1. Introduction

Now-a-days, fiber-to-the-home (FTTH) application is experiencing upward growth due to the number of subscribers using it for internet is steadily increasing in the world. As FTTH is used by much less users as compared to the trunk line with 1.55 µm optimized non-zero dispersion shifted fiber (NZDSF) based system, the optical fiber used in FTTH has to be cost effective to make it economically competitive. Therefore, very cost effective, conventional single-mode fibers (SMF, G.652) are used in this system and the uplink and downlink is done with 1.31 µm and 1.55 µm wavelength, respectively. However, apart from the economical advantage of SMF, several disadvantages appear in the home applications because the SMF fiber is needed to be bent at various corners of wall and the bends can be as small as 5 mm to 15 mm and therefore a huge power penalty is caused.

A typical bending loss characteristic of SMF (1.22 µm cutoff wavelength, Fiber-A) is illustrated in Fig. 1. As seen in the figure, a single-turn of bend with 20 mm diameter can cause a bending loss of about 1.9 dB at 1.55 µm. To overcome the problem of bend sensitivity of SMF (SMF-28, Fiber-A), specially designed step index SMF fibers with high refractive index and some other design with trenching in the cladding have been used [1–2]. As mentioned in [4], having combined the low bending loss with its easy entry cable designs, a very special bend-insensitive fiber (‘Sumitomo PureAccess’, Fiber-B), which facilitates easier fiber handling for tight bends at the edges of walls and tighter fiber coiling within entry ports and network interface devices located at the premise, multiple dwelling unit (MDU), or home have been realized.

 

Fig. 1. The bending loss characteristics of various fibers available in the market (bend radius=10 mm).

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These bend-insensitive fibers have been reported to have minimum bend radii of 15 mm, a 50% decrease in bend sensitivity of conventional single-mode fiber, which allows for even greater fiber density with low bending loss for component and tight-access wiring necessary in FTTP applications. It has been mentioned that when wrapped around a 30mm diameter mandrel, the fiber exhibits no additional attenuation loss, thereby preserving signal strength. This innovation also addresses the industrial need for component miniaturization and speeds the development of smaller and less intrusive devices, such as closures and entry boxes, at the subscriber’s location [4]. Another experimentally realized bend-insensitive fiber (‘Samsung WidePass Bendfree’, Fiber-C) has been reported to have about 0.05 dB/turn loss at 1.55 µm and 0.2 dB/turn loss at 1.625 µm (bend radius=10 mm) and excellent optical properties under severe bending environment has been reported for FTTH application [5]. Bending loss characteristics of these fibers available in the market are illustrated in Fig. 1 for bend radius of 10 mm. The bending loss for Fiber-A was calculated from the single-mode profile available with the FiberCAD software (Optiwave, Canada) and for the Fiber-B and Fiber-C, the bending losses were estimated from the reported data [4, 5].

Although reported bend-insensitive fibers, as described above, can suppress the bending loss by about 100 times per turn as compared to the conventional SMF, the bending loss is still significant even in these fibers for continuous turns just over a few tens of meters, which will be typical in city conditions. Therefore, it is most challenging to address the problem either by increasing the bending radius, or by reducing the number of bends of optical fiber, or by introducing a new profile structure of optical fiber, which can give ultra-low bending loss. Since last option to redesign the optical fiber is the most user friendly and convenient method, we address it in this current communication where we report a new design of SM fiber which can theoretically make the SMF fiber bend-insensitive over a long distance. We have also minimized the splicing loss with the conventional SMF as the MFD is optimized to be nearer to that of conventional SMF.

2. Theory

When a fiber is bent, the optical power in the fiber core leaks into the cladding, and when the bend is released, it couples back into the core. However, at the bend, the effective refractive index of cladding becomes larger than the effective index of core and this causes a large amount of power in the cladding to leak into the surrounding rather than couple back into the core after the bend is over. This results in the large bending loss in the conventional SMF as shown in Fig. 1. A key to avoid the leakage of cladding power into surrounding is to make its effective index at bend smaller than the core effective index. This can be done by adding multiple depressed index layers in the cladding structures. Single depressed index cladding layer with a large diameter will be useful but it is impractical in terms of fabrication using the MCVD process. Therefore, we have chosen a multiple depressed index cladding structure, which eventually gave a five depressed cladding layer structure. Such structure is easy to fabricate and we get various parameters to control the bending loss of fiber. Also, the splicing loss during splicing of proposed fiber with the conventional SMF can be minimized by making their mode field diameters (MFDs) as equal as possible. To satisfy the above requirements, we have selected stringent criteria for the design of five-cladding fiber: it must have MFD between 8–10.5 µm and bending loss must be less than 0.1 dB per turn of 5 mm radius.

 

Fig. 2. (a) Refractive index profile of bend-insensitive fiber with multiple depressed claddings; (b) Modal intensity pattern of the five-cladding fiber (X, Y Axis→Radial length).

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The prototype refractive index design of bend-insensitive fiber with multiple depressed claddings is shown in Fig. 2(a). It shows a step-index core surrounded by five depressed cladding layers and design parameters (Δn₁, Δn₂, a, r₁, r₂, r₃ and r₄) are also defined in the figure. A typical modal intensity distribution in the optical fiber is illustrated in Fig. 2(b).

To analyze the optical parameters of five-cladding optical fiber, we used the scalar wave equation for an evolution of an electrical field in the optical fiber as [6]:

where E is the electric field along radius r, k ₀ is the propagation constant in the free space, n(r) is the refractive index profile of fiber, L is the azimuthal mode number and β is the propagation constant. The resolution of mode present in the optical fiber and the effective index calculations is done using the direct integration of scalar wave equation with appropriate boundary conditions. The MFD of optical fiber is related to the field distribution in fiber and it provides useful information about joint, microbending and macrobending losses. The effective area of fiber has a direct relation to nonlinear distortions in the long haul fiber links. The effective core area (A_eff) of fiber is calculated from the electrical field distribution obtained in Eq. (1). The A_eff and MFD are defined as:

The macrobending loss is a radiative loss when the fiber bend radius is large compared to the fiber diameter. In the units of dB/km, it is given as [6, 7]:

where F ₀ is the radial field of fundamental mode, R_c denotes the fiber core radius, R_b is the bend radius, n_max and n_min are the maximum and minimum values of refractive index and other parameters appearing in above equation are given by:

Bending loss is estimated using the bend radius and the electrical field characteristics of single mode arbitrary index profile fiber using Eq. (3). We have used the FiberCAD to solve the propagation equations and to calculate the bending loss of five-cladding fiber. Although we have done the calculations only for step-index structure, the results are equally valid for graded or triangular core.

3. Results and discussion

To emphasize the advantage of five-cladding SMF structure over the SMF with single cladding, Eq. (1) and Eq. (3) were solved for both the fibers and a comparison of bending loss of a typical SMF fiber with and without five-cladding structure is given in Fig. 3, where the fiber parameters were adjusted so that cutoff wavelength was 1.22 µm. It is seen that with the introduction of multiple trenching, the bending loss is reduced by a factor of 10⁶ at 1.55 µm. A reason for such a tremendous decrease in the bending loss is the lowered effective index of cladding due to trenching.

To select the optimum conditions for choosing various parameters of the five-cladding fiber (Fig. 2(a)) so as to fulfill our design criteria, the index design parameters of fibers were optimized at 1.55 µm after rigorous simulations with the variation of different parameters at fixed LP₁₁ cutoff wavelength. Throughout the simulation, the values of Δn₁ and core radius a were adjusted to get cutoff at 1.22 µm. As per the criteria discussed above, to get bending loss less than 0.1 dB/turn, the MFD of 8 µm to 10.5 µm was selected and the respective index difference and core diameter values were obtained that can be used for the fabrication of optical fiber. A list of allowable parameters is given in Table 1. Three dimensional view of modal intensity pattern inside the fiber calculated using Eq. (1) with the typical parameters listed in Table 1 is shown in Fig. 2(b).

 

Fig. 3. Comparison of bending characteristics of the fiber with five-cladding (blue) and with single-cladding (black) structures (Δn=0.016, core diameter=4.33 µm, λ_c=1.22 µm, MFD=5.22 µm and bend radius=5mm).

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Table 1. Design parameters for the five-cladding SM fiber.

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Utility curves showing optimum parameters we obtained are given in Fig. 4(a). Optical fiber fabricating engineer can choose required MFD and allowed bending loss and design parameters such as index difference and core diameter can be directly obtained from the graph. In our discussion to be stated, we have chosen the MFD of 9.5 µm, which is the same as the MFD of Fiber-A (SMF-28).

Theoretical results of the five-cladding SMF proposed in this study are shown in Fig. 4(b) for 10 mm of bend radius and listed in Table 2 for bend radius of 10 mm and 5 mm at selected wavelengths. It showed nearly zero bending loss at bend radius of 10 mm and at bend radius of 5 mm (at 1.55 µm), clearly demonstrating the effect of trenching in the cladding region. Physics behind this process can be expressed in the following way. When the fiber is straight, most of the power is confined in the optical fiber core. But when a small radius of bending is applied, power in the core is leaked to the cladding region. Now because of curvature, field in the cladding will have to cross more distance as compared to the field in the core region and to maintain the phase between both fields, velocity of field in the cladding should be more than that of core field, otherwise cladding field does not couple back to core, thereby causing big bending loss. When trenching is used in the cladding region, its effective refractive index is reduced, thereby increasing the velocity of cladding field and increasing the coupling of cladding-field to core region when the fiber is straight. As can be noticed from Fig. 4(b), almost 100% power is coupled back to core even after 5 mm radius of bending in the five-cladding fiber.

 

Fig. 4. (a) Simulated bending loss at 1.55 µm for the bend radius of 5 mm as a function of MFD at 1.55 µm for the five-cladding index profile (λ_c=1.22 µm). (b) Bending characteristics of the proposed five-cladding optical fiber (Bend radius=10 mm).

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Table 2. Bending loss performance of the proposed five-cladding optical fiber.

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4. Summary

We have developed a new design for the refractive index parameters of optical fiber containing five-cladding structure, which theoretically showed bending loss of 0.002 dB/turn at 1.55 µm for single turn of 5 mm radius. For the bend radius of 10 mm, the bending loss was calculated to be as low as 4.4×10^-10 dB/turn.