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  Panda-type bias-preserving few-mode fiber assisted by concentric circular stress zones

  Liu Yanan, Lijin, Yuan Xueguang, Zhang Yangan, Zhang Zhen'
State Key Laboratory of Information Photonics and Optical Communication, Beijing University of Posts and Telecommunications, Beijing 100876, China

Abstract


Abstract A panda-type bias-preserving few-mode fiber structure with concentric circular-shaped stress zones is proposed, which can stably support 10 transmission modes. With the introduction of a low refractive index stress region, the effective refractive index difference between higher-order modes is improved by nearly an order of magnitude, and the minimum effective refractive index difference between neighboring modes reaches 2 × 10 − 4 2 × 10 − 4 2xx10^(-4)2 \times 10^{-4} at 1550 nm, and is not lower than 1.8 × 10 − 4 1.8 × 10 − 4 1.8 xx10^(-4)1.8 \times 10^{-4} in the C-band. (Mode dispersion is not higher than | − 55.0219 | ps / ( nm ⋅ km | − 55.0219 | ps / nm ⋅ km |-55.0219|ps//(nm*km:}|-55.0219| \mathrm{ps} /\left(\mathrm{nm} \cdot \mathrm{km}\right. ), and the maximum bending loss is in the order of 10 − 7 dB / m 10 − 7 dB / m 10^(-7)dB//m10^{-7} \mathrm{~dB} / \mathrm{m} (bending radius ⩾ 9.5 cm ⩾ 9.5 cm >= 9.5cm\geqslant 9.5 \mathrm{~cm} ). The research results provide ideas for the design of short-haul, high-capacity optical fibers.


Keywords Fiber optics; Few-mode fiber; Space division multiplexing; Bias preserving; Simple merged mode

CCS TN29 Literature Symbol Code A DOI: 10.3788/AOS230674

  1 Introduction


The emergence of new data services and the rapid development of cloud computing technology have put forward an urgent demand for the enhancement of transmission capacity in optical interconnection networks. Traditional single-mode fiber is limited by the nonlinear Shannon limit, and it is difficult to improve the capacity. For this reason, time division multiplexing (TDM), wavelength division multiplexing (WDM), and space division multiplexing (SDM) technologies have been applied to optical fiber design, of which SDM technology has received widespread attention for its ability to reach the maximum capacity [ 1 − 3 ] [ 1 − 3 ] ^([1-3]){ }^{[1-3]} . Few-mode fiber is a typical device that uses space-division multiplexing, but the mode crosstalk that occurs during transmission in few-mode fiber is a major problem. To solve this problem, multiple-input multiple-output (MIMO) digital signal processing techniques are usually introduced at the receiver side [ 4 ] [ 4 ] ^([4]){ }^{[4]} , but as the number of transmitted modes increases, the complexity of the system grows nonlinearly, resulting in large power consumption [ 5 ] [ 5 ] ^([5]){ }^{[5]} . For this reason, it is important to suppress mode coupling from the root cause, maximize the separation of intrinsic modes, achieve low crosstalk between fiber-guided modes, and simplify the communication system.

Theoretical studies have shown that when the effective refractive index difference of the modes ( Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} ) is greater than 10 − 4 10 − 4 10^(-4)10^{-4} , the modes can be considered to be free of merging, and the energy coupling is effectively reduced [ 6 − 7 ] [ 6 − 7 ] ^([6-7]){ }^{[6-7]} . In order to improve the intermode Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} and expand the transmission capacity, the optical fibers used usually include elliptical core fiber [ 8 − 9 ] [ 8 − 9 ] ^([8-9]){ }^{[8-9]} , ring core fiber [ 10 − 11 ] [ 10 − 11 ] ^([10-11]){ }^{[10-11]} , panda-type bias-preserving few-mode fiber [ 12 − 14 ] [ 12 − 14 ] ^([12-14]){ }^{[12-14]} , etc. Zhao et al. proposed a bias-preserving few-mode fiber consisting of a central circular hole and an elliptical ring core, which can transmit 10 modes, and the bias-preserving few-mode fiber in [ 12 − 14 ] [ 12 − 14 ] ^([12-14]){ }^{[12-14]} is able to transmit 10 modes at [ 12 − 14 ] [ 12 − 14 ] ^([12-14]){ }^{[12-14]} wavelength Δ n eff > 1.32 × 10 − 4 Δ n eff  > 1.32 × 10 − 4 Deltan_("eff ") > 1.32 xx10^(-4)\Delta n_{\text {eff }}>1.32 \times 10^{-4} ; Xiao et al. proposed a bias-preserving few-mode fiber with four apertures around the core, which provides an idea for separating the higher-order merging modes, and reaches a minimum of 1.65 × 10 − 4 1.65 × 10 − 4 1.65 xx10^(-4)1.65 \times 10^{-4} at 1550 nm, and then proposed a bias-preserving few-mode fiber with elliptical apertures in the center of core. After that, a bias-preserving few-mode fiber with elliptical aperture in the center was proposed [ 17 ] [ 17 ] ^([17]){ }^{[17]} , which is Δ n eff > 1.93 × 10 − 4 Δ n eff  > 1.93 × 10 − 4 Deltan_("eff ") > 1.93 xx10^(-4)\Delta n_{\text {eff }}>1.93 \times 10^{-4} between adjacent modes at 1550 nm; Chen et al.

A few-mode fiber with air holes introduced in the center and around the core, the number of modes is increased and the fiber is Δ n eff > 1.25 × Δ n eff  > 1.25 × Deltan_("eff ") > 1.25 xx\Delta n_{\text {eff }}>1.25 \times 10 − 4 10 − 4 10^(-4)10^{-4} in the 1520 ∼ 1580 nm 1520 ∼ 1580 nm 1520∼1580nm1520 \sim 1580 \mathrm{~nm} band. The above structure balances the number of modes and the separation of merged modes, which improves the minimum Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} It is worth noting that there is a contradiction between the fundamental mode separation and the higher-order mode separation, and balancing the separation of the lower-order and higher-order merged modes is expected to further improve the minimum Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} Δ n eff > 1.25 × Δ n eff  > 1.25 × Deltan_("eff ") > 1.25 xx\Delta n_{\text {eff }}>1.25 \times Δ n eff > 1.25 × Δ n eff  > 1.25 × Deltan_("eff ") > 1.25 xx\Delta n_{\text {eff }}>1.25 \times 10 − 4 10 − 4 10^(-4)10^{-4}.

In this paper, a panda-type bias-preserving few-mode fiber with concentric circular stress zones is proposed, which is highlighted by the concentric circular stress zones around the elliptical annular core. With suitable optical parameters and structural dimensions, the fiber structure is capable of stably transmitting 10 modes in the C-band, and all the modes are no longer concatenated and maintain good polarization characteristics. In addition, the fiber has good bending resistance, relatively small mode dispersion, and good process robustness in fabrication. Compared with the fiber without concentric circular-shaped stress region with the same parameters, the stress region of the designed fiber has excellent ability to separate higher-order simple merged modes and mode constraints. Therefore, the structure has important research value in optical interconnection networks for short-distance high-capacity transmission.

  2 Fiber structure and principle analysis


The cross-section of the fiber structure is shown in Fig. 1. Figure 1(a) shows the overall cross-section of the fiber, the cladding diameter is D D DD , the setting is 125 μ m 125 μ m 125 mum125 \mu \mathrm{~m} , the two apertures are distributed in the x x xx axis and symmetric about the y y yy axis, the aperture radius is r r rr , the center of the y y yy axis away from the distance of Λ Λ Lambda\Lambda . Figure 1(b) shows an enlarged schematic of the core section, with the half-length and half-short axes of the elliptical annular core being b x b x b_(x)b_{x} and b y b y b_(y)b_{y} , respectively, and the half-length and half-short axes of the elliptical core being a x a x a_(x)a_{x} and a y a y a_(y)a_{y} , and the radius of the concentric circular stress region being R R RR . The material of the cladding and the elliptical core is pure silica ( SiO 2 ) SiO 2 (SiO_(2))\left(\mathrm{SiO}_{2}\right) ; the core is silica doped with germanium dioxide ( GeO 2 ) GeO 2 (GeO_(2))\left(\mathrm{GeO}_{2}\right) , and the doping rate (mole fraction) is 23.75 % 23.75 % 23.75%23.75 \% with reference to the literature [15-16, 19]; the concentric circular stress zone is R R RR in radius.

Corresponding author: *xzhang@bupt.edu.cn

The stress region is a silica material doped with boron trioxide ( B 2 O 3 ) B 2 O 3 (B_(2)O_(3))\left(\mathrm{B}_{2} \mathrm{O}_{3}\right) . At 1550 nm, the refractive indices of the above three parts of the material are 1.444, 1.478, and 1.428, respectively, and the refractive index of the porous part is 1. The refractive index of the material is 1.444, 1.478, and 1.428, respectively. Concentric circles

The shaped stress zone forms a refractive index depression between the core and the cladding, and the fiber is able to further separate the simple and merged modes by using the high refractive index contrast of the core-stress zone-cladding and the non-circular symmetry of the fiber structure [ 7 , 17 ] [ 7 , 17 ] ^([7,17]){ }^{[7,17]} .

Fig. 1 Schematic diagram of the fiber structure. (a) Schematic of the overall cross-section of the optical fiber; (b) Schematic of the enlarged geometry of the fiber core
Fig. 1 Schematic of fiber structure. (a) Overall cross section of optical fiber; (b) schematic of enlarged geometrical structure of the fiber core

By mode analysis, the mode effective area ( A eff A eff  A_("eff ")A_{\text {eff }} ) in a few-mode fiber can be expressed as
A eff = [ ∬ | E ( x , y ) | 2 d x d y ] 2 / ∬ | E ( x , y ) | 4 d x d y , ( 1 ) A eff  = ∬ | E ( x , y ) | 2 d x d y 2 / ∬ | E ( x , y ) | 4 d x d y , ( 1 ) A_("eff ")=[∬|E(x,y)|^(2)(d)x(d)y]^(2)//∬|E(x,y)|^(4)dxdy,(1)A_{\text {eff }}=\left[\iint|E(x, y)|^{2} \mathrm{~d} x \mathrm{~d} y\right]^{2} / \iint|E(x, y)|^{4} \mathrm{~d} x \mathrm{~d} y,(1)

Where: E ( x , y ) E ( x , y ) E(x,y)E(x, y) is the mode intensity distribution. The optical beam method is used to analyze the fiber bending resistance. When the fiber is bent, the bending can be simulated by the equivalent refractive index distribution equation, i.e.
n ′ ( x , y ) = n ( x , y ) × [ 1 + ( x × cos ⁡ θ + y × sin ⁡ θ ) / R eff ] n ′ ( x , y ) = n ( x , y ) × 1 + ( x × cos ⁡ θ + y × sin ⁡ θ ) / R eff  {:[n^(')(x","y)=n(x","y)xx],[[1+(x xx cos theta+y xx sin theta)//R_("eff ")]]:}\begin{gathered} n^{\prime}(x, y)=n(x, y) \times \\ {\left[1+(x \times \cos \theta+y \times \sin \theta) / R_{\text {eff }}\right]} \end{gathered}

where n ( x , y ) n ( x , y ) n(x,y)n(x, y) is the refractive index of the straight fiber, θ θ theta\theta is the bending angle with respect to the x x xx axis, and R eff R eff  R_("eff ")R_{\text {eff }} is the equivalent bending radius in quartz fibers R eff / R ≈ 1.28 [ 20 ] R eff / R ≈ 1.28 [ 20 ] R_(eff)//R~~1.28^([20])R_{\mathrm{eff}} / R \approx 1.28^{[20]} . In an equivalent straight fiber, the bending loss ( L b ) L b {:L_(b))\left.L_{\mathrm{b}}\right) ) is related to the imaginary part of the effective refractive index of the guiding mode ( n eff n eff  n_("eff ")n_{\text {eff }} ) and the wavelength ( λ λ lambda\lambda ) ( [ 21 ] [ 21 ] ^([21]){ }^{[21]} ), which is given by
L b = 40 × π × Im ( n eff ) / ( λ × ln ⁡ 10 ) L b = 40 × π × Im n eff / ( λ × ln ⁡ 10 ) L_(b)=40 xx pi xx Im(n_(eff))//(lambda xx ln 10)L_{\mathrm{b}}=40 \times \pi \times \operatorname{Im}\left(n_{\mathrm{eff}}\right) /(\lambda \times \ln 10)

  3 Parameter optimization design


The structural parameters of the elliptical core are designated as a x = 3.39 μ m 、 a y = a x = 3.39 μ m 、 a y = a_(x)=3.39 mum、a_(y)=a_{x}=3.39 \mu \mathrm{~m} 、 a_{y}=、 2.42 μ m 2.42 μ m 2.42 mum2.42 \mu \mathrm{~m} . The larger the radius of the air holes and the closer they are to the y y yy axis, the greater the effect on the modes, and through preliminary adjustments, the values of r r rr and Λ Λ Lambda\Lambda are set to 20 μ m 20 μ m 20 mum20 \mu \mathrm{~m} and 26.05 μ m 26.05 μ m 26.05 mum26.05 \mu \mathrm{~m} , respectively. In this paper, the core of the fiber is no longer a conventional circle, but an elliptical ring structure, which changes the structure of the fiber from circular symmetry to axial symmetry, which results in the direction of the electric field vectors of the transmission modes in the fiber converging to a certain direction, forming a distribution similar to that of the linearly polarized modes, and therefore all the modes discussed in this paper are named in the manner of the "LP".

Too many modes in a few-mode fiber will lead to serious inter-mode crosstalk problems, while a smaller number is not conducive to the improvement of fiber capacity, so the target number of fiber modes in this experiment is 10. The main factor affecting the number of modes is the core area, so the half-length axis ( b x ) b x (b_(x))\left(b_{x}\right) and the half-short axis ( b y ) b y (b_(y))\left(b_{y}\right) of the elliptical ring core are optimized first. In λ = 1550 nm 、 b y = λ = 1550 nm 、 b y = lambda=1550nm、b_(y)=\lambda=1550 \mathrm{~nm} 、 b_{y}=、

In the case of 3.37 μ m 、 R = 5.12 μ m 3.37 μ m 、 R = 5.12 μ m 3.37 mum、R=5.12 mum3.37 \mu \mathrm{~m} 、 R=5.12 \mu \mathrm{~m}、 , the variation curve of Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} with b x b x b_(x)b_{x} between mode n eff n eff  n_("eff ")n_{\text {eff }} and neighboring modes is shown in Fig. 2. When b x < 5 μ m b x < 5 μ m b_(x) < 5mumb_{x}<5 \mu \mathrm{~m} , the n eff n eff  n_("eff ")n_{\text {eff }} of modes L P 21 b x L P 21 b x LP_(21 b)^(x)L P_{21 b}^{x} and L P 21 b y L P 21 b y LP_(21 b)^(y)L P_{21 b}^{y} are lower than the cladding refractive index and the modes are cut off. The n eff n eff  n_("eff ")n_{\text {eff }} of the four highest-order modes are extremely close to each other near b x = 5.2 μ m b x = 5.2 μ m b_(x)=5.2 mumb_{x}=5.2 \mu \mathrm{~m} , and the modes interconvert to each other, resulting in very small values of Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} between their next-nearest neighboring modes around b x = 5.2 μ m b x = 5.2 μ m b_(x)=5.2 mumb_{x}=5.2 \mu \mathrm{~m} , as shown in Fig. 2(b); and the two fundamental modes are extremely close to each other around b x b x b_(x)b_{x} before Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} reaches the 4.8 μ m 4.8 μ m 4.8 mum4.8 \mu \mathrm{~m} level, as shown in Fig. 2(c). b14> after Δ n eff > 10 − 4 Δ n eff  > 10 − 4 Deltan_("eff ") > 10^(-4)\Delta n_{\text {eff }}>10^{-4} is realized; the Δ n eff Δ n eff Deltan_(eff)\Delta n_{\mathrm{eff}} between LP 01 x LP 01 x LP_(01)^(x)\mathrm{LP}_{01}^{x} and LP 11 a y LP 11 a y LP_(11a)^(y)\mathrm{LP}_{11 \mathrm{a}}^{y} shows a decreasing trend with the increase of b x b x b_(x)b_{x} , and the energy crosstalk between the two modes increases significantly especially after b x > 5.35 μ m b x > 5.35 μ m b_(x) > 5.35 mumb_{x}>5.35 \mu \mathrm{~m} . Extending the core half-axis size from 4.46 μ m 4.46 μ m 4.46 mum4.46 \mu \mathrm{~m} to 5.56 μ m 5.56 μ m 5.56 mum5.56 \mu \mathrm{~m} solves the problem of polarization crosstalk and spatial mode crosstalk in the second mode group and between LP 11 b y LP 11 b y LP_(11b)^(y)\mathrm{LP}_{11 \mathrm{~b}}^{y} and LP 21 a x LP 21 a x LP_(21a)^(x)\mathrm{LP}_{21 \mathrm{a}}^{x} . To ensure the number of modes and the effective separation of all modes, b x b x b_(x)b_{x} can be 5.18 μ m 5.18 μ m 5.18 mum5.18 \mu \mathrm{~m} or in the range 5.04 ∼ 5.04 ∼ 5.04∼5.04 \sim 5.14 μ m 5.14 μ m 5.14 mum5.14 \mu \mathrm{~m} and 5.28 ∼ 5.31 μ m 5.28 ∼ 5.31 μ m 5.28∼5.31 mum5.28 \sim 5.31 \mu \mathrm{~m} .

At 1550 nm, setting b x = 5.04 μ m 、 R = 5.12 μ m b x = 5.04 μ m 、 R = 5.12 μ m b_(x)=5.04 mum、R=5.12 mumb_{x}=5.04 \mu \mathrm{~m} 、 R=5.12 \mu \mathrm{~m}、 , b y b y b_(y)b_{y} is insufficient for 3.3 μ m 3.3 μ m 3.3 mum3.3 \mu \mathrm{~m} , causing LP 21 b x LP 21 b x LP_(21 b)^(x)\mathrm{LP}_{21 b}^{x} and LP 21 b y LP 21 b y LP_(21 b)^(y)\mathrm{LP}_{21 b}^{y} modes to leak into the cladding. Therefore, this experiment explores the effect of b y b y b_(y)b_{y} on the mode characteristics in the 3.3 ∼ 5 μ m 3.3 ∼ 5 μ m 3.3∼5mum3.3 \sim 5 \mu \mathrm{~m} range. As shown in Fig. 3, the half-length axis of the fiber core mainly affects the number of modes, and the half-short axis has a more significant effect on mode separation. As b y b y b_(y)b_{y} increases, the core ellipticity decreases, the fiber birefringence effect is weakened, and the n eff n eff  n_("eff ")n_{\text {eff }} of the two pairs of orthogonally polarized modes ( LP 01 y LP 01 y LP_(01)^(y)\mathrm{LP}_{01}^{y} and LP 01 x LP 01 x LP_(01)^(x)\mathrm{LP}_{01}^{x} , and LP 21 a x LP 21 a x LP_(21 a)^(x)\mathrm{LP}_{21 a}^{x} and L P 21 a y L P 21 a y LP_(21 a)^(y)L P_{21 a}^{y} ) at 3.94 μ m 3.94 μ m 3.94 mum3.94 \mu \mathrm{~m} are approximately equal, and the Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} of both modes decrease by about 95 % 95 % 95%95 \% . are reduced by about 95 % 95 % 95%95 \% , creating a serious problem of polarization simplicity. In addition, the transverse electric field distributions of LP 11 a x LP 11 a x LP_(11a)^(x)\mathrm{LP}_{11 \mathrm{a}}^{x} and L P 11 b x L P 11 b x LP_(11b)^(x)L \mathrm{P}_{11 \mathrm{~b}}^{x} or L P 21 a y L P 21 a y LP_(21 a)^(y)L \mathrm{P}_{21 a}^{y} and LP 21 b x LP 21 b x LP_(21b)^(x)\mathrm{LP}_{21 \mathrm{~b}}^{x} are basically only angularly different from each other π / 2 π / 2 pi//2\pi / 2 , and thus the Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} between the two pairs of modes varies dramatically during the process of approaching the circular symmetry of the fiber core, and the spatial merger is especially aggravated around b y = 4.2 μ m b y = 4.2 μ m b_(y)=4.2 mumb_{y}=4.2 \mu \mathrm{~m} . around the same time, the spatial simplicity is exacerbated. Except for the above case, the Δ n eff Δ n eff  Deltan_("eff ")\Delta n_{\text {eff }} between the remaining modes all meet the requirement of greater than 10 − 4 10 − 4 10^(-4)10^{-4} . In order to suppress the mode energy coupling and guarantee the transmission performance, b y b y b_(y)b_{y} can be selected in the range of 3.3 ∼ 3.65 μ m 3.3 ∼ 3.65 μ m 3.3∼3.65 mum3.3 \sim 3.65 \mu \mathrm{~m} and 4.3 ∼ 4.58 μ m 4.3 ∼ 4.58 μ m 4.3∼4.58 mum4.3 \sim 4.58 \mu \mathrm{~m} .

The proposed fiber structure enhances the Δ n eff Δ n eff Deltan_(eff)\Delta n_{\mathrm{eff}} between higher-order modes while ensuring the separation of fundamental modes, which in turn improves the separation of all concatenated modes. Concentric circular stress zones with low refractive index are introduced between the core and the cladding.


Fig. 2 Relationship between modes n eff n eff  n_("eff ")n_{\text {eff }} and neighboring modes Δ n eff Δ n eff Deltan_(eff)\Delta n_{\mathrm{eff}} and b x b x b_(x)b_{x} at 1550 nm. (a) variation of n eff n eff n_(eff)n_{\mathrm{eff}} with b x b x b_(x)b_{x} ; (b) variation of Δ n eff Δ n eff Deltan_(eff)\Delta n_{\mathrm{eff}}