Design of a dielectric chiral micro-structured fiber applied in a fiber optic current sensor

Wei Gao; Hongze Gao; Xiuwei Xia; Guochen Wang; She Li; Yuxin Zhao; Yongguang Wang

doi:10.1364/OPTCON.450104

1. Introduction

Circular polarization maintaining fiber not only can improve transmission bandwidth and transmission speed [1], but also can supply a new degree of freedom for the light transmission in optical fiber [2]. Therefore, there is potential value in optical fiber communication field and optical fiber sensing field in circular polarization maintaining fiber. Especially, in the optical fiber sensing field, the research on circular polarization maintaining fiber and the optical device or sensor system composed of it is just in its initial stage. Therefore, this kind of fiber has a very wide application prospects and research value.

In fact, circular polarization maintaining fiber can also be called chiral fiber, which can be divided into two types according to the relationship between the size of chirality structure and that of optical wavelength. When the size of chirality structure (helical structure) in fiber is far less than that of optical wavelength, the corresponding fiber is called dielectric chiral fiber. When the size of chirality structure (helical structure) in fiber is equal to or more than that of optical wavelength, the corresponding fiber is called structured chiral fiber. At present, most of the circular polarization-maintaining fibers are of the order of millimeter pitch. Therefore, this kind of fiber can be considered as a structured chiral fiber, which is drawn by spanning two stress rods of the linear birefringence fiber in its hot state at a constant speed. And then the effective circular birefringence induced by the off-axis whirling stress filament is enhanced [3]. However, there are two disadvantages of this kind of circular polarization maintaining fiber. The first disadvantage is that during the process of drawing two stress rods, the non-uniform spanning rate makes the non-uniform pitch of the fiber, which leads to residual linear birefringence existing in fiber. As a result, the circular polarization maintaining characteristic will become bad. The second disadvantage is that the screwed silicon-based fiber (SSBF) is not easy to draw and costs too much. Therefore, we can consider exploring another kind of chiral fiber in theory, called dielectric chiral fiber, to avoid the above problems existing in SSBF.

Recent years, some researchers proved that the dielectric chiral fiber also has the circular polarization maintaining characteristic with the advantages of low cost and good toughness in theory [4]. Microstructure and photonic crystal structure has the advantages of good temperature stability and small bend loss. Because of its many advantages, it has been widely utilized in many fiber sensors such as photonic quasi-crystal fiber refractive index sensor [5,6], photonic quasi-crystal fiber methane sensor [7], photonic crystal fiber temperature sensor [8], photonic crystal fiber electric field sensor [9]. The perfect symmetrical structure can guarantee the pure circular polarization characteristic of dielectric chiral micro-structured fiber (DCMF) without linear birefringence. However, during the process of drawing fiber, the imperfect drawing technology will lead to the deformation of the air holes of DCMF, which will introduce linear birefringence and decrease the circular polarization degree. Meanwhile, the closer the air holes are to the fiber core, the greater the contribution of their deformations is to the reduction of circular polarization degree [10]. So we need to consider the influence of size error when designing the structure and parameters of fiber.

In this paper, we designed a refractive index-guided dielectric chiral microstructure fiber with a regular octagonal structure. Using the two-dimensional chiral plane wave expansion method, we studied the change of the circular polarization characteristics when the position of the innermost air holes in the fiber cross-section changes. Through designing the size, position and chirality parameters of the air holes, the fiber have a high degree of circular polarization maintaining characteristics. Next, through the comparison of the circular polarization degree between the fiber designed in this paper and the traditional circular polarization-maintaining fiber, it can be proved that the DCMF designed in this paper has better circular polarization-maintaining characteristics. Finally, this paper presented an application example of chiral optical fiber: fiber optic current sensor (FOCS). We used the optical fiber designed in this paper as the sensing coil of FOCS, and compared it with the original system that used the traditional circular polarization-maintaining fiber as the sensing coil in ratio error. The simulation results proved that when the optical fiber designed in this paper was utilized as the sensing coil in FOCS, the ratio difference of FOCS can be reduced by an order of magnitude through comparing SSBF utilized as the sensing coil in FOCS.

2. Principle and design of the fiber

2.1 Theoretical analysis of DCMF

In order to realize the circular polarization maintaining characteristic of the fiber, a regular octagonal structure index guiding DCMF was designed, which is shown in Fig. 1.

Fig. 1. The schematic diagram of cross section of index guiding DCMF.

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Figure 1 shows the schematic diagram of cross section of index guiding DCMF, where the blue background dielectric chiral material, which is composed of polymethyl methacrylate (PMMA) gel with griseofulvin [11]. The whole fiber is composed of air holes with five layers, whose corresponding diameters are all the same, called d. The air holes in each layer are arranged in a regular octagonal structure, the number of air holes in the first layer is eight, and the number of air holes will increase by eight for each additional layer of air holes. The distance between the air holes at the apex of the regular octagon in the first layer and the center of the fiber is Λ, and the distance between the air holes at the apex of the regular octagon in the second layer and the center of the fiber is 2Λ, and so on. Besides, in the same layer of air holes, the distance between each air hole is the same. When we simulated the parameters of fiber, the dispersion of the background was considered to be the dispersion of PMMA without considering the effect of dopant griseofulvin on PMMA in dispersion.

According to the Eq. (1) in Ref. [12], the dispersion of PMMA can be shown as

(1)$$n_0^2 = 1 + \sum\limits_{i = 1}^3 {\frac{{{A_i}{\lambda ^2}}}{{{\lambda ^2} - l_i^2}}}$$

where A_i and l_i represent the oscillator strength and the oscillator wavelength, respectively. The corresponding value is shown in Table 1. Considering the normal communication band of PMMA fiber is 650 nm, all the calculation need to be based on the optical wavelength 650 nm.

Table 1. Coefficients of the Sellmeier Equation

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In order to describe the dielectrically chiral background, Drude–Born–Fedorov’s constitutive relations [1] were adopted

(2)$$\left\{ \begin{array}{l} \vec{D} = {\varepsilon_0}{\varepsilon_r}(\vec{E} + \xi \nabla \times \vec{E})\\ \vec{B} = {\mu_0}{\mu_r}(\vec{H} + \xi \nabla \times \vec{H}) \end{array} \right.$$

where ɛ₀ and µ₀ denote dielectric constant and permeability in vacuum, respectively, ɛ_∇ and µ_∇ represent relative dielectric constant and permeability, respectively. ξ represents the chiral parameter.

According to the Eq. (5) in Ref. [11], when the thickness of griseofulvin powder in the PMMA gel was 0.067 g/cm³, the corresponding optical rotatory dispersion can be represented as

(3)$${\delta _0} = \frac{{{B_1}}}{{{\lambda ^2}}} + \frac{{{B_2}}}{{{\lambda ^4}}}$$

where B₁ and B₂ are constant value with the corresponding value 1.46×10⁴ °.nm²/mm and 1.82×10¹⁰ °.nm⁴/mm, respectively. The chiral parameter ξ₀ can be denoted as

(4)$${\xi _0} ={-} \frac{{{\delta _0}}}{{k_0^2n_0^2}}$$

where k₀= 2π/λ and ξ0=-1.1482×10⁻⁸ rad.µm.

According to Eq. (5.16), (5.21) and (5.22) in [13], the circular polarization degree can be represented by the third Stocks vector s₃ as

(5)$${s_3} = \frac{{2{E_x}{E_y}\sin \delta }}{{E_x^2 + E_y^2}} = \sin 2\varepsilon \sin \delta$$

where ɛ=tan^-1|E_x/E_y| (0≤ɛ≤π/2), E_x and E_y denote a pair of orthogonal light vectors, respectively. δ represents phase difference between them. However, the distributions of intensity and polarization of a guided mode in the DCMF are not uniform on the cross section. Therefore, in order to describe the distribution of the circular polarization degree of the whole fiber, a normalized parameter S₃ is introduced considering the weight of light intensity distribution [1,2]

(6)$${S_3} = \frac{{\int\!\!\!\int_{core} {{s_3}{{|E |}^2}dS} }}{{\int\!\!\!\int_{core} {{{|E |}^2}dS} }}$$

where dS indicates the micro-area element of the cross section in the fiber core.

S₃ ranging from -1 to 1 describes the modal polarization. When the absolute S₃ value |S₃| tends to 1, the modal tends to circular polarization. While |S₃| tends to 0, the modal tends to linear polarization. In actual situation, |S₃| can not reach to 1 or 0, so we defined |S₃|≥0.99 as pure circular polarization.

In order to calculate the circular polarization degree S₃, we can use the method two-dimensional chiral plane-wave expansion with the corresponding Eq. (3) in Ref. [1], which can be shown as Eq. (7) and Eq. (8)

(7)$${\beta ^2}\sum\nolimits_{q,b} {Q_{pq}^{ab}} H_q^b + \beta \sum\nolimits_{q,b} {W_{pq}^{ab}} H_q^b + \sum\nolimits_{q,b} {K_{pq}^{ab}} H_q^b = 0$$

(8)$$\begin{array}{l} Q_{pq}^{ab} = {M_{pq}}{{\vec{e}}_b}\cdot {{\vec{e}}_a}\\ W_{pq}^{ab} = (i2{N_{pq}}{{\vec{e}}_z} \times {{\vec{e}}_b})\cdot {{\vec{e}}_a}\\ K_{pq}^{ab} = [{{M_{pq}}\cdot ({{\vec{G}}_p}\cdot {{\vec{G}}_q}){\delta_{pq}}{{\vec{e}}_b} - {M_{pq}}\cdot ({{\vec{G}}_p} - {{\vec{G}}_q}) \times {{\vec{G}}_q} \times {{\vec{e}}_b} + k_0^2{{\vec{e}}_b}} ]\cdot {{\vec{e}}_a}\\ {M_{pq}} = \hat{\varepsilon }({{\vec{G}}_p} - {{\vec{G}}_q}) - k_0^2\hat{\zeta }^{\prime}({{\vec{G}}_p} - {{\vec{G}}_q})\\ {N_{pq}} = k_0^2\hat{\zeta }({{\vec{G}}_p} - {{\vec{G}}_q}) \end{array}$$

where p, q = 1, 2, 3…, l (l represents the plane wave number), e_a, e_b and e_c denote the unit vector x, y, z in inverted vector space, respectively. Hb q represents one of the components of qth fourier component of transverse magnetic field H_t(G). G_p and G_q represents two basic vector in inverted vector space. β denotes the propagation constant of fiber. ɛ_G, ζ_G and ζ′_G represents reciprocal permittivity, chiral parameter and the Fourier coefficients of chiral parameter squared in reversed lattice space, respectively. Due to the degeneracy of the paired fundamental mode of the optical fiber, for the convenience of research, we only studied the circular polarization degree of the left-handed fundamental mode.

Generally speaking, during the process of fiber drawing, inaccurate control of temperature, pressure, and drawing speed, coupled with uneven collapse, will cause changes in the shape and position of the air holes, which will destroy the original symmetry structure of the fiber to a certain extent. As a result, residual linear birefringence will be introduced. In this paper, we adopt the changes of position of air holes instead of all the possibilities of the deformation of air holes, as shown in Fig. 2.

Fig. 2. The schematic diagram of the position fluctuation of air holes of DCMF.

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Figure 2 shows the schematic diagram of the position fluctuation of air holes of DCMF. Since the transmission of light is mainly concentrated at the core of the fiber, the closer the air hole is to the core area, the greater the influence of its change on the circular polarization degree of the fiber. Therefore, we only consider the position change of the first layer of air hole to quantitatively analyze its changes in the circular polarization degree on the fiber in this paper. The first layer air holes have been marked by red solid circle, as shown in the left of Fig. 2. The right of Fig. 2 enlarges the left of Fig. 2 which is marked red solid circle. Besides, we mark these eight air holes from number 1 to number 8 by the order of clockwise to design the parameters of fiber to decrease the fluctuation of the circular polarization degree of air holes. Supposing that the fluctuation distance of each air hole is ΔΛ,when the air hole is far away from the center of the fiber, its distance from the center is Λ+ΔΛ, when the air hole is close to the center of the fiber, its distance from the center is Λ-ΔΛ.

2.2. Parameter design and position fluctuation analysis of the air holes of DCMF

Before analyzing the changes of the circular polarization degree with the changes of diameter of the air holes, it is necessary to select the appropriate diameter of air holes and distance between each adjacent air holes. In order to describe expediently, here we introduce two parameters. First, we define the distance from the vertex of the regular octagon in the first layer of air holes to the center of the fiber as the lattice constant Λ. Then, we define the ratio d/Λ of the air hole diameter d to the lattice constant Λ as the air filling ratio. Here we simulated each optical field distribution of various modes in optical fiber with the chiral parameter ξ=10ξ₀, lattice constant ranging from 1µm to 5µm, air filling ratio ranging from 0.1 to 0.7. Besides, the corresponding circular polarization degree S₃ can be obtained for each set of parameters. The light field distribution was shown in Fig. 3.

Fig. 3. The light field distribution of each modes in fiber (a). The light distribution of fundamental mode (b). The light distribution of first high-order mode.

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Figure 3 shows the light distribution of all the modes in fiber. Figure 3 (a) and Fig. 3 (b) show the light distribution of fundamental mode and that of first high-order mode in fiber, respectively. It can be seen from the above two figures that under the above-mentioned optical fiber parameters, light can guarantee stable single-mode transmission in the optical fiber. In particular, when the lattice constant of the fiber is 4 µm and the air filling ratio is 0.32, the circular polarization degree of the fiber reaches the maximum with the Stokes vector S₃=-0.9944. Therefore, the lattice constant of the fiber selected in this paper is 4µm, and the air filling ratio of the fiber is 0.32.

Based on the above structure parameters of the fiber (lattice constant Λ=4µm, air filling ratio d/Λ=0.32), we studied the influence of the diameter of the 8 air holes in the first layer of the fiber cross-section structure on the circular polarization degree of the fiber, and compensate by increasing chiral parameter. The maximum range of changes in the circular polarization degree caused by the eight air holes is also the maximum range of changes in the circular polarization degree caused by the same number of air holes at any position in the regular octagonal photonic crystal structure.

When considering the position fluctuation degree of the air holes’ diameter is ΔΛ/Λ=±10%, the relationship between the change of the air holes’ position and the change of optical fiber circular polarization degree S₃ is shown in Table 2. In order to find the corresponding changes of air holes situation where the circular polarization degree changes greatest, we make ξ=10ξ₀. Besides, according to the Ref. [14], the more the number of air holes changes, the greater the probability and degree of asymmetry in the fiber cross section. Therefore, we only need to study the changes in S₃ when the positions of all the 8 air holes are changed.

Table 2. The corresponding S₃ value with the changes of all the 8 air holes’ position

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Table 2 shows the corresponding S₃ value with the changes of all the 8 air holes’ position. We have defined 8 air holes of the first layer with the number 1 to 8. The regular octagonal structure has 45°rotational symmetry (that is, the regular octagonal structure rotated by an integer multiple of 45° can coincide with the original regular octagonal structure), which means that when the position of the air hole 1 changes, we can It is equivalent to the change of the position of any air hole in the middle of air holes 2-8, and so on. In Table 2, the circular polarization degree corresponding to the changes in the position of the 8 air holes are arranged in descending order of S₃ value. The smallest absoulte S₃ value is 0.5140, which corresponds the change situation of air holes (the air holes 1, 3, 6 are far from the fiber center by 10%, the air holes 2, 4, 5, 7, 8 are close to the fiber center by 10%).

In order to compensate the change in the circular polarization degree caused by the change in the position of the air holes, we need to increase the chiral parameter in the case of the air hole position shift corresponding to the minimum circular polarization degree S₃. The change rule is shown in Fig. 4.

Fig. 4. The changes of circular polarization degree S3 with the increase of chiral parameter ξ.

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Figure 4 shows the relationship between circular polarization degree S3 and chiral parameter ξ. Here the lattice constant and air filling ratio are 4µm and 0.32, respectively. The red dotted line indicates the circular polarization degree S₃ after compensation with corresponding S₃ value -0.99. It can be seen from Fig. 4 that with the increase of the chiral parameter ξ, the absolute value of circular polarization degree S₃ tends to 1. When |S₃|=0.99, we can find a chiral parameter ξ=118ξ₀ (This dot has been marked in Fig. 4 by orange square shape, and the corresponding specific rotation δ=2.811×10⁻⁴ rad/µm) which can guarantee that when the position variation degree of air holes is ΔΛ/Λ=±10%, the circular polarization degree S₃ of DCMF can be also guaranteed with the absolute value 0.99.

2.3. Comparison of circular polarization degree S3 between DCMF and SSBF

According to the Eqs. (1) and (5) in [15], with respect to SSBF, its coupled mode equation can shown as

(9)$$\left\{ \begin{array}{l} \frac{{d\vec{E}}}{{dz}} = \vec{K}\cdot \vec{E}\\ \vec{K} = \left[ {\begin{array}{*{20}{c}} {j\left( {\frac{{\Delta {\beta_1}}}{2}} \right)}&{\tau (z)}\\ {\tau (z)}&{ - j\left( {\frac{{\Delta {\beta_1}}}{2}} \right)} \end{array}} \right]\textrm{ }\vec{E} = \left[ \begin{array}{l} {{\vec{E}}_x}\\ {{\vec{E}}_y} \end{array} \right] \end{array} \right.\textrm{ }$$

where Δβ₁ represents the residual linear birefringence in the SSBF, τ denotes the spin rate of the SSBF relating to screw pitch l₀ and can be represented as τ = 2π∕l₀. According to Eq. (9), the eigen value can be obtained as

(10)$${\vec{E}_ \pm } = \left[ \begin{array}{l} \frac{1}{{\sqrt {1 + {{\left\{ {\frac{{\Delta {\beta_1}}}{{2\tau (z)}} \pm \sqrt {1 + {{\left( {\frac{{\Delta {\beta_1}}}{{2\tau (z)}}} \right)}^2}} } \right\}}^2}} }}\\ - i\frac{{\frac{{\Delta {\beta_1}}}{{2\tau (z)}} \pm \sqrt {1 + {{\left( {\frac{{\Delta {\beta_1}}}{{2\tau (z)}}} \right)}^2}} }}{{\sqrt {1 + {{\left\{ {\frac{{\Delta {\beta_1}}}{{2\tau (z)}} \pm \sqrt {1 + {{\left( {\frac{{\Delta {\beta_1}}}{{2\tau (z)}}} \right)}^2}} } \right\}}^2}} }} \end{array} \right].$$

According to the Eq. (5), δ represents the phase delay caused by linear birefringence in SSBF. It can be considered that the light amplitude in two orthogonal directions in a screw pitch, so the phase delay is

(11)$$\delta = \Delta {\beta _1} \cdot {l_0} + \frac{\pi }{2}.$$

The Eqs. (10) and (11) can be brought into Eq. (5), and then we can obtain the corresponding circular polarization degree S₃

(12)$${S_3} = \sin \left( {2\arctan \left( {\frac{{\Delta {\beta_1}}}{{2\tau (z)}} \pm \sqrt {1 + {{\left( {\frac{{\Delta {\beta_1}}}{{2\tau (z)}}} \right)}^2}} } \right)} \right) \cdot \sin (\Delta {\beta _1}{l_0} + \frac{\pi }{2}).$$

Figure 5 shows the comparison of the circular-polarization maintaining characteristic between SSBF and DCMF in different spin rates and different chiral parameters, respectively, where the blue line represents the |S₃| (abscissa) change of the SSBF with the change of the spin rate τ (ordinate), the red line denotes the most drastic change of air holes corresponding to the circular polarization degree |S₃| (abscissa) with the changing of the chiral parameter (ordinate) ξ, and the pink line indicates the circular polarization degree |S₃|=0.99. From the Fig. 5, we can see that the circular polarization degree of SSBF has a violent fluctuation with the increase of spin rate whose value is smaller than 6283 rad/m, the circular polarization degree of SSBF increase with the increase of the spin rate when its spin rate is larger than 6283 rad/m. When the spin rate is smaller than 6283 rad/m, there is a large fluctuation range for the phase delay because of the linear birefringence in SSBF, which makes S₃ have a periodical variation. However, the circular polarization degree will increase with the increase of the spin rate when the spin rate is larger than 6283 rad/m, meanwhile S₃ tends to 1. The circular polarization degree of the DCMF will increase with the increase of the chiral parameter. Moreover, the circular polarization degree |S₃| will equal to 0.99 when ξ=118ξ₀. To the best of our knowledge, the residual linear birefringence Δβ1 and the spin rate τ of the SSBF with the best circular-maintaining performance are 2π/0.004 rad/m and 38080 rad/m [16], respectively, where the corresponding circular polarization degree |S₃| is 0.9664, which is smaller than the circular polarization degree S₃= 0.99 of the DCMF. It is indicated that the DCMF has a better circular-maintaining performance in theory.

Fig. 5. The comparison of the circular polarization degree between SSBF and CPCF.

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3. Application of DCMF in FOCS and the ratio error comparison between two methods

DCMF designed in this paper has a high circular polarization maintaining characteristic, which can be considered as the fiber sensing coil of FOCS. With respect to FOCS system, in-line Sagnac FOCS is the mainstream structure of FOCS. The specific structure is shown in Fig. 6 [17].

Fig. 6. The schematic diagram of in-line Sagnac FOCS optical circuit structure.

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Because we replaced the SSBF sensing coil with a dielectric chiral fiber, we use a semiconductor laser with a center wavelength of 650 nm instead of the super luminescent diode light source with a center wavelength of 1310 nm in the original plan. The nature light transmitted from semiconductor laser (center wavelength is 650 nm) is changed to a beam of linear polarized light after passing through fiber coupler and polarizer. This beam of light is broken up into two beams of orthogonal linear polarized light after passing through 45° fusion splice point 1. These two beams of orthogonal linear polarized light reach the 45° fusion splice point 2 after passing through the straight waveguide phase modulator and the polarization-maintaining fiber delay coil. At this time, the two beams of orthogonal linear polarized light are decomposed into four beams of linear polarized light (two pairs of linear polarized light). After each pair of linearly polarized light passes through the λ/4 waveplate, there will be a phase difference of π/2 between the two beams of light, and the corresponding left-handed fundamental mode light and right-handed fundamental mode light enter the optical fiber sensing coil for transmission. When the light transmits to mirror which is at the end of the fiber, it will reflect back to the λ/4 waveplate, and at the same time it changes back to linearly polarized light. At this time, the optical signal carries the information of the measured current. Finally, the two beams of linear polarized lights interfere at the polarizer. When passing through the photo-detector, the light will be converted into an electrical signal, and outputs the information of the measured current as a digital signal through the signal processing system.

With respect to this FOCS structure, according to the Eq. (38) in Ref. [18], the ratio error can be represented as

(13)$$P = \left|{\frac{{\arctan \left( {\frac{{\sin \alpha \cos \sigma \sin \chi + \cos \alpha \sin \sigma \sin \gamma }}{{\cos \alpha \cos \sigma - \sin \alpha \sin \sigma \sin \chi \sin \gamma }}} \right) - 4NVI}}{{4NVI}}} \right|$$

(14)$$\begin{array}{l} \alpha = 2\sqrt {{{(NVI + T)}^2} + {{\left( {\frac{{\Delta \beta }}{2}} \right)}^2}} \textrm{ }\tan \chi = \frac{{2(NVI + T)}}{{\Delta \beta }}\\ \sigma = 2\sqrt {{{(NVI - T)}^2} + {{\left( {\frac{{\Delta \beta }}{2}} \right)}^2}} \textrm{ }\tan \gamma = \frac{{2(NVI - T)}}{{\Delta \beta }} \end{array}$$

where N, V, and I indicate turns of the sensing coil, verdet constant and current in the wire, respectively. Δβ represents the linear birefringence of the sensing coil, and T denotes intrinsic circular birefringence of the sensing coil. In terms of silicon-based fiber, when the optical wavelength λ₀= 0.65µm, the corresponding Verdert constant V₀= 4.37µrad/A. With respect to dielectric chiral fiber, we consider that the main fiber material is PMMA. So the Verdert constant value of DCMF is considered to be that of PMMA, with the corresponding value of DCMF V₀= 3.13µrad/A when the optical wavelength λ₀= 0.65µm [19].

The modal birefringence [20] can be represented as

(15)$$T = \frac{{2\pi }}{\lambda }|{{n_1} - {n_2}} |$$

where n₁ and n₂ represent the refractive index of the left-handed fundamental model and the right-handed fundamental model, respectively. The circular birefringence and linear birefringence of the DCMF can be calculated, whose values are 567.67 rad/m and 79.48 rad/m, respectively. The circular birefringence and the linear birefringence of the SSBF is T_SiO₂= gτ=0.08×38080 = 3046.4 rad/m and 1570.8 rad/m [21].

When the number of optical fiber turns are 3, 6, 9, 12, the ratio error comparison of FOCS using two different fiber sensing coil (DCMF and SSBF) is shown in Fig. 7.

Fig. 7. The ratio error comparison of FOCS with DCMF and that with SSBF. (a) 3 turns of fiber sensing coil. (b) 6 turns of fiber sensing coil. (c) 9 turns of fiber sensing coil. (d) 12 turns of fiber sensing coil.

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Figure 7 shows the ratio error comparison of FOCS with DCMF and that with SSBF, where the red lines and the blue lines represent the ratio error by using SSBF sensing coil and CPCF sensing coil, respectively. The number of turns of fiber sensing coil is gradually increasing from 3 to 12 in Fig. 7(a), Fig. 7(b), Fig. 7(c) and Fig. 7(d). It can be also seen obviously that the current measurement ratio error of the SSBF sensing coil in FOCS increases with the decrease of the current, which presents the obvious nonlinear error. While comparing to use SSBF sensing coil, the current measurement ratio error by using CPCF sensing coil is stable and smaller by an order of magnitude in the FOCS, and it was hardly affected by the changes of current and turns. It is demonstrated that it can decrease the polarization error and improve the accuracy of the FOCS through the CPCF sensing coil in theory.

4. Conclusion

In this paper, a DCMF with a regular octagonal structure with high circular polarization preserving characteristics was designed. The influence of the position of the first layer of air holes on the fiber section on circular polarization degree of the fiber was analyzed with designing fiber with the fitted parameters. The parameters lattice constant, air filling ratio and chiral parameter were 4µm, 0.32 and 2.811×10⁻⁴ rad/µm, respectively. It can be guaranteed the circular polarization degree |S₃| of the DCMF is larger than or equal to 0.99 when the position fluctuation of the air holes is ±10%, which is superior to |S₃|=0.9664 in the SSBF. Finally, the DCMF designed in this paper was utilized as the fiber sensing coil in FOCS. Compared with SSBF utilized in FOCS, the results showed that the ratio error of using DCMF as the sensing coil in FOCS is reduced by an order of magnitude. It is theoretically proved that the DCMF designed in this paper not only has the characteristics of high degree of circular polarization preserving, but also can be well used in FOCS to improve the current measurement accuracy of the system.

Funding

Foundation of Science and Technology on Near-Surface Detection Laboratory (6142414190404); China Postdoctoral Science Foundation (2019T120260, 2020T130625); National Natural Science Foundation of China (51909048, 52071121).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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The value of Stokes vector S₃ of the first fundamental modes
-0.9997	-0.9996	-0.9971	-0.9950	-0.9944	-0.9927	-0.9899
-0.9870	-0.9519	-0.9208	-0.9059	-0.9012	-0.8890	-0.8864
-0.8855	-0.8701	-0.8337	-0.8253	-0.8220	-0.8212	-0.8156
-0.8088	-0.7962	-0.7589	-0.7260	-0.7216	-0.7042	-0.6965
-0.6768	-0.6759	-0.6711	-0.6586	-0.5508	-0.5143	-0.5140

The value of Stokes vector S₃ of the first fundamental modes
-0.9997	-0.9996	-0.9971	-0.9950	-0.9944	-0.9927	-0.9899
-0.9870	-0.9519	-0.9208	-0.9059	-0.9012	-0.8890	-0.8864
-0.8855	-0.8701	-0.8337	-0.8253	-0.8220	-0.8212	-0.8156
-0.8088	-0.7962	-0.7589	-0.7260	-0.7216	-0.7042	-0.6965
-0.6768	-0.6759	-0.6711	-0.6586	-0.5508	-0.5143	-0.5140

Design of a dielectric chiral micro-structured fiber applied in a fiber optic current sensor

Abstract

1. Introduction

2. Principle and design of the fiber

2.1 Theoretical analysis of DCMF

2.2. Parameter design and position fluctuation analysis of the air holes of DCMF

2.3. Comparison of circular polarization degree S3 between DCMF and SSBF

3. Application of DCMF in FOCS and the ratio error comparison between two methods

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Tables (2)

Equations (15)

Optics Continuum