ). A triangular wave with an amplitude of $V_{π}$ and a period of $T$ is applied to the IOC [Fig. 4(a)], and the modulation phase for $W_{A}$ and $W_{B}$ , is shown in Figs. 4(b) and 4(c), respectively. In this Letter, $V_{π}$ is the half-wave voltage corresponding to the modulation phase of $π$ (rad) for the light passing the upper branch of the IOC. In addition, $W_{C}$ from the bear end of the coupler does not have any modulation phase because it never passes the IOC.

Figure 4.(a) Modulation voltage applied on an IOC; (b) corresponding modulation phase for the secondary wave $W_{A}$ ; (c) corresponding modulation phase for the secondary wave $W_{B}$ .

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Before the fusion splicing of Points A and B, the intensity $V_{C}$ must be measured at the detector. Then, splice the first point (Point A) through fusion; at the same time the endface of the other tail fiber of the IOC should be treated to avoid reflection and eliminate $W_{B}$ . Thus only $W_{A}$ and $W_{C}$ exist, with the interference intensity of $V_{A C}$ at the detector given by $V_{A C} = V_{A} + V_{C} + 2 \sqrt{V_{A} V_{C}} \cos [\frac{4 π}{T} t + Φ_{1} (t)],$ (1)where $t$ is time ( $n T$ to $n T + T / 2$ ), $V_{A C}$ is symmetric during the time [ $n T + T / 2$ to $(n + 1) T$ ], $n$ is an integer, $Φ_{m 1} (t) = 4 π t / T$ is the modulation phase for the interference signal, and $Φ_{1} (t)$ is a random phase which varies with environment. Equation (1) indicates that the interference signal has a peak-to-peak (PTP) intensity ( $V_{A C - PTP}$ ) of $4 \sqrt{V_{A}} \sqrt{V_{C}}$ at the detector. Both the phase modulation and instability of the external environment cause the interference signal to vary with time, but $V_{A C - PTP}$ does not change. Moreover, $V_{A C - PTP}$ is easily measured as long as the modulation period $T$ is small enough to make $Φ_{m 1} (t)$ vary faster than $Φ_{1} (t)$ . Consequently, the intensity $V_{A}$ can be acquired as $V_{A C - PTP}^{2} / (16 V_{C})$ .

In the next step, it is time to splice the other end (End B) of the PBF coil. The mirror face at the bear end of the coupler should be destroyed now to eliminate $W_{C}$ , in order that only two secondary waves ( $W_{A}$ and $W_{B}$ ), and two primary waves ( $W_{CW}$ and $W_{CCW}$ ), exist at the detector during the process of this fusion splicing. As a result of the special choice of coherence length of the laser source, the interference only between $W_{A}$ and $W_{B}$ , and $W_{CW}$ and $W_{CCW}$ , can happen. The interference intensity between $W_{A}$ and $W_{B}$ at the detector is given by $V_{A B} = V_{A} + V_{B} + 2 \sqrt{V_{A} V_{B}} \cos [\frac{8 π}{T} t + Φ_{2} (t)],$ (2)where the time $t$ has the same definition as in Eq. (1), $Φ_{m 2} (t) = 8 π t / T$ is the modulation phase for the interference signal, and $Φ_{2} (t)$ is also a random phase which varies with the instable environment. Equation (2) shows that the interference signal ( $V_{A B}$ ) has a PTP intensity ( $V_{A B - PTP}$ ) of $4 \sqrt{V_{A}} \sqrt{V_{B}}$ which can be directly measured at the detector. The intensity ( $V_{B}$ ) is therefore resolved as $V_{A B - PTP}^{2} / (16 V_{A}) = V_{C} V_{A B - PTP}^{2} / V_{A C - PTP}^{2}$ . Note that the intensity of the interference between $W_{CW}$ and $W_{CCW}$ is a fixed value due to the fact that they are reciprocal (with the only phase difference being the Sagnac phase shift), so it merely causes a bias to $V_{A B}$ and does not affect $V_{A B - PTP}$ when the PBF coil is in a static state.

An experimental setup has been established based on Fig. 3. A laser source with linewidth on the magnitude of megahertz (MHz) and power of $\sim 0.425 mW$ is used to provide the coherent light. The coupler has a split ratio of $\sim 50 ∶ 50$ . The detector has a transimpedance of $K_{PIN} \sim 100 k Ω$ and has a conversion efficiency of $E_{PIN} \sim 0.9 A / W$ . The IOC is a kind of proton-exchange ${LiNbO}_{3}$ waveguide with half-wave voltage $V_{π} = \sim 5.1 V$ . A triangular wave with an amplitude of $V_{π}$ and period of $T \sim 10 μs$ is applied to the IOC. Before splicing the PBF coil, we measure the output power from the IOC pigtails at Points A and B, and they are $P_{A} = 56.7 μW$ and $P_{B} = 61.8 μW$ . The bear end of the coupler is intentionally cut to be a mirror face and the secondary wave $W_{C}$ is produced with the intensity ( $V_{C}$ ) of $\sim 690 mV$ at the detector. While we splice the first end (End A) of the PBF coil, the other end (End B) is kept immersed into the index-matching liquid to avoid reflection. As a result, there are only two large secondary waves ( $W_{A}$ and $W_{C}$ ) in the PBFOG. Their interference signal at the detector is shown in Fig. 5(a), indicating that the PTP intensity $V_{A C - PTP} \sim 312 mV$ , so $V_{A} = V_{A C - PTP}^{2} / (16 V_{C}) \sim 8.8 mV$ , which corresponds to the reflectance of $R_{A} \sim 1.2 %$ based on the theory and experimental parameters mentioned previously. Then, we splice the other end (End B) of the PBF coil, and at the same time the mirror face at the bear end of the coupler is thoroughly destroyed to eliminate $W_{C}$ . As a result, $W_{A}$ interferes with $W_{B}$ , and the interference intensity has a dependence on the modulation phase, as shown in Fig. 5(b). Obviously, its period ( $\sim 2.5 μs$ ) is a quarter of that of the modulation phase, and half of that of the interference signal between $W_{A}$ and $W_{C}$ [Fig. 5(a)], which agrees well with the theory. The PTP intensity $V_{A B - PTP} \sim 54 mV$ , so $V_{B} = V_{C} V_{A B - PTP}^{2} / V_{A C - PTP}^{2} \sim 20 mV$ , which corresponds to the reflectance of $R_{B} \sim 2.5 %$ at Point B. Therefore, strong reflection between the PBF coil and the tail fibers of the IOC indeed exists, and the reflectance seems not the same for each time of the fusion splicing possibly because of random fluctuation of the fusion power, cutting angle, interface shape, and so on.

Figure 5.Modulation voltage and interference signals; (a) between $W_{A}$ and $W_{C}$ ; (b) between $W_{A}$ and $W_{B}$ .

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The method provides a tool for inline monitoring of reflection at Points A and B during the process of fusion splicing, and its measurement precision depends to a large degree on the intensity of the secondary wave $W_{C}$ . $W_{C}$ actually serves as an amplifier to make the small $W_{A}$ more easily measured, because the PTP intensity of the interference signal is $4 \sqrt{V_{C}} \cdot \sqrt{V_{A}}$ while the End A of the PBF coil is being spliced and $V_{C}$ is obviously much larger than $V_{A}$ . If the noise of the interference signals at the detector is $Δ V$ (to which many factors contribute such as shot noise, polarization noise, and scattering noise in a PBF), the precision of $V_{A}$ is approximately ${(Δ V)}^{2} / (16 V_{C})$ . Therefore, a large $V_{C}$ is very important to improve the measurement precision, but it should not be too large and cause the detector to be saturated. An increase of the reflectance at Interface C can be realized through some measures, such as attaching a short piece of fiber with angle-polished connector (APC)-type connector on one end and aluminum or gold coating at the other end, or temporarily covering the fiber end-face with liquid metal, although these measures are a little complex in the real-world process of fabricating a PBFOG.

On the other hand, if the reflection at Points A and B is so small that $V_{A B - PTP}$ cannot be measured during the process of splicing Point B, then we have to make some optimization to the method and let $W_{A}$ , $W_{B}$ , and $W_{C}$ simultaneously exist at the detector. As a result, they interfere with each other and the interference intensity ( $V_{A B C}$ ) is given by Eq. (3) with the omission of dc terms, where $Φ_{3} (t)$ is also a random phase like $Φ_{1} (t)$ . $V_{A B C} = 2 \sqrt{V_{A} V_{C}} \cos [\frac{4 π}{T} t + Φ_{1} (t)] + 2 \sqrt{V_{B} V_{C}} \cos [\frac{4 π}{T} t + Φ_{3} (t)] + 2 \sqrt{V_{A} V_{B}} \cos [\frac{8 π}{T} t + Φ_{2} (t)] .$ (3)

In Eq. (3), $\sqrt{V_{A}} \sqrt{V_{B}}$ is significantly smaller than $\sqrt{V_{A}} \sqrt{V_{C}}$ or $\sqrt{V_{B}} \sqrt{V_{C}}$ when the $V_{C}$ is large enough; therefore it can be neglected and the maximum PTP intensity ( $V_{A B C - PTP}$ ) is $4 (\sqrt{V_{A}} \sqrt{V_{C}} + \sqrt{V_{B}} \sqrt{V_{C}})$ . As a result, $V_{B} \approx {(V_{A B C - PTP} - V_{A C - PTP})}^{2} / (16 V_{C})$ which can also be more accurate with larger $V_{C}$ .

In conclusion, the reflection at the splicing points between the PBF coil and conventional tail fibers of IOC is an important factor affecting the precision and long-term stability of PBFOG. To precisely measure this reflection during the process of fusion splicing, we promote a method and also (theoretically and experimentally) prove its correctness and feasibility, using the interference among the secondary waves which are caused by reflection at the two fusion splicing points and bear end of the coupler. The method is very simple and need not require alteration of the optical configuration of the PBFOG except replacement of a conventional broad-spectrum source by a laser source having proper linewidth. Consequently, it is very helpful for process control in fabricating a high-performance PBFOG and also provides a tool to quantitatively analyze the reflection in a PBFOG.

Category: Fiber Optics and Optical Communications

Received: Sep. 27, 2014

Accepted: Dec. 22, 2014

Published Online: Sep. 25, 2018

The Author Email: Xiaobin Xu (xuxiaobin@buaa.edu.cn)

DOI:10.3788/COL201513.030601