1. Introduction

Multi-core and multi-mode fibers for space-division multiplexing (SDM) application are under intensive investigation because of their large potential for overcoming the capacity crunch facing optical fiber communication networks [1,2]. Photonic crystal fibers are promising candidates for SDM transmission because of their intrinsic advantages such as the potential to achieve a large effective mode area, a small bending loss, a higher threshold power for a fiber fuse and their excellent dispersion tailoring ability [3–6]. We have also demonstrated the advantage of few-mode PCFs for realizing a larger A_eff [7,8]. The fabrication process has been greatly improved to reduce the transmission loss of PCF. The lowest single-mode PCF attenuation level has been improved to 0.18 dB/km, and the Rayleigh scattering coefficient has been reduced to less than that of conventional pure silica core fiber [9,10]. However, to the best of our knowledge, few-mode PCF with very low loss has yet to be reported.

By contrast, several methods including the casting method and the stack-and-draw method [11–13] have been proposed for fabricating holey fibers. Of these methods, the drilling method is one of the most common approaches. Although this method can realize precise machining, the drilling and subsequent hole inner surface treatment processes are time consuming. Typically, the drilling speed is controlled to a few mm/min. Polishing the hole inner surface requires a lot of time. It has also been reported that treating the air hole inner surface is essential for reducing the transmission loss [9,13]. The mechanical drilling of holes in a fiber preform will inevitably result in additional loss due to the surface imperfections in the air holes (namely, a “defective layer”) in the fabricated fiber. Therefore, the inner surface treatment of air holes, such as polishing, is especially important to reduce the thickness of the defective layer of the drilled preform. By contrast, the inner surface treatment is not so important for fibers made by the stack-and-draw method, which usually starts with highly polished and dehydrated capillaries. The surface imperfections fall into two categories, namely imperfections caused by contamination and surface roughness caused by scratches or cracks in the holes. However, their effect on transmission loss is still unclear, especially in few-mode holey fibers.

The objectives of this paper are to devise a design theory that can minimize the effect of a defective layer on the transmission loss of few-mode PCF, and to find a more realistic way to fabricate low loss PCF by using an economically feasible drilling method. We report on the additional loss that results from the air hole surface and the dependence of the modal loss on the air hole structure both theoretically and experimentally. Moreover, we demonstrate that by employing suitable polishing processes for only the six innermost holes of few-mode PCF, its transmission loss can be reduced to less than 0.5 dB/km at around 1550 nm, which is suitable for various applications.

2. Theoretical study

We construct a theoretical model with a uniform “defective layer” to simulate the loss induced by surface imperfections in air holes. A schematic of the model is shown in Fig. 1. The use of a drilling process will inevitably result in a defective glass layer (depicted as red circle layers) with a rough surface, OH-ions, and other impurity particles. Since the air hole diameter is of the order of several micrometers and the defective layer is very thin, it is very difficult to measure the surface roughness and defective layer thickness precisely. For the sake of simplicity, we assume that the defective layer has uniform optical properties and an extinction coefficient κ. The complex refractive index of the defective layer is n-jκ, where n is the refractive index of the pure silica glass cladding structure. The thickness of the defective layer is t.

 

Fig. 1 Calculation model of PCF with defective layer.

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In the calculation we assume that the PCF model has 36 hexagonally allocated air holes. The hole diameter is d, and the distance between the centers of adjacent cores is Λ. We add an inset in Fig. 1 to make the definitions of d, t, and Λ more explicit. The cladding diameter is set at 125 μm. To guarantee the existence of more than two propagation modes at a wavelength of 1550 nm, d/Λ is set at larger than 0.6. (The single-mode operation condition is less than 0.43) [14]. Since we focus on the additional loss α_h that results from the surface imperfection of the air holes, in this study we ignore other loss factors such as Rayleigh scattering and infrared absorption. We calculated the additional loss α_h of the LP₀₁ and LP₁₁ modes at a wavelength of 1550 nm using the finite element method.

First, we determined reasonable initial values for parameters κ and t taking geometrical and experimental conditions into consideration. We assume empirically that the original thickness of the defective layer in a fiber preform is around 0.1 - 0.5 mm although the thickness depends on the type of drilling tool used. During the drawing process, the preform diameter is reduced more than 200-fold. Therefore, the thickness of the defective layer t in a fiber is considered to be micrometer order. It is 2 - 3 orders of magnitude larger than the surface roughness of PCFs fabricated by the stack-and-draw method estimated with an atomic force microscope (AFM) measurement [13,15]. However, this is probably because the glass tube used for capillary fabrication has already been highly polished and dehydrated prior to the capillary drawing process. As a result, we think that the defective layers of a preform made by the stack-and-draw method are almost eliminated. Then the surface roughness that remains in PCF fabricated by the stack-and-draw method is due to the existence of surface capillary waves (SCWs) generated during the fiber drawing process [15]. In addition, we considered the absorption of OH-ions in the defective layer as well as the roughness-induced scattering. Then we assumed t = 1 μm including the diffusion length of OH-ions [16], and κ = 3 × 10⁻⁹ as initial values of drilled preform, which are represented by the dotted lines in Fig. 3. This κ value is equivalent to a transmission loss of 100 dB/km if the entire PCF core has the same κ value. As described below, we calculated the additional loss α_h by using these initial values and it agrees well with the experimental results shown in Fig. 2 and Fig. 7.

 

Fig. 2 (a) α_h as a function of d/Λ; (b) α_h as a function of Λ.

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We next studied the relationship between α_h and d/Λ when Λ = 12.5 μm. α_h as a function of d/Λ is shown in Fig. 2(a). The α_h values of both the LP₀₁ and LP₁₁ modes decrease when d/Λ decreases from 0.9 to 0.6. These decreases are both about 50%. The reason for this is that when Λ is constant and d/Λ decreases, the core radius, namely, the distance between the fiber core and the defective layer of the innermost air holes, increases. The α_h value of the LP₁₁ mode is consistently larger than that of the LP₀₁ mode. This is probably because the effective area A_eff of the LP₁₁ mode is about 20% larger than that of the LP₀₁ mode, As a result, the LP₁₁ mode is more affected than the LP₀₁ mode. Figure 2(b) shows the relationship between α_h and Λ when d/Λ = 0.7. The α_h values of both the LP₀₁ and LP₁₁ modes decrease when Λ increases from 12.5 to 16.5 μm. They both decrease by about 50%. This is probably because the power confinement in the core becomes stronger when d/Λ is constant and Λ increases [17]. From the results in Fig. 2, it can be concluded that by choosing a larger Λ and a smaller d/Λ, we can reduce α_h. However, the effect of optimizing the fiber structure is limited because we also have to consider other properties such as bending loss and A_eff. To reduce α_h to a negligible level, the inner surfaces of the holes must be treated. The parameters, κ and t, depend largely on the treatment conditions used for the inner surfaces of the holes. Therefore, we next investigated the loss dependence on these parameters.

The relationships between α_h and κ and between α_h and t are shown in Fig. 3(a) and (b), respectively. For both the LP₀₁ and LP₁₁ modes, α_h decreases linearly with decreasing κ as we expected. α_h is also strongly dependent on the thickness t of the defective layer especially when t is less than 1 μm. For example, when t decreases from 1 to 0.3 μm the α_h values of the LP₀₁ and LP₁₁ modes decrease to 10% of their original respective levels. These results imply that reducing the surface roughness and contaminants is a simple and effective way to reduce α_h. Moreover, the treatment of the inner surface of the air holes is critically important and can have a large impact on α_h.

 

Fig. 3 (a) α_h as a function of κ; (b) α_h as a function of t.

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Polishing is a particularly effective way to alleviate the influence of a defective layer, because it reduces the defective layer thickness t. However, the polishing process is time consuming and difficult to carry out completely when the number of air holes is large. Then we simulated the effect of polishing on α_h. Here, we assumed a PCF structure with 36 hexagonally allocated air holes (Λ = 12.5 μm, d/Λ = 0.7). The parameter κ was set at an initial value of 3 × 10⁻⁹. We called the six innermost air holes the first layer (shown in yellow in Fig. 4(a)), the next 12 air holes the second layer (shown in green in Fig. 4(a)), and the outermost 18 air holes the third layer (shown in blue in Fig. 4(a)). We calculated three additional cases, namely where the polishing was applied to the first layer only, the first and second layers, and all three layers. We assumed that t = 1 μm in the unpolished layers and t = 0 in the polished layers.

 

Fig. 4 (a) Schematic showing names of polished layers; (b) α_h as a function of polished layer.

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The relationship between α_h and the layer numbers with the polishing treatment is shown in Fig. 4. The result for unpolished PCF (See Fig. 3) is also shown as a reference. It can be observed that by completely eliminating the defective layer (t = 0) of the first layer, the α_h values of the LP₀₁ and LP₁₁ modes are greatly reduced to less than 10⁻⁴ and 10⁻³ dB/km, respectively. The elimination of the second and third defective layers can further reduce α_h. However, these layers have 30 air holes and polishing them will take five times longer. In addition, polishing will inevitably increase the risk of damage to the preform. From the above discussion, we can expect the transmission loss of the PCF to be effectively decreased by eliminating the defective layer of just the six innermost air holes. Then, we fabricated PCFs to confirm the results of our calculation.

3. Experimental results

We fabricated fibers A and B using exactly the same glass preform with 36 air holes. The preform was elongated into a 25 mm diameter rod, and divided into two pieces. Fiber A was directly drawn from the first piece without any treatment. Next, the inner surface of the second piece was treated. The surfaces of only the six innermost air holes were polished. The second piece of preform was then washed and etched lightly to clean the inner surfaces of the air holes. Fiber B was then drawn from the second piece of preform under the same drawing conditions as fiber A.

Cross-sectional images of fibers A and B are shown in Fig. 5. The diameters of fibers A and B were 125 ( ± 1) μm, respectively. The structural parameter d/Λ was 0.78 in both fibers, and the Λ value of fiber A (13.3 μm) was slightly larger than that of fiber B (11.6 μm). The air holes of fiber B were slightly deformed compared with those of fiber A. This is probably because the inner surface treatment enlarged the six innermost air holes of the second preform, and structural deformation occurred during the fiber drawing. It should also be noted that the deformation of the air holes may affect the measurement of the values of d/Λ and Λ in fiber B. However, we consider the effect of the structural deformation on the transmission loss to be negligible according to the calculated results shown in Fig. 2.

 

Fig. 5 (a) Cross-sectional image of fiber A; (b) Cross-sectional image of fiber B.

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The experimental setup for modal loss dependence evaluation is shown in Fig. 6. To evaluate the transmission loss of the LP₁₁ mode precisely, we employed a previously reported planar lightwave circuit (PLC) type two-mode coupler [18]. When the light is coupled from Port 2, the input light beam in the LP₀₁ mode is converted to the LP₁₁ mode and is output from Port 3. The modal crosstalk of the PLC was less than −15 dB. The PCF under test was connected to Port 3.

 

Fig. 6 Experimental setup for modal loss and NFP measurement.

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First, to investigate the status of the transmission mode, we measured the near field pattern (NFP) at the output facet of the fiber at a wavelength of 1550 nm. When the light was input from Port 2, the NFP of the LP₁₁ mode was clearly observed as shown in Fig. 6. We next measured the transmission loss in the LP₀₁ and LP₁₁ modes using a cut-back method from 1530 to 1565 nm (C-band). We used Ports 1 and 2 to measure the LP₀₁ and LP₁₁ modes. The loss measurement results are shown in Fig. 7. The fibers were 2.0 km long. The minimum losses of fiber A were 2.4 dB/km for the LP₀₁ mode and 3.7 dB/km for the LP₁₁ mode in the C-band. By contrast, those of fiber B were 0.31 dB/km for the LP₀₁ mode and 0.43 dB/km for the LP₁₁ mode in the C-band. Therefore, we successfully obtained few-mode PCF whose transmission losses were less than 0.5 dB/km by employing polishing processes for only the six innermost air holes.

 

Fig. 7 (a) Measured transmission loss of fiber A; (b) Measured transmission loss of fiber B.

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Next, we discuss the experimental results. In Fig. 7(a), the losses of the LP₁₁ mode are always higher than those of the LP₀₁ mode. The absolute loss values and this trend agree well with our theoretical calculations as shown in Fig. 2. More specifically, the α_h ratio of the LP₁₁ and LP₀₁ modes in Fig. 2 is about 2.5. If we assume that the intrinsic loss (the sum of Rayleigh scattering and infra-red absorption) is 0.15 dB/km [9], the experimental value of the ratios is around 1.7 (3.55/2.25 and 0.28/0.16). This experimental value is slightly smaller than that of the calculated value (2.5). The discrepancy of the ratio of α_h is probably because we assumed a completely homogeneous and uniform PCF structure in the calculation.

As shown in Fig. 7, the α_h values of the LP₀₁ and LP₁₁ modes were reduced to less than 10% of their original levels (0.28/3.55 and 0.16/2.25) in the fabricated PCFs by employing polishing processes for only the six innermost air holes. However, the effect of the inner surface treatment was limited compared with the calculation in Fig. 4. This is probably because we assumed the complete elimination of the defective layer (t = 0) in Fig. 4. The experimental result in Fig. 7 is rather similar to the result in Fig. 3. As mentioned above, Fig. 3 indicates that the α_h values of the LP₀₁ and LP₁₁ modes fall to 10% of their original levels by eliminating 70% of the defective layer. Therefore, we probably did not completely eliminate the defective layer in fiber B with the inner surface treatment. We believe that further loss reduction is possible by optimizing both the air hole structure and the inner surface treatment conditions.

4. Conclusion

We studied both theoretically and experimentally the additional loss resulting from inner surface imperfections, such as contamination and the surface roughness of the air holes of photonic crystal fiber. Our theoretical studies based on a model with a “defective layer” suggest that higher order modes have a larger loss due to air hole imperfections. By minimizing the inner surface imperfections of the six innermost air holes, we could theoretically expect the additional loss to be reduced to a negligible level. We then fabricated few-mode PCFs by employing a suitable inner surface treatment for just the six innermost holes. As expected theoretically, the transmission loss was greatly reduced through the use of these processes. The lowest transmission losses in the 1550 nm band were 0.31 dB/km for the LP₀₁ mode and 0.43 dB/km for the LP₁₁ mode. Our theoretical model will be useful with a view to realizing few-mode PCF with a loss comparable to that of conventional fibers.