## Abstract

We have designed a bend insensitive single mode optical fiber with a low-index trench using spot-size definitions and their optimization technique. The bending loss at a 5 mm of bending radius was negligible, while single mode properties were intact.

© 2008 Optical Society of America

## 1. Introduction

Bend insensitive fibers are exciting engineers and scientists because of possibility of their use in FTTH applications and thereby reducing a huge power penalty caused by sharp bends in optical fibers used in the city network [1–4]. There are several advantages of using bend insensitive fibers: they allow compact design of the splice-boxes and there is a significant cost saving. Typical parameters of a single mode optical fiber (SMF) which are allowed as per ITU-T recommendations [5] are listed in Table 1, which shows a large bending loss at a small bending radius of 5 mm. When the single mode optical fiber is straight, the most power is confined in an optical fiber core. However, when a sharp bending is applied, the power in the optical fiber core is leaked to a cladding region and an outer lossy polymer coating due to a curve induced refractive index change in the cladding, giving rise to a large bending loss in the SMF.

To reduce a bending loss in the SMF, the mode field should be strongly confined in the optical fiber. This can be done by optimizing the SMF parameters, but then there is a penalty to be paid in the form of a change in a mode field diameter and dispersion characteristics of the SMF and the optical fiber becomes incompatible to conventional SMFs already present in the optical fiber network [4]. One of the different ways to reduce bending loss in the optical fiber, while maintaining single mode characteristics specified by ITU-T, is to introduce a low-index ring (trench) in the cladding structure. This is because when the trench is used in the cladding region, its effective refractive index is reduced and less power is leaked into the lossy polymer coating when bending is applied. Various designs are already reported with a trenched and a non-trenched optical fiber to reduce a bending sensitivity of the optical fiber [1, 2]. Recently, a statistical design methodology has been proposed for a design and a tolerance analysis of hole assisted bend insensitive fibers by using a statistical simulation tool [6]. However, none of reported works directly describes the effect of different trench parameters (such as trench width and refractive index) on optical properties of the SMF and how they are optimized to maintain SMF characteristics.

In a current communication, we systematically describe the effect of various parameters of low-index trench on a single mode operation as well as bending loss of the SMF and dig out optimized parameters based on calculated results. To do this, we use a method of spot-size optimization, which was previously used to optimize two-step profile dispersion shifted fibers, where the core index and width were optimized to get dispersion shift [7]. In our case, we have used spot size definitions to optimize cladding parameters (rather than core) as per mode field definitions used in the current communication to minimize the bending loss.

## 2. Theoretical design

Our aim is to design a bend insensitive single mode optical fiber (BI-SMF) while maintaining key optical properties of the SMF as per ITU-T recommendations. A trenched SMF index profile is shown in Fig. 1. Typical questions that need to be answered for trenched fibers are: (a) How much should be a trench width? If the trench width is too wide, then optical properties of the single mode fiber are significantly altered. (b) How much should be a trench index? This question is important because there are commercial and practical limitations to provide the low index trench inside the cladding region. (c) How far should be the trench placed from the core? If the trench is very near to the core, it can affect SMF properties and if it is too far, it is a very expensive to fabricate the optical fiber. We begin with defining certain parameters. A basic parameter that controls the dispersion is an effective mode field diameter (MFD_{eff}), which is defined as [8, 9]

where *E* is the mode field, which can be computed from its evolution in the optical fiber using a scalar wave equation [8, 9]:

where *E* is an electric field along a radius *r*, *k*
_{0} is a propagation constant in the free space, *n*(*r*) is a refractive index profile of the optical fiber, *L* is an azimuthal mode number and *β* is the propagation constant in the optical fiber.

A Petermann-3 spot size MFD for the SMF is defined as follows [7, 10]:

where *n*
_{max} and *n*
_{min} are maximum and minimum values of the refractive index, *n _{eff}*(=

*β*/

*k*

_{0}) is an effective refractive index,

*λ*is a wavelength of operation and

*k*

_{0}=2

*π*/

*λ*. A macrobending loss in units of dB/km can be calculated using a formula [8, 9]:

where *F*
_{0} is a radial field of fundamental mode, *R _{c}* denotes the fiber core radius,

*R*is a bend radius and other parameters appearing in Eq. (4) are given by:

_{b}$$W={r}_{c}\sqrt{{\beta}^{2}-{\left({k}_{0}{n}_{min}\right)}^{2}};\Delta =\frac{{n}_{max}^{2}-{n}_{min}^{2}}{2{n}_{max}^{2}}$$

The Petermann-3 spot size (*MFD*
_{∞}) is directly related to the bending loss. Earlier in the case of dispersion shifted fibers, the MFD ratio (*MFD*
_{∞}/*MFD _{eff}*) was used to optimize splicing and bending losses [7]. For the BI-SMF (if MFDs are determined using Eq. (1) and Eq. (3)), when

*MFD*

_{∞}<

*MFD*, the bending loss reduces as the MFD ratio approaches 1 and when

_{eff}*MFD*

_{∞}>

*MFD*, the bending loss reduces as the MFD ratio increases beyond 1. Therefore, one has to optimize the MFD ratio carefully considering

_{eff}*MFD*

_{∞}and

*MFD*values so that minimum bending loss is obtained. Parameters to be obtained for the design are: a separation between the core and the low index trench (

_{eff}*b*), the trench width (

*c*) and the trench index (Δ

*n*). To understand relationships among different trench parameters, the MFD ratio and the bending loss, bending losses with respect to

_{Trench}*b*,

*c*and Δ

*n*are shown in Figs. 2(a), 2(b) and 2(c), respectively at typical dimensions shown in figures (where

_{Trench}*MFD*

_{∞}<

*MFD*). In Fig. 2(a), it is noted that there exists minimum bending loss at an optimum value of

_{eff}*b*and increasing

*b*far beyond the optimum value does not produce any significant change in the bending loss. For

*c*and Δ

*n*, the bending loss decreases with increase in the MFD ratio (Figs. 2(b) and 2(c)).

_{Trench}To design the BI-SMF, initially we fixed the design criteria so as to follow ITU-T recommendations at 1550 nm: MFD_{eff}>=9.6 µm, dispersion <=18.5 ps/km.nm and dispersion slope <=0.095 ps/km.nm^{2}; additionally, theoretical bending loss <=0.035 dB/cm at 5 mm of bending radius. Considering practical constrains in fabricating the optical fiber, we set maximum limits to various trench parameters: *b*<=4*a*, *c*<=4*a* and Δ*n _{Trench}* >=-0.004. The scalar wave equation of the optical fiber was solved at each set of

*b*,

*c*and Δ

*n*to obtain the optimum MFD ratio where bending loss was minimum. Every time it was checked whether the design criteria was followed or not and the values were selected only if the criteria was followed. By repeating this procedure for several times, optimum MFD ratios were obtained and a set of trench parameters associated with an each optimized MFD ratio were selected as optimized trench parameters.

_{Trench}## 3. Results and discussion

By adopting a procedure for obtaining optimized parameters of the trenched SMF by simulation as explained in section 2, we obtained optimized trench parameters as illustrated in Figs. 3(a) to 3(e). These figures show variations of minimum bending loss with respective MFD ratios and optimized *b*, *c* values at particular Δ*n _{Trench}* values. These are utility curves to design the trenched SMF for minimum bending loss. For example, to design the bend optimized SMF with the bending loss of about 0.02 dB/turn at 1550 nm (for 5 mm of bending radius), one can look at Fig. 3(d), select the MFD ratio of 0.836, which gives

*b*=1.1

*a*,

*c*=4

*a*and Δ

*n*=-0.003 from the figure, where

_{Trench}*a*is the core radius.

Calculated optical parameters of typical BI-SMF using optimum profile dimensions as given above, are listed in Table 2 and are shown in Fig. 4, where the bending loss at 1550 nm (for 5 mm of bending radius) is about 474 times smaller than that of the SMF without trench and notably, all other parameters of the BI-SMF are similar to the SMF. This indicates a strong advantage of using the trench in the cladding region; the power loss is almost negligible even for the bending radius of 5 mm, which can be contributed to the reduced effective index of the optical fiber cladding.

Lastly, we analyze the double trenched BI-SMF, where additional trench is introduced with same dimensions as of the single trenched BI-SMF; its profile structure is shown in the inset of Fig. 4(b). The MFD, the dispersion, and the bending loss are almost similar to those of the single trenched BI-SMF as shown in Fig. 4 and Fig. 5. It appears that only one trench in the cladding region is enough to achieve the bend insensitivity in the SMF.

## 4. Summary

We have designed the trenched SMF having negligible bending loss at 1550 nm upon 5 mm of bending radius using the spot size definitions. Both single and double trenched SMFs showed the same bending insensitivity, while keeping all the other optical properties of SMF intact.

## Acknowledgments

This work was supported by the Brain Korea-21 Information Technology Project, Ministry of Education and Human Resources Development, by the National Core Research Center (NCRC) for Hybrid Materials Solution of Pusan National University, by the GIST Top Brand Project (Photonics 2020), Ministry of Science and Technology, and by the Samsung Electronics Hainan Fiberoptics-Korea Co. Ltd., South Korea.

## References and links

**1. **P. R. Watekar, S. Ju, and W. -T. Han, “Single-mode optical fiber design with wide-band ultra low bending-loss for FTTH application,” Opt. Express **16**, 1180–1185 (2008). [CrossRef] [PubMed]

**2. **S. Matsuo, M. Ikeda, and K. Himeno, “Bend insensitive and low splice loss optical fiber for indoor wiring in FTTH,” Proceedings of Optical Fiber Communication Conference (OFC), Anaheim, USA, Feb. 23–27, 2004, ThI3 (2004).

**3. **M. -J. Li, P. Tandon, D. C. Bookbinder, S. R. Bickham, M. A. McDermott, R. B. Desorcie, D. A. Nolan, J. J. Johnson, K. A. Lewis, and J. J. Englebert, “Ultra-low bending loss single-mode fiber for FTTH,” Proceedings of OFC/NFOEC-2008, San Diego, USA, Feb. 24–28, 2008, PDP10 (2008).

**4. **
Stokeryale bend insensitive fiber (2007), http://www.stockeryale.com/o/fiber/products/bif-1550-l2.htm

**5. **
ITU-T recommendation G.652.

**6. **J. Van Erps, C. Debaes, T. Nasilowski, J. Watt, J. Wojcik, and H. Thienpont, “Design and tolerance analysis of a low bending loss hole-assisted fiber using statistical design methodology,” Opt. Express **16**, 5061–5074 (2008). [CrossRef] [PubMed]

**7. **R. Tewari, B. P. Pal, and U. K. Das, “Dispersion shifted dual-shape core fibers: Optimization based on spot size definitions,” IEEE J. Lightwave Technology **10**, 1–5 (1992). [CrossRef]

**8. **A. W. Snyder and J. D. Love, *Optical Waveguide Theory*, (Chapman and Hall, 1983).

**9. **D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. **66**, 216–220 (1976). [CrossRef]

**10. **K. Petermann and R. Kuhne, “Upper and lower limits for the microbending loss in arbitrary single-mode fibers,” J. Lightwave Technology **4**, 2–7 (1986). [CrossRef]