Single-mode large-mode-area fibers (SM-LMAFs) have numerous amazing applications benefiting from their special properties, such as a high energy storage capacity and a high threshold of nonlinearities. For example, in unrepeated systems the large effective area allows for launching a higher optical power in the fiber with less nonlinear penalties. As a result, the SM-LMAFs can offer a longer reach and a higher capacity (e.g., Corning’s Vascade EX3000 and Vascade L1000 fibers).

A number of fiber structures have been proposed to achieve a large mode area (LMA) and single-mode operation since the LMA concept was introduced in 1997, for example low numerical aperture (NA) step-index fibers (SIFs)^[1], multilayer-core fibers (MLCFs)^[2], photonic crystal fibers^[3], and multi-trench fibers^[4]. These fibers usually have an ultra-LMA and they are mainly used in high-power fiber lasers but are not suitable for communication. The mode area of Corning’s EX3000 fiber is 150μm2 and it is far less than the fibers used in fiber lasers that have mode areas of hundreds or thousands of square microns. There are two approaches to achieving SM-LMAFs. One is to design a multimode LMAF with a few modes and the effective single-mode operation can be achieved by stripping higher-order modes (HOMs)^[5]. Another approach is to design an intrinsically SM-LMAF with the cutoff wavelengths of HOMs below the operating wavelength.

In consideration of the mode area scale of fibers for communication, the second way is appropriate to achieve one to two hundreds of square microns. The realization of a LMA in such fibers requires a low NA so that single-mode operation can be maintained. Low-NA is helpful in achieving an LMA, but it is harmful to the bending performance. The scaling of the mode field area is limited due to detrimental bending effects, as there is a trade-off between the LMA and bending performance.

A fiber with an LMA and excellent bending performance will have a wider range of applications. For example, with the vigorous development of fiber-to-the-home (FTTH) projects, the related optical fibers have attracted considerable attention in recent years. The SM-LMAF with an excellent bend performance could be a significant option for FTTH.

In this Letter, we present an intrinsically SM-LMAF with a low bending loss. The fiber core consists of several alternating rings with a low and high refractive index in order to get a low equivalent average core-cladding refractive index difference. The multilayer structure has a better bending performance than a traditional step-index core. The multilayer structure also contributes to forming a curved refractive index profile (RIP) in the core area that has a better bending performance^[6]. In the cladding, a low-index trench is introduced to dramatically reduce the bending loss^[7]. We have analyzed the influence of multilayer-core, curved RIP, and trench on the bending loss. Based on the theoretical analysis, the MLCF is fabricated and experimentally characterized.

A semianalytic method based on perturbation theory is applied here for the calculation of the attenuation coefficient. For a fiber bent in the x direction, the transformed equivalent refractive index distribution nb(x,y) can be represented by a straight fiber nb(x,y)=n(x,y)(1+2R),(1)where n(x,y) is the refractive index of the straight fiber and R is the radius of curvature. the attenuation coefficient α can be derived from^[8], 2α=−Im[2πΨBW(0,0)β0∬−∞∞Ψ02dxdy],(2)where β0 is the unperturbed propagation constant of the fundamental mode for a straight fiber, Ψ0 is the unperturbed fundamental mode field, and ΨBW is the backward evanescent field in the innermost cladding layer surrounding the fiber core. Finally, the bending loss Lb of the fiber can be evaluated as Lb=10lg[exp(2αl)]≅8.686αl,(3)where l is the length of the bending fiber.

Figure 1 shows the structure of the proposed MLCFs, where b is the separation between the trench and the core, c is the trench width, Δt is the refractive index difference between the cladding and the trench, and Δ11 is the valve of the highest point of the parabola. The MLCFs consist of three parts: the multilayer core, the curved RIP, and an index trench. We will analyze the influences of the three parts on the mode area and bending loss in the following paragraphs.

Fig. 1. RIP of an MAF with a curved RIP and a trench in the cladding.

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Before the following analysis, a performance index (PI) for comprehensively evaluating the fiber bending performance is introduced first with a consideration of the trade-off between the bending loss and the mode area^[6], PI=Lb/MFD(dB/turn/μm),(4)where MFD is the mode field diameter calculated from the Petermann I definition: MFD=22π(∫r∞E2rdr)2π∫r∞E4rdr.(5)

We construct the MLCF and SIF with the same core diameter and cutoff wavelength (ensuring single-mode operation), as shown in Figs. 2(a) and 2(b), to compare the bending performance. Figure 2(a) shows the MLCF with a uniform high-index layer, where Δ1=0.0021, a1=1μm, and a2=1μm. Figure 2(b) shows the SIF with a core radius of 10 μm and Δ=0.00115. The elasto-optical correction factor is set as Reff/R=1.28, where Reff is the effective bending radius. The comparison of the bending losses between the two fibers is shown in Fig. 2(c) at a wavelength of 1550 nm. For the MLCF shown in Fig. 2(a), the MFD is 22.65 μm at a wavelength of 1550 nm; meanwhile, the bend loss is about 14.35 dB/turn at a bend radius of 20 mm, and the corresponding PI is 0.634 (dB/turn/μm). For the SIF shown in Fig. 2(b), the values of the MFD, bending loss, and PI are 22.36 μm, 154.4dB/turn, and 6.91 (dB/turn/μm), respectively.

Fig. 2. (a) Uniform high-index layer MLCF with parameters Δ1=0.0021, a1=1μm, and a2=1μm. (b) An SIF with core radius 10 μm and Δ=0.00115. (c) A bending loss comparison between MLCF and SIF.

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In summary, with the same core diameter and cutoff wavelength, the MLCF and SIF have a similar mode field area while the MLCF has a much better bending performance than the SIF.

The previous study indicates that fibers with curved core RIPs provide a better bending performance than the traditional SIF^[6]. In the following discussion, we take the parabolic RIP-based MLCF as an example to illustrate the improvement of the fiber performance. The refractive index difference of high-index layers in the core region can be defined as Δ1m=Δ11(1−((m−1)/M)2),(6)where Δ11 is the valve of the highest point of the parabola and Δ1m is the refractive index difference of layer m, m is the ordinal number of layers, and M is the total number of layers. The refractive index of the low index-layer is same as the cladding.

We constructed an MLCF with a curved RIP to compare the bending performance of different RIPs. Figure 3(a) shows the MLCF with uniform high-index layers and the parameters are same as in Fig. 2(a). Figure 3(b) shows the MLCF with a parabolic RIP. The parameters are set as Δ11=0.004, M=10, a1=1μm, and a2=1μm to obtain the same core diameter and cutoff wavelength as the MLCF shown in Fig. 3(a). The bending losses of the two MLCFs are shown in Fig. 3(c). For the MLCF shown in Fig. 3(a), the value of the MFD is 22.65 μm at a wavelength of 1550 nm and the bend loss is about 149.9 dB/turn at a bend radius of 10 mm, and the corresponding PI is 6.62 (dB/turn/μm). For the MLCF shown in Fig. 3(b), the corresponding values are 17.25 μm, 18.12 dB/turn, and 1.05 (dB/turn/μm), respectively. Although the MFD declines compared with the MLCF shown in Fig. 3(a), the bending performance improves obviously.

Fig. 3. (a) Uniform high-index layer MLCF with parameters Δ1=0.0021, a1=1μm, and a2=1μm. (b) A curved RIP MLCF obtained from Eq. (6) with Δ11=0.004. (c) A bending loss comparison between the MLCFs in (a) and (b).

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In summary, with same core diameter and cutoff wavelength, the curved RIP is helpful to improve the bending performance. In addition, the multilayer-core structure can achieve the very low equivalent refractive index and curved RIP simultaneously and it is easier to form different curved RIPs compared with traditional single-layer core fibers.

For improving the bending performance significantly, a trench is introduced to the cladding of the MLCF in Fig. 3(b) and then the structure shown in Fig. 1 is obtained. Figure 4 shows the bending loss evolution as a function of the core-trench separation b with a bending radius of 10 mm at a wavelength of 1550 nm. The other parameters are a1=1μm, a2=1μm, Δ11=0.004 (ensure single-mode operation), Δ1m can be calculated with Eq. (6), c=8μm, and Δt=−0.004. First, as b increases, the bending loss decreases and reaches the minimum at point A (bA≈7.6μm), then the bending loss increases rapidly and reaches the maximum at point B (bB≈15.9μm) because of the resonant coupling. The other high-loss peaks beyond point B are resonant couplings of the core mode and the high-order modes of the innermost cladding^[8].

Fig. 4. Bending loss evolution as a function of core-trench separation b with a bending radius of 10 mm at a wavelength of 1550 nm.

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The optimal b (the value of bA) is different with different bending radii during calculation. There is an approximate linear correlation between the parameters bA and the bending radius, as shown in Fig. 5(a). The bending performance of the MLCF with different bA is shown in Fig. 5(b). We find that the bending loss curves change like a seesaw. This phenomenon illustrates that we cannot improve the bending performance further at all bending radii simultaneously. The specific parameters can be chosen according to practical requirements. The optimized value of b also is related to parameters Δt and c. With the same parameters, but with the Δt, b, and c used in Fig. 4, the value of bA is shown in Fig. 5(c) as a function of the trench index Δt for different trench widths. The b decreases as c increases with constant Δt, but decreases as Δt decreases with constant c^[8].

Fig. 5. (a) bA evolution as a function of the bending radius. (b) The bending loss evolution as a function of the bending radius, with different bA at 1550 nm [the r in the legend denotes the bending radius in (a)]. (c) The bA evolution as a function of the trench index for different widths.

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For an MLCF with b=7.7μm (calculated at bending radius 10 mm) and Δt=−0.004, c=8μm, the bending loss of the MLCFs with a trench or without a trench evolves as a function of the bending radii, as shown in Fig. 6, respectively. With the trench introduced, the mode field area declines slightly from 244.5 to 241.1μm2, but the PI declines from 1.05 to 0.0017 (dB/turn/μm) with a bending radius 10 mm at a wavelength of 1550 nm.

Fig. 6. Bending loss comparison between the MLCF with a trench and the MLCF without a trench.

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To summarize, the bending performance can be improved tremendously with the trench introduced.

The MLCFs are fabricated by a conventional standard MCVD process. The micrograph of the MLCF and the RIP of the fabricated MLCF are shown in Fig. 7. The radius of the core is about 9 μm, the outside diameter of the MLCF is about 125 μm, and the highest refractive index difference of the high-index layers is 0.0042. The Δt of the trench is −0.0044 and the width of the trench is about 8.7 and 5 μm at the top and bottom, respectively. The value of b is about 5 μm.

Fig. 7. RIP of the fabricated fibers. The inset is the micrograph of the MLCF.

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We use an improved bend reference technique to measure the cutoff wavelength^[9]. According to several measurements, the cutoff wavelength is about 1425 nm. We measure the dispersion of the fabricated MLCF in the wavelength range from 1530 to 1570 nm, in increments of 1 nm, as shown in Fig. 8. For verifying the accuracy of the measurement, the dispersion of a single-mode fiber (Corning SMF-28) is measured with the same method and instrument. The measured dispersion of the fabricated MLCF is 19.18 ps/(km·nm) at 1550 nm.

Fig. 8. Measured dispersion of the fabricated MLCF and SMF-28.

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We measured the bending loss of the MLCF in curvature radius range from 4 to 11 mm, in increments of 0.5 mm, and the wavelength range from 1200 to 1800 nm, in increments of 0.2 nm. Figure 9 shows the spectral bending loss as a function of the bending radius and wavelength. The fluctuations are caused by the reflection mainly between the cladding and coating (slightly between coating and air).

Fig. 9. Spectral bending loss as a function of the bending radius and wavelength.

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The measured bending losses of the fabricated MLCF and the SMF-28 fiber with different bending radii at two different wavelengths, namely 1310 and 1550 nm, are presented in Figs. 10(a) and 10(b), respectively. The theoretical calculation results are also presented in Fig. 10, for comparison. The infinite cladding assumption is implemented in the calculation, thus the fluctuations are neglected and the curve is smooth. In order to estimate the bending performance of the MLCF, the bending loss of the SMF-28 is presented in Fig. 10, as a reference. As shown in Fig. 10, the bending loss of the MLCF is less than for the SMF-28 at shorter bending radii. At point E, the bending losses of the two fibers are equal and then the bending loss of the MLCF is greater than for the SMF-28 as the bending radius continuously increases. Although the bending loss of the MLCF is larger than for the SMF-28 at the longer bending radii, the bending performance has been improved considerably. Figures 11(a) and 11(b) show the bending loss spectrum at two different bending radii, 5 and 10 mm, respectively.

Fig. 10. Comparison of the bending losses between the fabricated MLCF and the SMF-28 fiber at 1310 and 1550 nm. The curves and markers represent the results of the simulation and the measurement, respectively.

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Fig. 11. (a) Comparison of the measured and calculated bending loss as a function of the wavelength, with a bending radius of 5 and 10 mm.

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Attributes (including the cutoff wavelength, dispersion, MFD, and bending losses) of the fabricated MLCF and SMF-28 fiber are listed in Table 1. The efficient mode area of the MLCF is about 3 times larger than for the SMF-28 at 1550 nm and the bending performance is superior to SMF-28 at a bending radius of 5 mm.

In conclusion, the MLCF is proposed for achieving an LMA with excellent bending performance. The influences of a multilayer core, curved RIP, and refractive index trench on the mode area and bending loss are analyzed. The MLCF is fabricated with the standard MCVD method. The measured cutoff wavelength is about 1425 nm, and the measured dispersion is 19.18 ps/(km·nm) at 1550 nm. The mode area is about 215.5μm2 at 1550 nm; meanwhile the bending loss is 0.58 dB/turn at a bending radius of 10 mm. By using the curved RIP and a trench in the MLCFs, the proposed fiber has low bending losses, especially at tight bending radii. Meanwhile, the efficient mode field area that is as large as possible is also achieved in MLCFs. The presented work is considered to be of significance for the field of LMA fibers with low bending loss applications.