Fiber birefringence measurement by an external ... - OSA Publishing

Research Article

Vol. 57, No. 9 / 20 March 2018 / Applied Optics

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Fiber birefringence measurement by an external applied strain method and a polarimetric fiber laser sensor XIUJUAN YU,1,2,3 YACHEN GAO2,*

YUNXIN HU,1 XUEFENG CHEN,1 JINTAO ZHANG,1 SHENGCHUN LIU,1

AND

1

College of Physical Science and Technology, Heilongjiang University, Harbin 150080, China Department of Electronic Engineering, Heilongjiang University, Harbin 150080, China 3 e-mail: [email protected] *Corresponding author: [email protected] 2

Received 5 December 2017; revised 9 February 2018; accepted 12 February 2018; posted 13 February 2018 (Doc. ID 314968); published 14 March 2018

In this work, a high-sensitivity and low-cost sensing scheme for measuring intrinsic and induced fiber birefringence change is reported based on a polarimetric fiber laser sensor interrogated by the beat frequency technique. The fiber birefringence measurement is achieved by an external applied strain method. A detailed theoretical analysis of the principle for fiber birefringence measurement is carried out. Two alternative equations are given for determining the change of fiber birefringence, which make it very convenient for users to choose different order beat signals. To verify the performance of the sensing system, the external applied strain-induced fiber birefringence change is measured experimentally. The experiment result shows that the fiber birefringence experiences a linear increase with the increase of applied strain. A strain response coefficient of 4.646 × 10−11 ∕με is obtained. Furthermore, the repeatability and stability performances of the polarimetric fiber laser sensor are also investigated. © 2018 Optical Society of America OCIS codes: (280.3420) Laser sensors; (060.2370) Fiber optics sensors; (060.2300) Fiber measurements; (060.3735) Fiber Bragg gratings. https://doi.org/10.1364/AO.57.002033

1. INTRODUCTION Fiber birefringence is a very important parameter in the application areas of fiber communication systems, polarization sensitive fiber device fabrication, and optical fiber sensor technology, because it determines many polarization properties in optical devices and fibers including polarization mode dispersion, polarization controlling, and nonlinear polarization rotation [1–12]. Polarization mode dispersion induced by fiber birefringence will cause degradation of the transmission signal, which limits the transmission rate and distance for high-bit-rate optical fiber communication systems [2–5]. Many optical devices such as polarizers, depolarizers, and polarization controllers are realized based on the fiber birefringence effect [6–10]. In addition, many polarimetric sensors are also developed according to the fiber birefringence mechanism [11–17]. Therefore, precise measurement of fiber birefringence plays an important role in the above application fields. Several methods have been proposed and demonstrated for measuring fiber birefringence, including the fiber birefringence measurement systems for high-birefringence fibers [18,19] as well as for 1559-128X/18/092033-07 Journal © 2018 Optical Society of America

low-birefringence fibers [20,21]. Typical measurement systems for fiber birefringence are mainly based on the fiber interferometric technique, for example, by employing a Sagnac interferometer [22], Lyot–Sagnac interferometer [23], and Michelson interferometer [24,25] to measure fiber birefringence through analyzing the interferometer spectrum. However, the above methods usually require building complex interferometer systems and require expensive optical equipment such as an optical spectrum analyzer for wavelength scanning, which limits their practical applications. So it is significant and urgent to develop a fiber birefringence measurement scheme with a simple structure and low cost. The laser polarimetric sensing technique is very promising since it was first used to measure very small anisotropies of optically transparent media by a He–Ne laser, and a high sensitivity of 2.3 × 10−3 of the phase type was obtained for the mirror anisotropy [26]. Polarimetric fiber lasers have been reported for current measurement [14], stress measurement [15], strain and temperature measurement [16,17], as well as for differential pressure and force measurements [27]. In recent years, a

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multi-longitudinal-mode fiber laser based on beat frequency interrogation has been reported and employed to measure many parameters [28–33]. Liu et al. reported a multi-longitudinalmode fiber laser for strain measurement [28]. Yin et al. presented a beat frequency interrogated multi-longitudinal-mode fiberring laser for measurement of temperature [29] and vibration [30]. In these three sensing systems [28–30], only the longitudinal mode beat frequency is detected for sensing without using the polarization mode beat signal. Furthermore, the measurement of fiber birefringence [31], acoustic pressure [32], as well as double parameters of strain and temperature [33] have been reported based on the polarimetric fiber lasers by monitoring both the longitudinal mode beat signal and polarization mode beat signal. The proposed fiber laser sensing system only needs a well-developed photodetector (PD) and a frequency spectrum analyzer (FSA) to interrogate beat frequency signal, which makes it have several advantages such as simple structure, decrease in complexity, and immunity to intensity perturbation. Furthermore, the proposed fiber laser operates in the state of multi-modes, and the radio frequency spectrum exhibits a number of beat frequencies between different longitudinal modes, making it very convenient to choose different order beat frequencies for different application fields. In this work, an external applied strain method is applied to measure the induced fiber birefringence change. A simple and high-sensitivity fiber birefringence measurement scheme is developed based on a beat frequency interrogated polarimetric fiber laser. In the polarimetric fiber laser sensor, two types of beat frequency signals, including the longitudinal and polarization mode beat signals, exist simultaneously in the long cavity. Since these two types of beat signals have different responses to the applied strain, the strain-dependent fiber birefringence change can be obtained by measuring the frequency shift of these two types of beat signals. The principle of fiber birefringence measurement is analyzed theoretically in detail. Two alternative expressions for fiber birefringence change are provided, which make it very convenient for users to choose different order longitudinal and polarization mode beat signals. The influence of the beat frequency mode order on the sensitivity of the fiber laser has also been discussed, which is helpful for reader to know how to choose the beat frequency mode order in practical applications. To validate the feasibility of the designed system, the strain-induced birefringence in single-mode erbium-doped fiber (EDF) is measured experimentally. The repeatability and stability of the fiber laser sensor are also investigated. Compared to the conventional fiber birefringence measurement approaches, there is no need to analyze the modal interference spectrum, and the well-developed fiber laser and electronic beat frequency demodulation system make the proposed birefringence measurement approach possess several advantages, such as simple structure, low cost, and high sensitivity. The structure of this paper is as follows: Section 2 describes the principles of fiber birefringence measurement by the proposed polarimetric fiber laser sensor. Section 3 presents the experimental setup for measuring the fiber birefringence change and discusses the experimental results. In addition, the repeatability and stability performance are also discussed in Section 3. Finally, Section 4 summarizes the conclusions of this paper.

Research Article 2. OPERATION PRINCIPAL ANALYSIS Figure 1 shows the measurement setup of fiber birefringence by the polarimetric multi-longitudinal-mode fiber laser. The pump light from a 1480 nm laser diode transmits through an optical isolator (ISO) and a wavelength division multiplexer (WDM). After that, the pump light is injected into the cavity of the optical fiber laser. The function of the ISO is to suppress the backward reflected light. The cavity of the polarimetric fiber laser is made up of a piece of EDF and two fiber Bragg gratings (FBGs) with identical operating wavelengths. When the pump power is beyond the threshold power, the laser is stimulated in the cavity. The reflected fiber laser signal is launched into a photodetector (PD) and changed into electrical beat frequency signal. A radio frequency spectrum analyzer (FSA) is employed in the system to monitor the beat frequency signals. For the polarimetric fiber laser, when the pumping threshold condition is satisfied, many stable longitudinal modes are stimulated in the laser cavity since the laser cavity is very long. Therefore, there are many beat frequency beat signals in the frequency spectrum. If the fiber is ideal, there is no intrinsic birefringence in the fiber, and thus the two orthogonal polarization modes with the same mode order are degenerate. However, the fiber usually has intrinsic birefringence because of the geometric asymmetry of the fiber core, the internal residual stress. Therefore, the two orthogonal laser polarization modes will split slightly. Thus, two types of beat frequency signals are generated simultaneously in the polarimetric fiber laser: the first type is a longitudinal mode beat frequency signal induced by two different longitudinal modes with the same polarization direction, and the second type is the polarization mode beat frequency signal caused by two different orthogonal polarization modes. According to the laser principle, the frequency of longitudinal mode beat signal of fiber laser can be expressed as c Nc ; (1) f N j − i 2nL 2nL where j and i are laser mode numbers, N is the mode number of the beat signal and its value is N j − i (N 1; 2; 3…), c is light speed in empty space, n is the effective refractive index of fiber, and L is the total cavity length of the fiber laser. The frequency of the polarization mode beat signal induced by the fiber birefringence effect can be calculated by [32] Bjc B (2) f B 2 f j; 2n L n

Fig. 1. Schematic diagram of the polarimetric fiber laser (ISO, isolator; WDM, wavelength division multiplexer; FBG, fiber Bragg grating; SMF, single-mode fiber; EDF, erbium-doped fiber; PD, photodetector; FSA, frequency spectrum analyzer; SS, stationary stage; TS, translation stage).

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where B is the fiber birefringence and its value is B ny − nx , nx and ny are the effective refractive indices of polarization modes in the x and y directions, and f j jc∕2nL is the frequency of the jth laser longitudinal mode. Allowing for the polarization mode beat signals induced by other order laser modes with different polarization directions, a general expression for describing the frequency of polarization mode beat signals can be expressed as [32] B Nc B f ; f (3) ff B ; f N f B g: fP n j 2nl n j When axial strain is applied on the cavity of the fiber laser, the frequency will change due to the variation of cavity length, the effective refractive index, and the fiber birefringence. The variation of longitudinal mode beat signal induced by the applied strain can be expressed as l (4) Δf N − 1 − P e f N Δε; L where P e is the effective strain-optic coefficient, l is the effective length of the stretched fiber laser cavity, and Δε is the variation of the strain acting on the cavity. The change of the polarization mode beat frequency caused by the exerted strain could be expressed as [33] l 1 ΔB − 1 − 2P e f B Δε (5a) Δf B L B Δε and Δf N f B Δf N Δf B l 1 ΔB −1 − P e f N − 1 − 2P e f B Δε; L B Δε

(5b)

where ΔB is the variation of fiber birefringence induced by the exerted axial strain. Equations (5a) and (5b) describe the strain response of the lowest polarization mode beat signal f B and other polarization mode beat signals f B f N , respectively. From the mode generation principle of beat frequency signals, we can know that the longitudinal and polarization mode beat signals are the sum of many beat signals with the same laser frequency. If one laser mode is hopping, these two types of beat signals still exist. The amplitude of the beat signal will suffer dynamic change, but the strain is only determined by beat frequency. So the fiber laser has a relatively stable frequency characteristic and it is not influenced by mode hopping. Combining Eqs. (4) and (5a), the external straininduced fiber birefringence change can be calculated, which is expressed as L 1 Δf B 1 Δf N l −2 − Δε: (6) ΔB B l f B Δε f N Δε L The intrinsic fiber birefringence B in the case of no strain exerted on the laser cavity can be calculated by B

λf B ; Δf L

(7)

where λ is the laser operating wavelength, and it can be measured in the experiment. Δf is the frequency separation

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between any two adjacent longitudinal modes, and its value is c∕2nL. Substituting Eq. (7) into Eq. (6), the final expression of the strain-induced fiber birefringence change can be obtained as follows: λf B 1 Δf B 1 Δf N l ΔB −2 − Δε: (8) l Δf f B Δε f N Δε L In the bracket of Eq. (8), the first and second terms represent the strain response of the beat signals of f B and f N . Therefore, the fiber birefringence change can be calculated by Eq. (8) through the measurement of frequency shift of f B and f N with the applied strain. Furthermore, the fiber birefringence change can also be calculated by measuring the strain response of f N and its adjacent polarization beat signal of f N f B or f N − f B according to Eqs. (4) and (5b), which can be expressed as λf 2 Δf N l Δf P Δf N ΔB B − − fB − Δε; l Δf Δε Δε f N Δε L (9) where f P f N f B represent two polarization mode beat signals located at both sides of f N . For the case of f P f N f B , the sign in Eq. (9) is positive. For the case of f P f N − f B , the sign is negative. In Eq. (9), Δf P ∕Δε and Δf N ∕Δε describe the strain response of the selected polarization mode beat signal and the longitudinal mode beat signal. The measurement of the beat frequency shift of f P and f N at different strain levels allows us to work out the fiber birefringence change according to Eq. (9). Both Eqs. (8) and (9) can be used to calculate fiber birefringence change. Such two alternatives allow us to choose different order longitudinal and polarization mode beat signals as monitored signals according to the trade-off between the sensitivity and signal-to-noise ratio (SNR) of beat frequency signals. 3. EXPERIMENTS AND RESULTS The proposed scheme for measuring the fiber birefringence is illustrated as Fig. 1. The polarimetric fiber laser is made up of a pair of wavelength-matched FBGs and a section of 1.2 m long EDF. The total cavity length is equal to the fiber length between the middle of two FBGs, including the length of EDF, and the length of a single-mode fiber (SMF) at both ends connected to two FBGs. In this experiment, the total fiber laser cavity length is about 2.089 m. The FBGs are used as cavity reflectors. The central wavelength, 3 dB bandwidth, and reflectivity of FBGs are about 1550.92 nm, 0.2 nm, and 90%, respectively. The absorption coefficient of the EDF is about 37.2 dB/m at 1531 nm. As the pump power is beyond the threshold of the laser, a stable fiber laser is established, and many longitudinal laser modes are stimulated in the laser cavity. The reflected laser light is transformed into electrical signal through the PD, and then many beat frequency signals can be monitored by the FSA. The wavelength spectrum is measured by an optical spectrum analyzer and shown in Fig. 2. It can be observed that the operating wavelength of the fiber laser is about 1550.92 nm, which is equal to the central wavelength of FBG.

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Fig. 2. Wavelength spectrum of the polarimetric fiber laser.

The beat frequency signals are measured by the FSA, and the frequency spectrum is shown in Fig. 3. A number of beat frequency signals are generated in the frequency spectrum from 0 to 3 GHz, which means that the reported polarimetric fiber laser has a very large frequency band. Figure 3(b) shows the beat signals of the polarimetric fiber laser in the frequency range from 0 to 160 MHz. The above-mentioned two types of beat signals (i.e., longitudinal mode beat signals and polarization mode beat signals) can be observed clearly in Fig. 3(b). The longitudinal mode beat signals have higher SNR than the polarization beat signals. The dominant longitudinal mode beat signals are positioned at the locations with equal frequency spacing of 48.7 MHz. According to Eq. (1), f 1 c∕2nL Δf 48.7 MHz, we can predict that the effective refractive index of fiber used in this experiment is about 1.474. The SNRs of these longitudinal mode beat signals are greater than 50 dB. Besides the primary longitudinal mode beat signals, two polarization mode beat signals always appear at the symmetric positions on both sides of the primary longitudinal beat signals with an equal frequency separation of f B . In this experiment, the lowest polarization mode beat signal is located at 18.758 MHz, which means that f B 18.758 MHz. According to Eq. (7), the intrinsic fiber birefringence B is ∼2.854 × 10−7 , and it is in the same order of ∼10−7 as reported in Ref. [23] for low-birefringence fiber. Figure 3(c) shows the beat frequency signals in high frequency range from 1263 to 1463 MHz. As seen in Fig. 3(c), both longitudinal and polarization mode beat signals also have relative high SNR in high frequency range. It should be pointed out that according to Eq. (4), the higher the frequency of beat signals, the higher the sensitivity for measuring strain-induced birefringence. However, when the mode order goes up, the SNR of beat frequency signals decreases. Therefore, if the higher-order beat signals have relatively high SNR, it is better to choose a much higher beat frequency as a detecting signal for improving the sensitivity of the sensor. When the fiber laser cavity is stretched, the fiber birefringence will change due to the external perturbation induced by strain. To measure the induced fiber birefringence change, a section of 1 m long EDF is chosen as sensing fiber. To make sure that the sensing fiber is straight and does not undergo

Fig. 3. (a) Frequency spectrum of the laser in the range of (a) 0– 3 GHz, (b) 0–160 MHz, (c) 1260–1460 MHz. (LMBF, longitudinal mode beat frequency; PMBF, polarization mode beat frequency.)

bend-induced birefringence, two ends of the sensing fiber are fixed. One end of the sensing fiber is fixed on a stationary stage (SS), and the other end is fixed on a translation stage (TS). During the test, the stationary stage is fixed, and the translation stage can be moved manually with a stepping resolution of 0.01 mm. The axial strain from 0 to 4000 με is applied on the sensing fiber. The longitudinal mode beat signal of f 28 located at 1363.374 MHz, and the polarization mode beat signal of f B positioned at 18.758 MHz are chosen as the detecting beat frequency signals. The linewidth of the beat signal will

Research Article affect the measurement precision. In theory, the narrower the linewidth is, the higher the measurement precision could be obtained. In our experiment, the SNR and linewidth for f 28 and f B are about 44.5 dB, 19.4 dB, 37.2 kHz, and 32.4 kHz, which can provide relatively good precision for strain measurement. The frequency spectra of beat signals f 28 and f B are plotted in Figs. 4(a) and 4(b). It is obvious that when the applied strain is increased from 0 to 4000 με, the two beats signals experience an opposite shift direction. With the increase of applied strain, the beat frequency signal of f 28 drifts to lower frequency, whereas the beat frequency signal of f B drifts to higher frequency. The experimental result shows that the fiber birefringence increases with the increase of strain according to Eq. (4). Figure 5 plots the relationship of the beat frequency and the applied strain for f 28 and f B . It can be seen that the beat frequency shows a good linear change trend with the increase of strain. By performing linear fitting to the experimental data of strain and beat frequency for f 28 and f B , the slopes of fitting lines can be obtained and shown in Fig. 5. It indicates that the strain sensitivities of f 28 and f B are −0.490 kHz∕ με and 1.45 kHz/ με, respectively, with the correlation coefficients of 0.9998 and 0.9998, respectively. The experimental data shows that the frequency of the beat signals experience a good linear change with the increase of strain. So the proposed fiber

Fig. 4. Frequency spectra at different strain levels (a) for the beat frequency f 28 and (b) for the beat frequency f B.


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Fig. 5. Strain response of f 28 and f B .

laser can be employed to measure the strain-induced fiber birefringence change for a single-mode fiber with short length, which is also applied to EDF. According to the strain response of f 28 and f B , the strain-induced fiber birefringence change could be calculated according to Eq. (8). The change of fiber birefringence at different levels is plotted in Fig. 6. It is obvious that the fiber birefringence increases linearly with the increase of the applied strain. When the applied strain changes from 0 to 4000 με, the fiber birefringence varies from 2.854 × 10−7 to 4.696 × 10−7 . The change of fiber birefringence is about 1.842 × 10−7 . By performing linear fitting, we can obtain the strain sensitivity coefficient of fiber birefringence, which is about 4.646 × 10−11 ∕ με. The experimental result indicates that the polarimetric fiber laser can be used to measure very tiny fiber birefringence change for short fiber, such as in the order of 10−11 for short fiber length of a meter. In this experiment, we have also investigated the repeatability and stability of the polarimetric fiber laser sensor, since they are very important for practical applications when measuring fiber birefringence. To test the repeatability performance of the fiber laser, two-cycle tests of strain rising up and down are carried out. The strain response of the beat signals of f 28 and f B are plotted in Figs. 7(a) and 7(b) for the two-cycle tests. By performing linear fitting to the experimental data, the slopes of the fitting line can be obtained, which are shown in Fig. 7. The strain sensitivities of f 28 are −0.49 kHz∕ με,

Fig. 6. Fiber birefringence at different strain levels.

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standard deviation of the strain sensitivities is about 1.85 × 10−13 ∕ με. This indicates that the polarimetric fiber laser sensor possesses good repeatability performance for measuring fiber birefringence change. The stability performance of the fiber laser sensor is also investigated. The fiber laser is kept at room temperature without strain exerted on the cavity of the fiber laser. The beat frequencies of the polarization mode beat signal and the longitudinal mode beat signal are recorded every 5 min for 100 min. The fluctuation of the two-beat frequency signals of f 28 and f B is about 2.8 kHz and 3.2 kHz. The corresponding strain precision for f 28 and f B are about 5.7 με and 2.2 με. The strain sensitivity of the fiber birefringence is about 4.646 × 10−11 ∕ με, and a precision of 2.64 × 10−10 can be obtained for the fiber birefringence change. 4. CONCLUSIONS

Fig. 7. Repeatability test of (a) the longitudinal mode beat signal f 28 and (b) the polarization mode beat signal f B .

−0.475 kHz∕ με, −0.487 kHz∕ με, and −0.473 kHz∕ με, and the correlation coefficients are about 0.9996, 0.9994, 0.9995, and 0.9993. The strain sensitivities of f B are about 1.45 kHz/με, 1.43 kHz/με, 1.45 kHz/με, and 1.41 kHz/με, with the correlation coefficients of 0.9997, 0.9992, 0.9997, and 0.9993. The corresponding birefringence changes in the two-cycle tests are shown in Fig. 8. The sensitivity coefficients of fiber birefringence are 4.616 × 10−11 ∕ με, 4.618× 10−11 ∕ με, 4.644 × 10−11 ∕ με, and 4.653 × 10−11 ∕ με, respectively. The correlation coefficients of the linear fittings are 0.9998, 0.9992, 0.9997, and 0.9993, respectively. The

Fig. 8. Fiber birefringence change in the repeatability test.

In summary, a high-sensitivity and low-cost fiber birefringence measurement scheme has been proposed by a polarimetric multi-longitudinal-mode fiber laser and a well-developed electronic beat frequency demodulation technique. The straininduced fiber birefringence change is obtained by using the external applied strain method. The principle of fiber birefringence measurement is analyzed in detail. The theoretical expression for the strain-induced fiber birefringence change has been deduced theoretically in terms of the strain response of beat frequency signals, the laser operating wavelength, and the sensing cavity length. By measuring the frequency shift of a longitudinal mode beat signal and a polarization mode beat signal, the fiber birefringence change induced by the applied strain can be measured. The experimental result indicates that the intrinsic fiber birefringence in the case of without applying strain is about 2.854 × 10−7 , which is in the order of ∼10−7 and agrees well with what is reported in previous works [23]. The fiber birefringence increases linearly with the increase of the axial strain, with a strain sensitivity coefficient of 4.646 × 10−11 ∕ με. The repeatability and stability performance of the polarimetric fiber laser are also investigated experimentally. A precision of 2.64 × 10−10 can be obtained for fiber birefringence change. The proposed fiber birefringence measurement system is of low cost, simple structure, high sensitivity, and it will provide great convenience for short fiber birefringence measurement. The developed sensing system can be used to measure a very tiny fiber birefringence change induced by strain in very short low-birefringence single-mode fiber, and it is also applied to commercial EDF for measuring fiber birefringence change. The sensitivity is up to the order of ∼10−11 ∕ με. It helps us to know deeply the birefringence characterization of the commercial single-mode fiber, which is available to describe the polarization optics of single-mode fiber samples. Furthermore, many other parameters, such as temperature, lateral force, bending, and twisting can also cause the change of fiber birefringence, so the proposed measurement scheme has great potential in the field of fiber active sensing applications. Funding. National Natural Science Foundation of China (NSFC) (61575061, 61605043); China Postdoctoral Science

Research Article Foundation (2016M601466, 2017T100254); Natural Science Foundation of Heilongjiang Province (F2017026); Postdoctoral Foundation of Hei Long Jiang Province (LBH-Z16713); Science and Technology Innovation Talents Special Fund Project of Harbin province (2016RQQXJ111); Fundamental Research Funds for the Universities in Heilongjiang Province (HDRCCX-2016208); Outstanding Youth Science Foundation of Heilongjiang University (HU) (JCL201606). Acknowledgment. We thank the reviewers for helpful suggestions and thank L. Gao, Z. Yin, H. Zhang, and other authors for their technical support in the previous works cited in the reference list.

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