High-resolution distributed polarization crosstalk measurement for polarization maintaining fiber with considerable dispersion

Zhangjun Yu; Jun Yang; Yonggui Yuan; Hanyang Li; Changbo Hou; Chengcheng Hou; Haoliang Zhang; Shuaifei Tian; Xu Lu; Xiaojun Zhang; Fuqiang Jiang; Zheng Zhu; Jianzhong Zhang; Yu Zhang; Zhihai Liu; Libo Yuan

doi:10.1364/OE.26.029712

1. Introduction

Polarization maintaining fiber (PMF) is widely used in the field of optical fiber sensing, especially in distributed stress sensing [1,2] based on the polarization mode coupling effect (i.e., polarization crosstalk). Polarization crosstalk occurs at internal defects or external stresses of the PMF. Thus, the variation of the polarization crosstalk can sense the intensity and the position of the external stress. Another modality of sensing applications requires a PMF being wound to a coil. A PMF coil provides an optical path difference of several kilometers in a small volume. It can be used as the sensing unit of an angular rate sensor based on the Sagnac interferometer [3–7]. It can also be used in an acceleration sensor [8] based on the Michelson or Mach-Zehnder interferometer. In such sensors, the polarization crosstalk will degrade the sensing performance. Therefore, quality evaluation of a PMF coil based on the distributed polarization crosstalk measurement is necessary [9].

Optical coherence domain polarimetry (OCDP) based on white light interferometry is a common method for measuring distributed polarization crosstalk [9,10]. In OCDP, we inject light into one polarized axis of a PMF and examine the wave packets coupled to the other axis, thereby measuring the interferogram generated from the wave packet output from the input polarized axis and the wave packets output from the other axis [11]. However, the inter-mode chromatic dispersion [12], birefringence dispersion for short [13,14], between the LP₀₁_x mode and LP₀₁_y mode of the PMF obscures the interferogram [15]. The second-order birefringence dispersion broadens and decays the envelope of an interferometric peak, thus degrading the spatial resolution of the distributed polarization crosstalk measurement [16]. The third-order birefringence dispersion distorts the envelope of the interferometric peak and results in an oscillatory tail. In the case of two or more interferometric peaks, the second-order birefringence dispersion gives rise to peak splitting [17].

In other coherent measurement fields such as the optical coherence tomography, dispersion compensation can be implemented using a dispersion-matching medium inserted in one arm of the interferometer [18,19]. However, this method is not flexible compared to software methods in the field of optical fiber measurement. Li et al. presented a multiplier method to improve the spatial resolution against birefringence dispersion. They measured a 1.05-km-length PMF coil with a second-order birefringence dispersion coefficient of 0.0014 ps/nm/km [13], yet this method required the accurate position of the interferometric peak as prior information. When the birefringence dispersion is considerable, the interferometric peaks corresponding to a small coupling coefficient will decay and submerge in the noise. We could not determine the accurate position of an interferometric peak, and are not sure whether there is an interferometric peak.

Zhang et al. fitted the envelope of an interferometric peak to estimate its real amplitude, by which they mitigated the birefringence dispersion effect on the distributed polarization crosstalk measurement for a 500-m-length PMF coil with a second-order birefringence dispersion coefficient of 0.018 ps/nm/km [20]. However, this method is also valid only for visible interferometric peaks. Jin et al. presented a phase packet method that eliminates birefringence-dispersion-induced phase distortion in the Fourier domain. They measured a 20-m-length PMF with a second-order birefringence dispersion coefficient of 0.0014 ps/nm/km [12]. Nonetheless, they only considered the case of a single interferometric peak with modest birefringence dispersion. In the case of considerable birefringence dispersion and numerous interferometric peaks, dealing with every peak using the phase packet method directly is an impossible task.

In this paper, we present an iterative matched filter (IMF) method that copes with the considerable birefringence dispersion situation, and apply our method to characterize the distributed polarization crosstalk of a PMF coil wound by a PMF with a length of 3 km. The PMF coil has an internal and external diameter of 12.7 and 14.5 cm, respectively. The PMF coil has a considerable birefringence dispersion coefficient (0.235 ps/nm/km) owing to the internal stress. In the theory section, we review the measurement principle of the OCDP, the dispersion effect in the measurement result, and introduce the IMF method.

In the simulation section, we demonstrate the dispersion compensation results using different matching dispersions for the conventional phase packet method and of different iterations for the IMF method. These simulations show the reasonability of using the IMF method. In the experiment section, we compare the spatial resolution of the distributed polarization crosstalk direct measurement result and its counterpart with dispersion compensation using the IMF method. This is the only one method that can thoroughly solve the problem of the dispersion effect for PMF coils with considerable birefringence dispersion coefficient. There is no reference method to confirm the correctness of the results. Therefore, we design a self-proof experiment in the end.

2. Theory

2.1 Birefringence dispersion effect in OCDP

Figure 1 shows the measurement principle of the optical-fiber-based OCDP system. The broadband light emitted from a superluminescent diode (SLD) is injected into the slow axis of the PMF through a 0° polarizer and excites the LP₀₁_x mode, also known as the excited mode (EM). One end of the PMF coil under test is spliced with the pigtail of the polarizer at point P_n. The polarization crosstalk occurs at the perturbation point, P_n, and excites the LP₀₁_y mode of the PMF, i.e., the coupled mode (CM). The coupled mode corresponding to the perturbation point, P_n, is denoted by CM_n.

Fig. 1 Schematic diagram of measurement principle of optical-fiber-based OCDP system. SLD: superluminescent diode; C1, C2: couplers; PC: polarization state controller; PD: photodiode; DAQ: data acquisition; EM: excited mode; CM: coupled mode; OPD: optical path difference.

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We use a purple flashes to show the polarization coupling process. The group refractive index of the fast axis, N_gy, is slightly smaller than that of the slow axis, N_gx. Therefore, the wave packet, or wavetrain, transmitting in the fast axis has the larger group velocity. This is the reason that we call it the fast axis. Over a period, the excited mode and the coupled mode transmit different distances in the PMF but go through the identical optical path. We use a pair of dashed-line Gaussian envelopes and a pair of solid-line Gaussian envelopes to express this process. The length of the horizontal axis represents the optical path. The distance between the perturbation point P_n and the 45° analyzer is L_n.

At the end of the PMF, the optical path difference between the excited mode (EM) and the coupled mode (CM_n) is $Δ N_{g} L_{n}$ , where $Δ N_{g} = N_{g x} - N_{g y}$ is the group birefringence of the PMF. These modes are coupled to a single-mode fiber with the same insertion loss by the 45° analyzer, and we use a green flash to show this process. Owing to other perturbation points of the PMF, such as the splicing point of the PMF and the analyzer, P₁, there are numerous coupled modes in the fast axis: CM₁, CM₂, …, CM_n.

All of these coupled modes, or wave packets, are then coupled to the single-mode fiber. These wave packets carry the information of the polarization crosstalk coefficient and the positions of the corresponding perturbation points. In the end, we use a scanning interferometer and a data acquisition system to detect these wave packets based on interferometry. The splitting ratios of the two 2 × 2 couplers, C1 and C2, are both 50:50. The upper arm of the interferometer that contains moving components is referred to as the scanning arm, while the other arm is referred to as the reference arm.

Two GRIN-lenses are mounted on the scanning stage for optical path scanning. The polarization state controller in the reference arm is used to suppress the polarization fading effect. The wave packets above, including the excited mode and all coupled modes, are divided into two identical replicas by coupler C1. They interfere after transmitting through coupler C2. The photodiode detects the interferogram, and the data acquisition card records it. We can obtain the polarization crosstalk coefficient and the position of the perturbation point from the corresponding interferometric peak.

If the electric field of the light emitted from the light source is denoted as $E_{in} (t) = E (ω) \exp (- i ω t)$ , the series of wave packets output from the analyzer can be expressed as

E_{HE} = \frac{\sqrt{2}}{2} [E_{x} (t) + \sum_{j = 1}^{n} E_{y j} (t)]

where

E_{x} (t) = \sqrt{2} E_{in} (t) / 2 \cdot \exp [i β_{x} (ω) L]

is the electric field of the excited mode,

E_{y j} (t) = Γ (L_{j}) \cdot \sqrt{2} E_{in} (t) / 2 \cdot \exp [i β_{x} (ω) (L - L_{j}) + i β_{y} L_{j}]

is the electric field of the coupled mode at the perturbation point P_j, and i is the imaginary unit. The length of the PMF between the polarizer and the analyzer is L, including their pigtails and the PMF coil under test. The distance between the perturbation point P_j, and the analyzer is L_j. The polarization crosstalk coefficient at perturbation point P_j is

Γ (L_{j})

. The propagation constants of the slow axis and fast axis of the PMF are

β_{x} (ω)

and

β_{y} (ω)

, respectively.

The interferogram is expressed as

I (τ) = \frac{1}{4} 〈 {[E_{x} (t + τ) + \sum_{j = 1}^{n} E_{y j} (t + τ)]}^{*} \cdot [E_{x} (t) + \sum_{j = 1}^{n} E_{y j} (t)] 〉

where

〈 \cdot 〉

denotes the ensemble average,

{[\cdot]}^{*}

denotes the complex conjugate operator, and τ is the delay. We are mainly concerned with the interferometric peaks occurring in the interference between the excited mode and every coupled mode:

\begin{array}{l} I_{c ouple} (τ) = \frac{1}{4} \sum_{j = 1}^{n} 〈 E_{x}^{*} (t + τ) E_{y j} (t) 〉 \\ \begin{matrix}  \end{matrix} = \frac{1}{8} \sum_{j = 1}^{n} {Γ (L_{j}) \int_{ω} | E (ω) |^{2} \cdot \exp [i ω τ - i Δ β (ω) L_{j}] d ω} \end{array}

where

Δ β (ω) = β_{x} (ω) - β_{y} (ω)

is the propagation constant difference. Using a Taylor series, we expand it as

\begin{array}{l} Δ β (ω) = Δ n_{g} \cdot ω_{0} / c + Δ N_{g} (ω - ω_{0}) / c - \frac{Δ D}{2!} \frac{2 π c}{ω_{0}^{2}} {(ω - ω_{0})}^{2} \\ \begin{matrix}  \end{matrix} + \frac{1}{3!} \frac{4 π c}{ω_{0}^{3}} (\frac{π c}{ω_{0}} \cdot Δ S + Δ D) {(ω - ω_{0})}^{3} + \dots \end{array}

where ∆D is the second-order birefringence dispersion coefficient at angular frequency ω₀, ∆S is the third-order birefringence dispersion coefficient at angular frequency ω₀, ∆N_g is the group birefringence, ∆n_g is the phase birefringence, and c is the light velocity in a vacuum. If there is no birefringence dispersion, the perturbation point P_j corresponds to an interferometric peak centered at

τ = Δ N_{g} L_{j} / c

.

If there is no dispersion, the spatial resolution of the OCDP is estimated as [17]

l_{c} = \frac{4 \ln 2}{π Δ N_{g}} \frac{λ_{0}^{2}}{Δ λ}

where λ₀ is the central wavelength of the light source, and ∆λ is the full width at half maximum of the light source spectrum.

Figure 2 shows the birefringence dispersion effect on the shape of the interferometric peaks, which we mentioned in the introduction. Equation (3) indicates that the interferogram is a simple superposition of all interferometric peaks. However, the envelope of the interferogram superposed by several interferometric peaks is complicated and confused by the birefringence dispersion.

Fig. 2 Birefringence dispersion effect on envelope shape of interferometric peaks. “None reported” means that such cases have never been reported before in any literature.

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2.2 Iterative matched filter algorithm

In the case of a single interferometric peak, the interferogram can be expressed as

\begin{array}{l} I_{couple} (τ) = \frac{1}{8} Γ (L_{j}) \int_{ω} | E (ω) |^{2} \exp [i ω (τ - Δ N_{g} L_{j} / c)] \\ \begin{matrix}  \end{matrix} \times \exp [i L_{j} φ (ω, Δ D, Δ S)] d ω \end{array}

where

φ (ω, Δ D, Δ S)

is the phase distortion induced by the birefringence dispersion of a unit-length PMF. The interferogram with dispersion compensation by the phase packet method can be expressed as [12]

\begin{array}{l} I_{c} (τ) = F^{- 1} {F [I_{c o u p l e} (τ)] \times e x p [- i L_{j} φ (ω, Δ D, Δ S)]} \\ = \frac{1}{8} Γ (L_{j}) \int_{ω} {| E (ω) |}^{2} e x p [i ω (τ - Δ N_{g} L_{j} / c)] d ω \end{array}

where

L_{j} φ (ω, Δ D, Δ S)

is the phase packet constructed using the birefringence dispersion and the position of the interferometric peak.

F

and

F^{- 1}

are the Fourier transform operator and the inverse Fourier transform operator, respectively.

In the case of a PMF coil with a considerable birefringence dispersion coefficient, interferometric peaks at different positions require distinct phase packets. Additionally, we do not know the positions of the peaks.

Fortunately, we noticed the matched filter property of the phase packet method. We constructed a phase packet, $ξ φ (ω, Δ D, Δ S)$ , using an arbitrarily chosen position ξ and used it to remove the birefringence dispersion effect of the interferogram expressed by Eq. (3). The result can be expressed as

\begin{array}{l} I_{c ouple} (τ) = \frac{1}{8} \sum_{j = 1}^{n} {Γ (L_{j}) \int_{ω} | E (ω) |^{2} \exp [i ω (τ - Δ N_{g} L_{j} / c)] \\ \begin{matrix}  \end{matrix} \times \exp [i (L_{j} - ξ) φ (ω, Δ D, Δ S)] d ω \end{array}

where

Δ φ = (L_{j} - ξ) φ (ω, Δ D, Δ S)

is the residual dispersion-induced phase.

In Fig. 3(a), we used a blue line to illustrate the second-order birefringence dispersion distribution of the interferogram expressed in Eq. (3). After the dispersion compensation procedure using the phase packet method, the second-order birefringence dispersion distribution of the interferogram expressed in Eq. (8) is shown as the red line in Fig. 3(a).

Fig. 3 (a) Matched filter property of phase packet method; (b,c,d) Birefringence dispersion evolution of interferogram when using IMF method; (e) Flowchart of IMF algorithm.

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In other words, the phase packet method could eliminate the birefringence dispersion of the interferogram at an arbitrary matching position, or rather matching dispersion, regardless of whether there is a perturbation point at this position. At the same time, the birefringence dispersion of the interferometric peaks at a nearby position is suppressed to some extent. However, the position without birefringence dispersion, $η = 0$ , imposes a dispersion phase identical to the phase packet.

In Fig. 3(b), we show the birefringence dispersion of the interferogram without (blue line) and with (red line) dispersion compensation using the phase packet, $l φ (ω, Δ D, Δ S)$ . This time, we chose a matching position l quite close to the zero dispersion position. The birefringence dispersion at position l is small enough that the birefringence dispersion effect is negligible. Therefore, the birefringence dispersion of the interferometric peaks located at section $η = [0, l]$ is negligible.

In addition, we cut section $η = [0, l]$ from the interferogram, and the dispersion compensation is taken only on section $η = [l, L]$ . After this procedure, the birefringence dispersion of the interferogram at section $η = [l, 2 l]$ is negligible. We continue the above operation iteratively until the birefringence dispersion of all sections of the interferogram is negligible, and stitch all of the sections in the end. Figures 3(c) and (d) show the evolution of the birefringence dispersion. Figure 3(e) shows a flowchart of the IMF algorithm.

The matching position l is an essential parameter in our method, which is closely related to the birefringence dispersion threshold as shown in Fig. 3(d). The dispersion threshold is the maximum residual dispersion after dispersion compensation with our method. The residual dispersion induces the intensity error of the interferometric peak. Therefore, the intensity error that we can tolerate determines the matching position l. In addition, a large birefringence dispersion coefficient (slope of the birefringence dispersion curve) implies a short length of l. The birefringence dispersion-induced intensity of an interferometric peak can be expressed as [16]

{\begin{matrix} I = \frac{1}{\sqrt[4]{1 + η^{2}}} I_{0} \\ η = 2 π c \cdot Δ D \cdot l \cdot {(\frac{1}{2 \sqrt{2 \ln 2}} \cdot \frac{Δ λ}{λ_{0}})}^{2} \end{matrix}

where I₀ is the intensity of the interferometric peak without birefringence dispersion, I is the intensity of the interferometric peak with birefringence dispersion, c is the velocity of light in a vacuum, ΔD is the second-order birefringence dispersion coefficient, l is the PMF length, Δλ is the full width at half maximum of the light source spectrum, and λ₀ is the central wavelength of the light source. Therefore, the birefringence-dispersion-induced intensity attenuation can be expressed as

Δ I = - 20 \lg (I / I_{0}) = 5 \lg (1 + η^{2})

. Moreover, the matching position l can be calculated as

l = \frac{4 \ln 2}{π c} \cdot \frac{\sqrt{10^{Δ I / 5} - 1}}{Δ D} \cdot {(\frac{λ_{0}}{Δ λ})}^{2}

3. Simulation

3.1 Matched filter property of phase packet method

In this subsection, we demonstrate the matched filter property of the phase packet method by simulation, which is the basis of the IMF method.

Let us consider a 406-m-length PMF with ∆D = 0.235 ps/nm/km and ∆S = 8 × 10⁻⁴ ps/nm²/km. There are nine perturbation points located at η = 2.5 m, 3 m, 3.5 m, 102.5 m, 103 m, 103.5 m, 402.5 m, 403 m, and 403.5 m. The polarization crosstalk coefficients of these nine points are identical. The distributed polarization crosstalk of the PMF is partly shown in Figs. 4(a1)–4(a3). The inset of Fig. 4(a1) shows a close-up view of an interferometric peak with negligible birefringence dispersion. In Fig. 4(a1), we can distinguish the three perturbation points clearly and obtain the polarization crosstalk coefficient. However, in Figs. 4(a2) and (a3), we fail to do so.

Fig. 4 Dispersion compensation results using phase packet method with different matching dispersions. There are nine perturbation points with identical polarization crosstalk coefficients located at η = 2.5 m, 3 m, 3.5 m, 102.5 m, 103 m, 103.5 m, 402.5 m, 403 m, and 403.5 m. (a1–a3) Original simulation data of distributed polarization crosstalk of nine points; (b1–b3) Dispersion compensation results using phase packet method with position matched at 100 m; (c1–c3) Dispersion compensation results using phase packet method with position matched at 400 m.

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The dispersion compensation result with position matching at 100 m using the phase packet method is partly shown in Figs. 4(b1)–4(b3). The interferometric peaks near 103 m can be distinguished now. The interferometric peaks near 3 m are severely obscured by the birefringence dispersion.

The dispersion compensation result with position matching at 400 m using the phase packet method is partly shown in Figs. 4(c1)–4(c3). Similarly, the interferometric peaks near 403 m can be distinguished now. The results in Figs. 4(a2), (a3), and (b3) are nearly symmetrical to those in Figs. 4(b1), (c1), and (c2), respectively, which is because their third-order birefringence dispersions are opposite in sign.

3.2 Iterative matched filter simulation

In this subsection, we demonstrate the validity of the IMF method. A PMF coil with a diameter of 15.92 cm has weak perturbation points at every 50 cm. Thus, in this simulation, we considered an 8-m-length PMF with 16 perturbation points every 50 cm. We chose a few perturbation points in order to obtain a clear result. Accordingly, the length of the PMF is short, and the birefringence dispersion coefficient used in the last simulation is small. Thus, we chose the birefringence dispersion coefficients as ∆D = 2.35 ps/nm/km and ∆S = 0.008 ps/nm²/km, which are 10 times those of the previous simulation.

The distributed polarization crosstalk of the PMF is shown in Fig. 5(a). The noise floor is −60 dB. The polarization crosstalks of the perturbation points are 0 dB, −3 dB, −6 dB, −9 dB, −12 dB, −15 dB, −18 dB, −21 dB, −24 dB, −27 dB, −30 dB, −33 dB, −36 dB, −39 dB, −42 dB, and −45 dB. In the presence of birefringence dispersion, the original data in Fig. 5(a) are obscure.

Fig. 5 Dispersion compensation results using IMF method with different iterations. (a) Original simulation data of distributed polarization crosstalk of 16 perturbation points with identical polarization crosstalk coefficients; (b2–b4) Dispersion compensation results of first three iterations using the IMF method; (c5–c8) Dispersion compensation results of last four iterations using IMF method.

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Using the IMF method with l = 1 m, we obtained the results shown in Figs. 5(b1)–5(b5) after three iterations. Because of the residual dispersion of the interferogram shown in Fig. 5(b5), it becomes the “data to be processed.” Figures 5(c1)–5(c8) show the dispersion compensation results after seven iterations. The residual dispersion of the interferogram in all eight sections is acceptable. Thus, we stitched them together as the output, from which we could distinguish the 16 interferometric peaks.

The intensities of these interferometric peaks with dispersion compensation are 0.03 dB, −3.13 dB, −5.97 dB, −9.15 dB, −11.98 dB, −15.16 dB, −17.97 dB, −21.15 dB, −23.93 dB, −27.13 dB, −30.01 dB, −33.20 dB, −36.05 dB, −38.95 dB, −42.01 dB, and −45.10 dB. There are two interferometric peaks in every subplot of Fig. 5(c). The intensity error of the left peak, less than 0.1 dB, is owing to the noise. The intensity error of the right one peak, less than 0.2 dB, is owing to the noise and residual dispersion. The residual dispersion can induce an intensity error of 0.15 dB from Eqs. (9)–(10).

4. Experiment and results

The experimental setup for measuring the distributed polarization crosstalk of the 3-km-length PMF coil is shown in Fig. 6. The OCDP instrument is homemade and contains a light source, scanning interferometer, and data acquisition system. The optical fiber polarizer and analyzer are spliced to the PMF coil under test at points, A and B, respectively. A 3-km-length PMF coil is usually wound with an inner diameter and an external diameter of 10–20 cm, ~100 turns every layer, and ~64 layers.

Fig. 6 Configuration of experimental setup. (rad.: radius)

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The yellow color is owing to the glue. The winding starts from the midpoint of the fiber length and proceeds out toward the fiber ends. Half the fiber is wound clockwise (denoted by a circle with a cross) and the other half counterclockwise (denoted by a circle). Such a winding pattern requires a high level of expertise and experience to manage the alternating layers of optical fiber. Winding defects will degrade the performance of the PMF coil. The distributed polarization characteristics of a PMF coil are entirely different from a PMF without winding owing to the axial- and lateral-strain.

4.1 High-resolution distributed polarization crosstalk measurement

Figure 7(a) shows the direct measurement result of the distributed polarization crosstalk of the 3-km-length PMF coil. Insets (i–iii) show different sections of the interferogram. From inset (i), we can see some comb-like interferometric peaks with quite a low signal-to-noise ratio (SNR), yet from inset (ii), we cannot. In inset (iii), we can see only one peak with a width of 12.36 m. The birefringence dispersion severely obscures the result. Thus, we can obtain no useful information about the PMF coil under test.

Fig. 7 (a) Distributed polarization crosstalk direct measurement result of 3-km-length PMF coil; (b) Dispersion compensation result using IMF method. Inset: close-up view of labeled dashed boxes, (i)–(vi).

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The dispersion compensation result using the IMF method is shown in Fig. 7(b). Insets (iv), (v), and (vi) are counterparts to insets (i), (ii), and (iii), respectively. The comb-like interferometric peaks have higher SNRs than those in inset (i). The interferometric peaks in inset (v) show up normally. In addition, the one broad peak in inset (iii) changes to two peaks with a width of only 0.09 m. After dispersion compensation with the IMF method, we obtained the high-resolution distributed polarization crosstalk of the PMF coil.

The second-order birefringence dispersion coefficient of the 3051m-length PMF is ΔD = 0.235 ps/nm/km, the full width at half maximum of the light source spectrum is Δλ = 40 nm, and the central wavelength of the light source is λ₀ = 1550 nm. Thus, the dispersion parameter can be calculated as η ≈162.3, and the intensity attenuation can be calculated as ~22.1 dB. The intensities of the interferometric peaks in Figs. 7(iii) and 7(vi) are −37.9 dB and −17.85 dB, respectively, which implies that the intensity attenuation is 20.05 dB. The difference between the estimated theoretical value and the measured value is perhaps owing to the two peaks in Fig. 7(vi).

4.2 Correctness verification via different measurement directions

From the result in Fig. 7(b), we see a high-resolution distributed polarization crosstalk of the PMF that can distinguish every peak, but we are more concerned with the actual intensity and the position of the peak. Because the IMF method is the only one that can thoroughly solve the problem of the dispersion effect for PMF coils with considerable birefringence dispersion coefficients, there is no reference method to demonstrate the correctness of the results.

Here, we designed a self-proof experiment to solve this problem. The birefringence dispersion of an interferometric peak is proportional to the distance between the perturbation point and the analyzer. If we splice end A and end B of the PMF coil in Fig. 6 to the analyzer and the polarizer, respectively, the directly measured distributed polarization crosstalk will be entirely different than that shown in Fig. 7(a). One perturbation point in the PMF coil will be affected by different birefringence dispersion in the two measurements. However, the actual polarization crosstalk of the perturbation point is identical, and the measurement result should also be the same without birefringence dispersion. The dispersion compensation results of the two measurements with the light injected from A and B are shown in Fig. 8. The intensity and position of the interferometric peaks of the two results match well.

Fig. 8 Comparison between different measurement directions. Inset: close-up view of labeled dashed boxes, (i)–(ii).

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The periodic peaks every ~50 cm correspond to the cross-talk associated with the diameter of the coil (i.e., the fiber length of a turn), and the periodic peaks every ~50 m correspond to the cross-talk associated with the fiber length of a layer. However, the the specific causes of the periodic peaks are still unknown. At present, we attribute them to the variation of the lateral strain between fiber and fiber. Nevertheless, the causes of the periodic peaks are beyond the scope of this manuscript, and this is research that we will conduct in the future.

5. Conclusion and discussion

We theoretically analyzed the matched filter property of a dispersion compensation algorithm based on the phase packet method, and demonstrated it by simulation. We presented the IMF method to compensate the birefringence dispersion of the distributed polarization crosstalk measurement result for a PMF coil with a considerable birefringence dispersion coefficient. The simulations demonstrate the validity of the IMF method. Using it to process the distributed polarization crosstalk measurement result of a 3-km-length PMF coil resulted in a spatial resolution of 0.09 m at any position of the PMF, which is an enhancement of two orders of magnitude.

In addition, we designed a self-proof experiment that measured the distributed polarization crosstalk of the PMF coil with different directions and compared their dispersion compensation results. The intensities and positions of the interferometric peaks in the two results matched well. There was a tradeoff between the matching position l and the time consumption of data processing when we used the IMF method. To reduce the residual birefringence dispersion, we should choose a small length of l. However, the time consumption of data processing is inversely proportional to the length of l.

In general, we chose the length of l as 4 m, which corresponds to a residual dispersion-induced intensity attenuation of 0.1 dB. Because the IMF method requires no prior information about the PMF parameters except for the birefringence dispersion, the proposed method is also valid for uncoiled PMF or PMF coils with other parameters.

Funding

National Key R&D Program of China (2016YFF0200700, 2017YFB0405502); National Natural Science Foundation of China (NSFC) (61635007).

References

1. H. Zhang, Y. Wang, G. Wen, D. Jia, and T. Liu, “Frequency demodulation of dynamic stress based on distributed polarization coupling system,” J. Lightwave Technol. 36(11), 2094–2099 (2018). [CrossRef]

2. H. Zhang, Y. Wang, G. Wen, D. Jia, and T. Liu, “Frequency measurement of dynamic stress in polarization maintaining fibers,” IEEE Photonics J. 10(3), 1–11 (2018). [CrossRef]

3. P. Liu, X. Li, X. Guang, G. Li, and L. Guan, “Bias error caused by the Faraday effect in fiber optical gyroscope with double sensitivity,” IEEE Photonics Technol. Lett. 29(15), 1273–1276 (2017). [CrossRef]

4. P. Lu, Z. Wang, R. Luo, D. Zhao, C. Peng, and Z. Li, “Polarization nonreciprocity suppression of dual-polarization fiber-optic gyroscope under temperature variation,” Opt. Lett. 40(8), 1826–1829 (2015). [CrossRef] [PubMed]

5. Z. Wang, Y. Yang, P. Lu, R. Luo, Y. Li, D. Zhao, C. Peng, and Z. Li, “Dual-polarization interferometric fiber-optic gyroscope with an ultra-simple configuration,” Opt. Lett. 39(8), 2463–2466 (2014). [CrossRef] [PubMed]

6. Z. Wang, Y. Yang, P. Lu, C. Liu, D. Zhao, C. Peng, Z. Zhang, and Z. Li, “Optically compensated polarization reciprocity in interferometric fiber-optic gyroscopes,” Opt. Express 22(5), 4908–4919 (2014). [CrossRef] [PubMed]

7. Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. 37(14), 2841–2843 (2012). [CrossRef] [PubMed]

8. F. Peng, Y. Lv, H. Li, S. Tian, W. Chen, and J. Yang, “Sensitivity prediction of multiturn fiber coil-based fiber-optic flexural disk seismometer via finite element method analysis,” J. Lightwave Technol. 35(18), 3870–3876 (2017). [CrossRef]

9. Z. Li, X. S. Yao, X. Chen, H. Chen, Z. Meng, and T. Liu, “Complete characterization of polarization-maintaining fibers using distributed polarization analysis,” J. Lightwave Technol. 33(2), 372–380 (2015). [CrossRef]

10. C. Li, J. Yang, Z. Yu, Y. Yuan, B. Wu, F. Peng, J. Zhang, A. Zhou, Y. Zhang, Z. Liu, and L. Yuan, “Dynamic range beyond 100 dB for polarization mode coupling measurement based on white light interferometer,” Opt. Express 24(15), 16247–16257 (2016). [CrossRef] [PubMed]

11. Y. Jun, Y. Yonggui, Z. Ai, C. Jun, L. Chuang, Y. Dekai, H. Sheng, P. Feng, W. Bing, Z. Yu, L. Zhihai, and Y. Libo, “Full evaluation of polarization characteristics of multifunctional integrated optic chip with high accuracy,” J. Lightwave Technol. 32(22), 4243–4252 (2014). [CrossRef]

12. J. Jin, S. Wang, J. Song, N. Song, Z. Sun, and M. Jiang, “Novel dispersion compensation method for cross-coupling measurement in PM-PCF based on OCDP,” Opt. Fiber Technol. 19(5), 495–500 (2013). [CrossRef]

13. Z. H. Li, Z. Meng, X. J. Chen, T. G. Liu, and X. S. Yao, “Method for improving the resolution and accuracy against birefringence dispersion in distributed polarization cross-talk measurements,” Opt. Lett. 37(14), 2775–2777 (2012). [CrossRef]

14. H. Zhang, J. Yang, C. Li, Z. Yu, Z. Yang, Y. Yuan, F. Peng, H. Li, C. Hou, J. Zhang, L. Yuan, J. Xu, C. Zhang, and Q. Yu, “Measurement error analysis for polarization extinction ratio of multifunctional integrated optic chips,” Appl. Opt. 56(24), 6873–6880 (2017). [CrossRef] [PubMed]

15. Z. Yu, J. Yang, Y. Yuan, F. Peng, H. Li, C. Hou, C. Hou, Z. Liu, and L. Yuan, “High-resolution distributed dispersion characterization for polarization maintaining fibers based on a closed-loop measurement framework,” IEEE Photonics J. 9(3), 1–8 (2017). [CrossRef]

16. F. Tang, X. Z. Wang, Y. Zhang, and W. Jing, “Characterization of birefringence dispersion in polarization-maintaining fibers by use of white-light interferometry,” Appl. Opt. 46(19), 4073–4080 (2007). [CrossRef] [PubMed]

17. C. K. Hitzenberger, A. Baumgartner, and A. F. Fercher, “Dispersion induced multiple signal peak splitting in partial coherence interferometry,” Opt. Commun. 154(4), 179–185 (1998). [CrossRef]

18. E. D. Smith, A. V. Zvyagin, and D. D. Sampson, “Real-time dispersion compensation in scanning interferometry,” Opt. Lett. 27(22), 1998–2000 (2002). [CrossRef] [PubMed]

19. X. Liu, M. J. Cobb, and X. Li, “Rapid scanning all-reflective optical delay line for real-time optical coherence tomography,” Opt. Lett. 29(1), 80–82 (2004). [CrossRef] [PubMed]

20. H. Zhang, X. Chen, W. Ye, T. Xu, D. Jia, and Y. Zhang, “Mitigation of the birefringence dispersion on the polarization coupling measurement in a long-distance high-birefringence fiber,” Meas. Sci. Technol. 23, 025203 (2012).

High-resolution distributed polarization crosstalk measurement for polarization maintaining fiber with considerable dispersion

Abstract

1. Introduction

2. Theory

2.1 Birefringence dispersion effect in OCDP

2.2 Iterative matched filter algorithm

3. Simulation

3.1 Matched filter property of phase packet method

3.2 Iterative matched filter simulation

4. Experiment and results

4.1 High-resolution distributed polarization crosstalk measurement

4.2 Correctness verification via different measurement directions

5. Conclusion and discussion

Funding

References

Cited By

Figures (8)

Equations (10)

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