A Weakly-Coupled Double Bow-Tie Multi-Ring Elliptical Core Multi-Mode Fiber for Mode Division Multiplexing across C+L+U Band

Abstract

We herein present a weakly-coupled double bow-tie multi-ring elliptical core multi-mode fiber (DBT-MREC-MMF) supporting 22 eigenmodes for mode division multiplexing across the C+L+U band. The proposed fiber introduces a multi-ring elliptical core, bow-tie air holes, and bow-tie stress-applying areas to effectively split adjacent eigenmodes. By utilizing the finite element method (FEM), we accordingly optimized the fiber to support the 22 modes under the weakly-coupled condition. We evaluated the impact of fiber parameters on the minimum effective refractive index difference (min Δn_eff) between adjacent eigenmodes, model birefringence (B_m), and bending loss at a wavelength of 1550 nm. Additionally, broadband performance metrics, such as effective modal index (n_eff), effective index difference (Δn_eff), effective mode area (A_eff), differential mode delay (DMD), and chromatic dispersion (D), were comprehensively studied over the entire C+L+U band, ranging from 1530 to 1675 nm. The proposed fiber is capable of supporting 22 completely separated eigenmodes with a min Δn_eff between adjacent eigenmodes larger than 3.089 × 10⁻⁴ over the entire C+L+U band. The proposed DBT-MREC-MMF holds great potential for use in short-haul communication systems that require MDM to improve transmission capacity and expand bandwidth.

1. Introduction

The exponential growth of new data traffic, social networks, and rapid technological advancements has stimulated the need to expand the capacity of optical fiber communication [1,2,3]. However, the transmission capacity of traditional single-mode fiber has approached the nonlinear Shannon limit [4,5]. The development of space division multiplexing (SDM) technology has been instrumental in overcoming the limitations of traditional single-mode fiber transmission [6,7]. SDM, using few-mode fiber (FMF) and multi-core fiber (MCF), has been shown to significantly improve transmission system capacity [8,9]. In particular, few-mode fibers (FMFs) in mode division multiplexing (MDM) systems are one of ways to break through the limitations of traditional single mode fiber. However, mode coupling-induced crosstalk remains a key challenge in MDM transmission using FMFs, necessitating a complex and costly multi-input multi-output (MIMO) digital signal processing (DSP) system for effective mitigation [10,11,12]. To reduce or even eliminate the need for MIMO-DSP, enlarging the mode effective refractive index difference between degenerate modes to larger than 10⁻⁴ is a promising approach [13].

There have been several works on weakly coupled FMFs, including the ring core fiber [14], elliptical core fiber [15], elliptical ring core fiber [16,17,18], panda type fiber [19], bow-tie type fiber [20], and air hole fiber [21,22,23]. While the previously proposed weakly-coupled FMFs have demonstrated promising characteristics for mode division multiplexing, they still have limitations in terms of the number of supported eigenmodes and bandwidth. For example, Zhang et al. [24] proposed a panda-type separated-circles-formed elliptical ring core FMF capable of supporting 10 modes, with a min Δn_eff of 1.2 × 10⁻⁴ over the whole C+L band. Du et al. [25] proposed a segmented ring-core panda-type fiber, which also supports 10 modes, with a min Δn_eff of 3.5 × 10⁻⁴ over the whole C+L band. Yang et al. [26] proposed a bow-tie ring-core FMF that can support 14 modes, with a min Δn_eff of 1.6 × 10⁻⁴ over the whole C+L band. Behera et al. [27] proposed an M-type few-mode fiber that supports 10 modes, with a min Δn_eff of 5 × 10⁻³ over the C band. Han et al. [28] proposed a cladding rods-assisted depressed-core FMF that supports nine modes, with a min Δn_eff of 1 × 10⁻³ over the C band. However, the number of eigenmodes and bandwidth supported by the fiber need to be further improved.

In this paper, we propose a weakly-coupled double bow-tie multi-ring elliptical core multi-mode fiber supporting 22 eigenmodes across the C+L+U band. The multi-ring elliptical core, bow-tie air holes, and symmetrical bow-tie stress-applying areas improve modal birefringence and effectively separate two adjacent degenerate modes. In particular, the introduction of a multi-ring elliptical fiber with a high-index ring and a trench improves the minimum effective refractive index difference between adjacent eigenmodes and reduces the bending loss. The implementation of a double bow-tie structure enhances birefringence, resulting in a greater separation of degenerate modes. We investigated the effects of various parameters of the proposed fiber on n_eff between adjacent eigenmodes, min Δn_eff, A_eff, B_m, bending loss, and the number of supported eigenmodes at the wavelength of 1550 nm. Moreover, we evaluated n_eff, min Δn_eff, A_eff, DMD, and dispersion of the C+L+U band. Simulation results demonstrate that the DBT-MREC-MMF effectively splits adjacent eigenmodes by combining bow-tie stress-applying, bow-tie air holes, and multi-ring elliptical core structures. The proposed fiber achieves min Δn_eff between adjacent eigenmodes larger than 3.515 × 10⁻⁴ across the C+L+U band. The proposed fiber has potential applications in MIMO-free eigenmode-division multiplexing systems to increase transmission capacity and spectral efficiency. Furthermore, the proposed fiber has potential in MIMO-free eigenmode-division multiplexing systems to increase transmission capacity and spectral efficiency.

2. Fiber Design

Figure 1 presents the schematic cross-section and refractive index profile of the proposed DBT-MREC-MMF. The fiber comprises a cladding made of pure SiO₂, two bow-tie air holes, two bow-tie stress-applying areas doped with B₂O₃-doped silica, and three different step-index cores doped with GeO₂-doped silica. The refractive index difference between the elliptical core and the cladding of the fiber is denoted as Δn₁, and the long and short semi-axes of the elliptical core are a₃ and b₃, respectively. A high-index ring with the same ellipticity as the elliptical core is introduced by addition to the elliptical core. The high-index ring has an inner radius of long semi-axis a₁ and short semi-axis b₁, and an outer radius of long semi-axis a₂ and short semi-axis b₂, with a relative refractive index difference between the high-index-ring and cladding of Δn₂. Moreover, a trench layer with the same ellipticity as the core is added close to the outer side of the elliptical core, with long semi-axis a₄ and short semi-axis b₄. The relative refractive index difference between the trench and the cladding is Δn₃. The ellipticity of the core, high-index ring, and trench is defined as e = a₁/b₁ = a₂/b₂ = a₃/b₃ = a₄/b₄. The bow-tie stress-applying areas have parameters of an inner radius of r₁, width h, and angle θ, with an outer radius of r₂ = r₁ + h. The bow-tie air hole parameters have the long semi-axis a₅ and short semi-axis b₅, angle θ₀, and ellipticity e₀ = a₅/b₅. The refractive index of air is 1. The diameter of the fiber cladding is 125 μm.

The relative refractive index differences between the cores and cladding are denoted as $∆{=(n}_{\mathrm{core}}^2 –{ n}_{\mathrm{clad}}^2{)/2n}_{\mathrm{core}}^2$. The cladding material is SiO₂ with n_eff of 1.444 at a wavelength of 1550 nm according to the Sellmeier equation [29]. The mole fraction (mol%) of GeO₂ and B₂O₃, corresponding to Δn₁, Δn₂, and Δn₃, and the stress-applying area refractive index can be theoretically calculated using the hybrid Sellmeier equation [29,30]. The hybrid Sellmeier equation describes the relationship between the refractive index, wavelength, and concentration of dopants.

The thermal expansion coefficient (α) of the doped material is defined as α = (1 − m) α₀ + mα₁ [31], where m and α₁ represent the mole percentage and thermal expanding coefficient of the doped material, and 1 − m and α₀, respectively, are the mole percentage and thermal expanding coefficient of raw material. Thermal expansion coefficients of SiO₂, GeO₂, and B₂O₃ are 5.4 × 10⁻⁷ (1/K), 7 × 10⁻⁶ (1/K), and 10 × 10⁻⁶ (1/K), respectively. In practical fiber fabrication, a 30% mol-doped fraction of B₂O₃ in the stress-applying area has been utilized [31]. Based on this calculation, the refractive index of the stress-applying area is 1.468 at 1550 nm, and the thermal expansion coefficient is 3.378 × 10⁻⁶ (1/K). Further details regarding the fiber elastic parameters are summarized in [31], including the thermal expansion coefficient (α), Young’s modulus (E), Poisson’s ratio (v), the first and second stress optical coefficients (C₁, C₂), and operating and reference temperature. All simulations in this work were implemented using the finite element method at a wavelength of 1550 nm.

3. Results Simulation Analysis and Optimization

The main work of this section was to optimize parameters of the proposed fiber.

3.1. Optimization of Multi-Ring Elliptical Core Parameters

Figure 2 presents the schematic cross-section of the bow-tie muti-ring elliptical multi-mode fiber (BT-MREC-MMF). In this study, we first optimized the parameters of the optical fiber without adding bow-tie air holes. That is, we optimized the parameters of the bow-tie type multi-ring elliptical core optical fiber.

We first optimized the parameters of the fiber high-index ring structure. We fixed a₁ = 3 μm, a₃ = 9 μm, a₄ = 12 μm, ∆n₁ = 0.012, ∆n₂ = 0.018, ∆n₃ = 0.005, r₁ = 20 μm, h = 8.9 μm, θ = 90°, and r₂ = 28.9 μm. The paraments a₂ and e were adjusted to optimize the Δn_eff between adjacent eigenmodes. The influence of a₂ and e on min Δn_eff and the number of supported eigenmodes are shown in Figure 3. It can be seen that the min ∆n_eff first increases, and then decreases, with increasing a₂ and e, while the number of supported eigenmodes gradually increases with increasing a₂ and decreasing e. Within the region of 5.7 μm ≤ a₂ ≤ 6.3 μm and 1.6 ≤ e ≤ 1.71, the proposed fiber supports 22 eigenmodes, and min Δn_eff between adjacent eigenmodes is larger than 2.3 × 10⁻⁴. To obtain a larger min Δn_eff and better-designed tolerances, we selected the middle point a₂ = 6.1 μm and e = 1.65 (i.e., b₂ = 3.7 μm) in the region as the parameters of the high-index ring structure, which is marked by the red dot in Figure 3a. The preparation error ranges are ± 0.2 μm and ± 0.5 μm, respectively. The proposed MMF can support 22 eigenmodes and the effective refractive index difference between adjacent eigenmodes is greater than 2.58 × 10⁻⁴.

We continued to optimize the parameters of the high-index ring; here, we fixed a₁ = 3 μm, a₂ = 6.1 μm, a₃ = 9 μm, a₄ = 12 μm, ∆n₁ = 0.012, ∆n₃ = 0.005, r₁ = 20 μm, h = 8.9 μm, θ = 90°, and e = 1.65. Figure 4a,b shows variations of n_eff and the min Δn_eff as a function of the relative refractive index ∆n₂ in the high-index ring. Within the range of 1.6% ≤ ∆n₂ ≤ 2%, the min Δn_eff is related to the Δn_eff of the ${\mathrm{HG}}_{12}^{\mathrm{x}}$ and ${\mathrm{HG}}_{12}^{\mathrm{y}}$ modes. As shown in Figure 4b, with increasing Δn₂, min Δn_eff decreases. To obtain a larger min Δn_eff, we took Δn₂ = 1.8%, such that the min Δn_eff could reach 2.5 × 10⁻⁴.

As shown in Figure 5, we investigated the influence of a₁ and a₃ on min Δn_eff and the number of supported eigenmodes by the fiber at a₂ = 6.1 μm, a₄ = 12 μm, ∆n₁ = 0.012, ∆n₃ = 0.005, r₁ = 20 μm, h = 8.9 μm, θ = 90°, and e = 1.65. From the rectangular area of Figure 5, within the region of 2.5 μm ≤ a₁ ≤ 3.6 μm and 8.4 μm ≤ a₃ ≤ 9.2 μm, the proposed fiber supports 22 eigenmodes, and the min Δn_eff between adjacent eigenmodes is larger than 2 × 10⁻⁴. To obtain a larger min Δn_eff and better-designed tolerances, we chose the points a₁ = 3.3 μm (i.e., b₁ = 2 μm) and a₃ = 9 μm (i.e., b₃ = 4.45 μm) in the region as the parameters of the elliptical core. This parameter is marked by a red dot in Figure 5a. The effective refractive index difference between adjacent eigenmodes is greater than 2.58 × 10⁻⁴.

We investigated the influence of the core parameter ∆n₁ on Δn_eff at a₁ = 3.3 μm, a₂ = 6.1 μm, a₃ = 9 μm, a₄ = 12 μm, ∆n₂ = 0.018, ∆n₃ = 0.005, r₁ = 20 μm, h = 8.9 μm, θ = 90°, and e = 1.65, as shown in Figure 6. It can be seen that the min Δn_eff first increases and then decreases with increasing Δn₁. Min Δn_eff is larger than 2.3 × 10⁻⁴ within the range of 1% ≤ Δn₁ ≤ 1.48%. Here, we took Δn₁ = 1.3% to keep supporting 22 fully separated eigenmodes in the whole C+L+U band. This corresponds to a 13 % mol fraction of GeO₂ doped in SiO₂.

Adding a trench structure can effectively reduce bending loss and obtain a larger design tolerance at the same time [32]. We fixed a₁ = 3 μm, a₃ = 9 μm, a₄ = 12 μm, ∆n₁ = 0.012, ∆n₂ = 0.018, ∆n₃ = 0.005, r₁ = 20 μm, h = 8.9 μm, θ = 90°, and e = 1.65, and adjusted a₄ and Δn₃ accordingly, to optimize min Δn_eff between adjacent eigenmodes. The effect of a₄ and ∆n₃ on min Δn_eff and the number of supported eigenmodes are shown in Figure 7. Within the region of 10.25 μm ≤ a₄ ≤ 13 μm and 0.0055 ≤ ∆n₃ ≤ 0.009, the proposed fiber supports 22 eigenmodes, and min Δn_eff between adjacent eigenmodes is larger than 2.3 × 10⁻⁴. The trench has a significant effect on lifting min ∆n_eff between adjacent eigenmodes. Considering the feasibility of the fabrication process, we chose the parameters of the red dot (a₄ = 11 μm and Δn₃ = 0.7%) for further optimization.

3.2. Optimization of Stress-Applying Parameters

To optimize the structure size of the stress-applying area, we analyzed the influence of r₁, h, and θ on Δn_eff, B_m, and bending loss. Figure 8 shows the colormaps of min Δn_eff versus r₁ and h with θ set as 60°, 90°, and 120°, respectively. The influence of structure parameters of optical fiber r₁, h, and θ on bending loss along the direction of the x-axis and y-axis at bending radius R = 30 mm are shown in Figure 9. It can be clearly seen that the error range gradually decreases with the increase of angle θ. B_m increases with increasing h and decreasing r₁. The increase in the area of the bow-tie stress-applying areas has a significant effect on improving the birefringence of the optical fiber. As shown in Figure 8b, within the region of 7 µm ≤ h ≤ 15 µm and 16 µm ≤ r₁ ≤ 26 µm, the proposed fiber continues to support 22 eigenmodes with a min Δn_eff larger than 2 × 10⁻⁴. To obtain a larger min Δn_eff, lower bending loss, and larger manufacturing error range with reasonable parameter values, we finally choose the red point θ = 90°, r₁ = 20 μm, h = 11 μm as the target fiber structure size. At this point, the min Δn_eff value is 3.29 × 10⁻⁴, and modal birefringence B_m = 3.28 × 10⁻⁴ N/m².

3.3. Optimization of Bow-Tie Air Holes Parameters

The bow-tie air holes were introduced between the multi-ring elliptical core and the bow-tie stress-applying areas. We optimized the parameters of the bow-tie air holes of the DBT-MREC-MMF to increase min Δn_eff and reduce modal coupling. Figure 10 shows the colormaps of min Δn_eff versus e₀ and a₅, with θ₀ taking 30°, 45°, and 60°, respectively. The influence of structure parameters e₀, a₅, and θ₀ on bending loss along the direction of the x-axis and y-axis at bending radius R = 30 mm is shown in Figure 11. It can be seen from Figure 11 that B_m increases with the decrease of e₀ and the increase of a₅ and θ₀. This is because decreasing the ellipticity e₀ and increasing a₅ and θ₀ implies an increase in the geometric asymmetry and area of the bow-tie air hole. That leads to an increase in the contribution of geometric birefringence to overall birefringence. Considering larger min Δn_eff, appropriate manufacturing tolerances, and lower bending loss, e₀ = 1, a₅ = 18.5 μm, and θ₀ = 45° were selected as the parameters of the bow-tie air holes, as shown in the red dot in Figure 10b. At this point, the min Δn_eff value increases from 3.289 × 10⁻⁴ to 3.515 × 10⁻⁴, and the modal birefringence value increase from 3.26 × 10⁻⁴ N/m² to 3.627 × 10⁻⁴ N/m². The results show that the introduction of bow-tie air holes effectively increases the min Δn_eff between adjacent eigenmodes.

In summary, we optimized the parameters of the fiber structure to support 22 eigenmodes. The results indicate that the DBT-MREC-MMF exhibits a large min Δn_eff between adjacent eigenmodes. We selected the optimal parameters to achieve a larger min Δn_eff and better-designed tolerances.

4. Mode Properties and Broadband Characteristics

4.1. Birefringence

Figure 12 shows mode field intensity distributions with electric vectors (white arrows) distributions of modes supported by the DBT-MREC-MMF for all 22 eigenmodes at 1550 nm. It is apparent that all polarization directions of eigenmodes are approximately horizontal or vertical, and all the eigenmodes are well confined within the core region, which displays a superior capacity to maintain polarization.

Birefringence performance is important for studying the polarization properties of fibers. High values of birefringence provide superior polarization retention. Modal birefringence is related to many factors, such as the size of the stress-applying area, temperature, core ellipticity, core-cladding refractive index difference, thermal expansion coefficient, and wavelength of light. When a fiber has an asymmetric structure and stress-applying areas, it is necessary to analyze its modal birefringence (B_m). B_m can be classified into two types: geometric birefringence (B_g) and stress birefringence (B_s). B_g is caused by the anisotropy of the refractive index of the material due to the asymmetry of the fiber structure. B_s is caused by the photoelastic effect in the fiber after the addition of stress-applying areas. B_m is defined as [31]:

B_m = N_x − N_y = B_g + B_s = N_x0 − N_y0 + (C₁ − C₂) (σ_x − σ_y),

(1)

where N_x and N_y are the refractive indices of the material along the x and y directions. N_x0 and N_y0 are the refractive indices of the stress-free material. σ_x and σ_y are the normal stress along the x and y directions of the material, respectively. C₁ and C₂ are the stress-optic coefficients. B_s is defined as:

$$B_{\mathrm{s}}{=(\mathrm{C}}_1-{ \mathrm{C}}_2{\left)\right(\mathsf{\sigma }}_1-{ \mathsf{\sigma }}_2).$$

(2)

Figure 13a,b shows the distribution of the normal stress σ_x and σ_y in the transverse cross-section of the proposed MMF. Stress along the x-axis (σ_x) is much larger than that along the y-axis (σ_y). The normal stress along the x-axis (σ_x) and y-axis (σ_y) are ~5.38 × 10⁷ N/m² and ~−5.19 × 10⁷ N/m², respectively. Stress-induced birefringence, B_s = (C₁ − C₂) × (σ_x − σ_y), is ~3.626 × 10⁻⁴. According to Equation (1), we obtain the B_m of each point in the cross-section of the MMF. Figure 13c,d shows the distributions of the von Mises stress distribution and geometric and stress-induced birefringence (N_x − N_y) in the transverse cross-section of the DBT-MREC-MMF. From Figure 13d, the maximum birefringence is 9.55 × 10⁻⁴ N/m², and birefringence at the core is ~3.627 × 10⁻⁴ N/m². As for the B_g, which can be derived from Equations (1) and (2), the value is ~0.001 × 10⁻⁴. Since the B_s is much larger than the B_g, the main part of the B_m is B_s.

4.2. Bending Loss

For fiber in the actual transmission process, the loss generated by bending will decrease the quality of signal transmission. The bending loss of each eigenmode is obtained from the imaginary part of the effective index, shown as follows [33],

$$Bending Loss=\frac{20·2\pi ·Im\left(n_{\mathrm{eff}}\right)}{ln\left(10\right)·\lambda }$$

(3)

The DBT-MREC-MMF is asymmetric. The bending loss is different for different bending directions. The bending losses along the x and y-axis are calculated here. As shown in Figure 14, at the bending radius of 24, 22, and 10 mm along the x or y-axis, the number of eigenmodes reduces to 20, 18, and 16, respectively. Under an identical bending radius, the bending loss value of the low-order mode is lower than that of the high-order mode. When R is 30 mm, the bending loss along the x and y-axis is below 10⁻⁴ dB/m. Numerical results show that the proposed fiber has excellent bending resistance. When R is larger than 30 mm, the proposed fiber supports 22 eigenmodes, and the corresponding maximum bending losses of the fiber along the x and y-axis are 8.05 × 10⁻⁴ and 3.789 × 10⁻⁴ dB/m, respectively.

4.3. Broadband Performances

We further investigated the relationship between wavelength and mode properties (n_eff, Δn_eff, DMD, D, and A_eff) of DBT-MREC-MMF covering the whole C+L+U band. The variations of n_eff and Δn_eff as a function of the wavelength for each eigenmode are presented in Figure 15a,b. It was found that the DBT-MREC-MMF supports 22 eigenmodes over a range of wavelengths from 1530 to 1675 nm, and the min Δn_eff between adjacent eigenmodes is larger than 3.089 × 10⁻⁴ at 1530 nm. Results indicate that the DBT-MREC-MMF can work across the whole C+L+U band.

The differential mode delay (DMD) is important to reduce the complexity and power loss of MIMO processing. The DMD between mode A and mode B can be defined as [34]:

$$\mathrm{DMD}={\tau }_{\mathrm{B}}-{\tau }_{\mathrm{A}}=\frac{n_{\mathrm{gB}}-n_{\mathrm{gA}}}{\mathrm{c}}=\frac{n_{\mathrm{effB}}-n_{\mathrm{effA}}}{\mathrm{c}}-\frac{\lambda }{\mathrm{c}}\left(\frac{\partial n_{\mathrm{effB}}}{\partial \mathsf{\lambda }}-\frac{\partial n_{\mathrm{effA}}}{\partial \mathsf{\lambda }}\right)$$

(4)

where τ_B and τ_A are the group time delays of the two modes, n_gB and n_gA are the group refractive indices, n_effB and n_effA are the effective refractive indices, and c and λ are the speed of light and the operating wavelength in vacuum, respectively. Fiber dispersion is a key factor in determining transmission capacity, and the dispersion of each eigenmode is calculated by [16]:

$$\mathrm{D}=-\frac{\lambda }{\mathrm{C}}\frac{{\partial }^2{n}_{\mathrm{eff}}}{\partial {\lambda }^2}$$

(5)

As shown in Figure 16a,b, the DMD and dispersion of all 22 eigenmodes as a function of wavelength were calculated. All of the eigenmodes exhibit a relatively small DMD (−15.41~12.4 ns/km), which can induce negligible power penalties in short-haul optical communication links. Moreover, the dispersion values for lower-order eigenmodes covering the whole C+L+U band vary from 17.39 to 63.75 ps/nm/km, indicating that dispersion can be neglected when applied in short-haul optical interconnects. The dispersion value for higher-order eigenmode ${\mathrm{HG}}_{31}^{\mathrm{y}}$ is larger, and ranges from −77.57 to −70.85 ps/nm/km over the whole C+L+U band. To compensate for the dispersion problem in fibers, specialized dispersion-compensating fibers can be used. This method helps to ensure that the signal transmitted through the fibers remains intact and undistorted, enabling high-quality data transmission [35,36,37]. Hence, this fiber can be considered to be a promising candidate for MIMO-free MDM systems.

The mode effective area (A_eff) of the fiber reflects the lateral distribution of the optical field on the fiber cross-section. The nonlinear coefficient and A_eff are reciprocal to each other. A_eff is calculated by Equation (6) [38]:

$$A_{\mathrm{eff}}=\frac{{\left(\iint {\left|E\right|}^{2}dxdy\right)}^2}{\iint {\left|E\right|}^{4}dxdy}$$

(6)

where E represents the mode field power distribution across the fiber cross-section wavelength. The A_eff of the proposed DRT-MREC-MMF within the wavelength range of 1530 to 1675 nm is shown in Figure 17. The effective area gradually increases with increasing wavelength. The A_eff values range from 66.8 to 96.39 µm² over the whole C+L+U band.

5. Fabrication Method and Tolerance

Table 1. Optimal parameters with fabrication tolerance of the DBT-MREC-MMF.

	Tolerance Range	Target Value		Tolerance Range	Target Value		Tolerance Range	Target Value
a2/μm	5.7~6.3	6.1	e	1.6~1.71	1.65	Δn2	0.016~0.02	1.78
a1/μm	2.5~3.6	3.3	a3/μm	8.4~9.2	9	Δn1	0.01~0.0148	0.013
a4/μm	10.25~13	11	Δn3	0.0055~0.009	0.007	h/μm	7–15	11
r1/μm	16~26	20	θ	70~100	90	e0	0.9~1.9	1
a5/μm	17.5~20.5	18.5	θ0	30~60	45

clearly lists the tolerance parameters of the DBT-MREC-MMF. The min Δn_eff of the target value is 3.515 × 10⁻⁴. It is noteworthy that, within all the tolerance ranges listed in Table 1, the value of min Δn_eff is greater than 2 × 10⁻⁴, and the fiber supports 22 eigenmodes. These results demonstrate that the fiber exhibits a considerably high tolerance and exceptional performance.

The fabrication process of the proposed weakly-coupled DBT-MREC-MMF typically involves the following steps: (1) Preform fabrication: The first step is to fabricate a preform of the proposed fiber structure. This is typically done using the modified chemical vapor deposition (MCVD) method, where a glass tube is heated and rotated while reactive gases are introduced to deposit the desired dopants and form the core and cladding. (2) Drawing the fiber: After the preform is fabricated, it is placed in a fiber drawing tower where it is heated and drawn into a thin fiber. The fiber diameter is controlled by the drawing speed and the temperature gradient along the preform. 3. Etching: Once the fiber is drawn, it is etched to create the air-hole structure. This can be done using hydrofluoric acid or a similar etchant, which selectively removes the cladding material around the air holes. 4. Cleaving and polishing: The final step is to cleave the fiber to the desired length and polish the end faces to ensure good optical coupling.

Several novel ring core fibers have been successfully developed [39,40], exhibiting excellent performance in data transmission. The fabrication process of stress-applying regions, particularly the widely experimented bow-tie or panda-type in polarization-maintaining fibers, has reached a mature stage [41,42]. Additionally, air-hole-assisted fibers have been extensively studied and manufactured [43,44]. Drawing on these well-established fabrication techniques and experiences, it is reasonable to suggest that the proposed fully degeneracy-lifted DBT-MREC-MMF for MIMO-free direct fiber MDM transmission could be manufactured. We are confident that the fabrication of the proposed fiber will be successfully realized.

6. Conclusions

In conclusion, we have presented a weakly-coupled double bow-tie multi-ring elliptical core multi-mode fiber capable of supporting 22 independent eigenmodes across the C+L+U band. The proposed fiber structure, incorporating bow-tie air holes, a multi-ring elliptical core, and bow-tie stress-applying areas, exhibits enhanced modal birefringence and effectively separates adjacent eigenmodes. The proposed fiber design utilizes a multi-ring elliptical core created by inserting a high-index ring and adding an outer trench, resulting in improved separation and transmission between adjacent eigenmodes. The bow-tie air holes lead to enhanced modal birefringence and improved separation of adjacent eigenmodes. The bow-tie stress-applying areas induce stress on the fiber, further enhancing modal birefringence and improving polarization maintaining performance.

Through parameter optimization, the proposed fiber achieves a Δn_eff between adjacent eigenmodes larger than 3.089 × 10⁻⁴ over the whole C+L+U band. The fiber has a high effective area (66.8~96.39 µm²), low differential mode delay (−15.41~12.4 ns/km), and negligible bending loss (<10⁻⁴ dB/m). Overall, our simulation results suggest that the proposed DBT-MREC-MMF holds great promise for applications in eigenmode-division multiplexing transmission, offering significant bandwidth improvements and increased transmission capacity. By analyzing and optimizing the structural parameters, the proposed fiber has potential applications in eigenmode-division multiplexing transmission to increase bandwidth and improve transmission capacity.