1. Introduction

Large Mode Area fibers (LMA) is a growing research field, notably due to the increase of available high power fiber laser sources and the need of all-fiber components for high quality optical beam delivery. The challenge lies in designing fibers that support, in practice, only one core-guided mode with limited bending losses. Thus, during the past few years, considerable efforts have been made to develop original flexible Single-Mode - LMA fibers (SM-LMA) and different solutions have been proposed in the literature [1–6]. We will focus herein on ARROW fibers [7] and more precisely on Bragg fibers since they have proven to be good potential candidates for SM-LMA applications [5]. As shown in Fig. 1(a), their cladding is made of alternate high refractive and low refractive index layers [8]. The mechanism responsible for light confinement in the core is similar to the one at the origin of the reflection of light in a planar Bragg stack [9]. In such fibers, a MFD as high as about 33 μm has already been reported [5].

 

Fig. 1 (a) Cross section of a Bragg fiber, (b) the corresponding Pixelated Bragg fiber and (c) SEM picture of the realized fiber. In the 2 first schemes, darker blue stands for higher refractive index. Lighter gray corresponds to Ge-doped silica in the SEM picture (c).

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Nevertheless, Bragg fibers are not true PBG fibers, even if often described as so in the literature, since their cladding’s structure is commonly compared to an infinite plannar supercell, which is not totally true. In fact, the transmission windows (TW) for the core-guided modes lie between the cutoff wavelengths of LP_0m modes (m = 1, 2, ···) of the annular waveguides of the cladding. For example, the 1^st TW is located between the cutoffs of LP₀₁ and LP₀₂ rings modes. However, LP_lm modes with l ≠ 0 are also guided within the rings and their effective indices fill up entirely the TW [10, 11]. Even if the effective index of such cladding modes can cross the one of the core modes in the TW of the fiber, coupling between core and cladding modes can only occur when their azimutal numbers l are the same for symmetry reasons. For example, the LP₀₁ core mode (fundamental mode) cannot couple with cladding LP_l1 ring modes if l is greater than zero in the perfect fiber. But, what is predicted in perfect straight fibers becomes discutable in a real fiber since imperfections inevitably couple - at specific crossing points - light between guided modes as the cylindrical symmetry is broken. This leads to spectrally located increase of the attenuation in the TW, as it has been already reported in the literature [10,12]. By definition, such fibers do not support real PBG as defined by Joannopoulos et al. [13].

It is the aim of this paper to present the theoretical and experimental description of a new design of Bragg fiber that eliminates some drawbacks of Bragg fibers while preserving some of there singular properties. The proposed design permits to reach a MFD of more than 25 μm together with SM behavior.

2. Principle and design

The new type of Bragg fiber proposed in this work is composed of a cladding where the conventional continuous high index rings are replaced by discontinuous rings made of circular high index rods (Fig. 1(b)). We call hereafter this new type of fiber: “Pixelated Bragg Fiber” (PiBF). The basic idea underlying the improvement of the transmission characteristics lies in the fact that, for a given isolated HII mode, a ring made of a finite number, N, of high index rods supports only, depending on their degeneracies, 2N or 4N supermodes formed by linear combinaisons of this isolated HII mode [14]. As a result, the limited number of cladding modes will create a coupling-free region where only the core modes can exist, thus enabling a true PBG guiding mechanism. Note that ring-structured Bragg fibers with large refractive index contrast have been already reported in the literature [15], but with low index rings that are made of air-holes, and not with high index pixels. Such fibers suffer a priori from the same drawbacks than standard Bragg fibers since the high index rings support also LP_lm modes that can couple with the core modes.

As a proof of concept, a PiBF with three pixelated rings is presented hereafter. It is designed and realized to guide light above 1 μm in the first TW. For the modeling, the core radius r_c (defined here as the distance from the fiber center to a first circular HII center, see Fig. 1) has been fixed to 20 μm. According to the ARROW model that is also relevant in the case of the PiBF, the diameter d and the refractive index profile of the HII (see Fig. 1) directly fixes the spectral position of the TW. To guide light beyond 1 μm in the first TW, the cutoff wavelength of the HII LP₁₁ mode has been fixed to approximately 830 nm, which leads to a diameter, d, about 3.1 μm in the case of graded-index HII with a maximal refractive index difference of 30 · 10⁻³ [16]. The ratio, d/Λ, (see Fig. 1) is fixed to 0.5 leading to a first ring made of 20 HII. Calculations have been made with a commercial finite element method. An anisotropic circular perfectly matched layer has been added to the domain boundary to determine accurately the Confinement Losses (CL) [17].

Contrary to Solid Core (SC)-PBGF with HII arranged in a hexagonal geometry [18], the distance Δr between two adjacent rings can be easily adjusted is such a way that some higher order modes exhibit high CL. Such a condition is well-known in standard Bragg fibers [19] and corresponds to:

Under the assumptions that (i) the wavelength is much smaller than the core diameter and (ii) the effective index of the guided modes is close to the refractive index of the core, then the electric field is roughly null at the interface between the core and cladding. In this case, κ_lm takes the simple following form [20, 21]:

In this study, Δr has been chosen to increase the CL of the LP₁₁ core mode (u₁₁ = 3.83) and is equal to ≈ 16.4 μm in this case, which leads to a second and third ring composed of respectively 38 and 56 HII.

Note that in the case of low index contrast Bragg fibers, the guided core modes can be considered as Linearly Polarized (LP), that is why the LP notation is used throughout the paper. The demonstration of this assertion is out of the scope of this paper, but elements are given in ref. [21] for the reader interested in.

Figure 2 (bottom) shows the CL of the four first core modes namely LP₀₁, LP₁₁, LP₀₂ and LP₂₁, the other modes having CL orders of magnitude higher. As expected, the shape of the CL proves to be the one of a PBG fiber [9]. The minimum CL is equal to 23 dB/km at 1.14 μm for the LP₀₁ core mode and is about 3 orders of magnitude greater for the LP₁₁ core mode. The CL for the LP₂₁ and LP₀₂ core modes are in between those of the two first core-guided modes. Such a behavior results from the value of Δr that has been chosen to maximize the CL of the LP₁₁ core mode. It has to be pointed out that a 19-cells core SC-PBGF with similar core diameter and same HII (same index, same diameter, same pitch) arranged in a hexagonal geometry does not present this efficient LP₁₁ mode rejection: CL ratio between LP₀₁ and LP₁₁ core-guided modes in the SC-PBGF is less than 10 as compared to more than 1000 in the PiBF.

 

Fig. 2 Top: effective indices of the 4 first core-guided modes: LP₀₁ (black), LP₁₁ (green), LP₂₁ (red) and LP₀₂ (blue). The 40 LP₀₁ ring supermodes of the first ring HII (open red circles) are also displayed above the silica line together with the 80 LP₁₁ ring supermodes. Refractive index of silica is also shown in dashed blue. Bottom: CL of the LP₀₁ (black), LP₁₁ (green), LP₂₁ (red) and LP₀₂ (blue) core-guided modes for the modeled PiBF.

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The effective indices of the first four LP_lm core-guided modes are also shown in Fig. 2 (top) in continuous lines (LP₀₁ in black, LP₁₁ in green, LP₂₁ in red and LP₀₂ in blue). The refractive index of silica corresponds to the dashed blue line. All the cladding modes indices corresponding to the light that is confined in the HII of the first ring are also displayed in open red circles above the silica line. As written earlier, such cladding modes correspond to supermodes that are a combination of 40 LP₀₁ HII modes at higher wavelength and 80 LP₁₁ HII modes that define the blue edge of the TW. As can be seen, this fiber structure prevents effective index crossing between cladding modes and LP₀₁ core-guided mode, and this on a large spectral window between about 900 nm and 1700 nm. Moreover and contrary to annular modes of a standard Bragg fiber, all the HII modes form a thin band when the wavelength is shorter (converging to the effective index of one isolated rod mode as in SC-PBGF [22, 23]). This behavior is also true with the two other larger rings that form the PiBF. Note that such a behavior can be easily deduced from the ARROW model since the spectral position of the TW can be roughly determined by the cutoff of one isolated HII and is well known in solid core PBGF with a triangular lattice of HII for which a true band gap guidance is observed whatever the number of rings and the shape of the HII [24].

3. Characterization and discussion

Based on this design, a PiBF has been realized (see Fig. 1(c)). More precisely the core and the two inner low index rings have been made by drawing a pure silica rod and two pure silica tubes (F300 from Heraeus) respectively. These silica elements have been stacked concentrically within one another inside a third pure silica tube (forming the outer silica ring). The gaps between these tubes and the central core have then been filled with solid rods drawn from a graded index preform (from Prysmian-Group), forming the three high index inclusions rings. This preform has a central doped part with a quasi parabolic index profile embedded into a region of constant refractive index (equal to the pure silica one). The maximum refractive index difference, compared to pure silica, is close to 30.10⁻³. The ratio between the doped region diameter (d_c) and the entire preform diameter (d_ext) is 0.5. As can be seen, the first ring exhibits 19 HII (lighter gray), the second 37 and the third 53. The mean distance Λ between two adjacent HII (center to center) is estimated to be around 5.7 μm. Assuming that the ratio d/Λ is equal to d_c/d_ext, d is estimated to be about 2.85 μm. The core radius r_c is about 17.2 μm. Δr is around 16 μm (center to center). Comparing with theory, some HII are missing in the rings, the core is slightly smaller and HII slightly deformed from the perfect circle due to the specific process - high-index rods inserted between low-index tubes - used to realized the micro-structured preform. However, the geometrical parameters are similar enough to enable comparison between the modelled and fabricated fiber.

The experimental attenuation spectrum for the LP₀₁ core-guided mode is displayed in Fig. 3 (top) as a function of the wavelength. It has been obtained by the standard cut-back technique (the fiber length was cut from 32 m to 7 m), the PiBF being spliced to HI1060 (Corning ®) fiber at the output end. Care has been taken to hold the fiber as straight as possible, maximizing its radius of curvature (¿0.75 m) to avoid the effects that bending might induce on the guidance properties. After cut-back, it has been checked that only LP₀₁ core-guided mode is observed after 7 m-long propagation.

 

Fig. 3 Top: Attenuation spectrum of the PiBF obtained by the cut-back technique. Bottom: Group Velocity Dispersion for the LP₀₁ core mode. Red circles correspond to the experimental data, the black line being the GVD for the theoretical PiBF, and the blue one being the one of silica.

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The attenuation spectrum presents a typical curve of SC-PBGF with a minimum of about 310 dB/km at 1350 nm. Note that this value is one order of magnitude greater than the theoretical one and that the TW appears reduced on its blue edge as compared to prediction. This slight disagreement could be explained by fiber micro-bending and/or deformations of HII. No extra peaks have been observed in the TW even for long lengths of fiber (40 m) validating the fact that HII ring-guide modes do not cross the core-guided modes.

Near field patterns have been recorded by imaging a 1 m-long fiber output, and they are displayed in Fig. 4 for the selected wavelengths λ = 1100 nm, 1200 nm, 1400 nm and 1600 nm. A Δx shift of respectively 0, 5 μm and 10 μm with respect to the center of the fiber was also applied to identify wether higher order modes can propagate into the fiber core. The observed mode paterns are in accordance with the theoretical CL evolution shown in Fig. 2, since no LP₁₁ mode could be observed in the TW, which proves once again the efficiency of the application of the HWS condition. The fiber exhibits a robust SM (LP₀₁) behavior for wavelengths greater than 1400 nm, but for shorter wavelengths, LP₀₂ and LP₂₁ were also observed, as can be seen in the first two lines in Fig. 4. Such an observation is also predicted in Fig. 2, where the CL difference between LP₀₁ and (LP₂₁ − LP₀₂) is reduced as the wavelength decreases.

 

Fig. 4 Near field patterns of the core-guided modes. From left to right: figures obtaines with a shift of the pump beam of Δx with respect to the core center. Each line corresponds to a wavelength. Intensity patterns are displayed in log scale so that intensities in the low index annular rings can be seen without saturation of the intensity within the core.

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The MFD has been measured at λ = 1400 nm. Figure 5 shows a transverse cut of the intensity guided within the core. A MFD of 26 μm is measured (at 1/e²) at this wavelength.

 

Fig. 5 Transverse cut of the intensity for the LP₀₁ core-guided mode, recorded at λ = 1400 nm (linear scale). Inset: spatial profile shown in linear scale.

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Finally, the Group Velocity Dispersion (GVD) of the fundamental core mode has been measured using a low-coherence interferometric technique [25] with a 50 cm-long fiber and is displayed in red circle in Fig. 3 (bottom). The theoretical one is displayed as a black continuous line. For comparison, the GVD of the material only (silica) is displayed also in continuous blue line. The GVD is a monotonic function of the wavelength with a zero at ≈ 1275 nm and is in good accordance with the theoretical one except near the TW edges, which is attributed to geometrical differences between the ideal and realized fiber (the shape of the HII could be mainly responsible for this phenomenon). With such a large fiber core, the GVD is close to that of pure silica as can be seen, and the influence of the waveguide is only seen at the TW edges.

4. Conclusion

In summary, a new type of Bragg fiber has been proposed and realized. As compared to conventional Bragg fibers, the continuous annular rings have been replaced by pixelated rings. This gives the possibility for the fiber to exhibit a true PBG guidance, leaving a wide spectral region where the core mode is guided without any coupling with cladding modes. Moreover, similarly to conventional Bragg fibers and contrary to hexagonal SC-PBGF, this new design makes it possible to finely adjust the differential loss between the fundamental mode and higher-order modes, so as to reach a practically single-mode behavior while preserving the benefits of SC-PBGF [26, 27]. Preliminary results in the realized fiber validate this behavior and MFD of 26 μm is reported at 1400 nm.