A simple and reliable method to determine LP<sub>11</sub> cutoff wavelength of bend insensitive fiber

Pramod R. Watekar; Seongmin Ju; Lin Htein; Won-Taek Han

doi:10.1364/OE.18.013761

1. Introduction

To reduce a huge power penalty caused by sharp bends in single mode optical fibers used in city FTTH (fiber-to-the-home) networks and to support compact design of splice-boxes, bend insensitive fibers have attracted researchers to develop specialty fibers having high bend insensitivity [1–10]. Various designs are already reported with trenched, holes assisted and non-trenched fiber structures to reduce the bending sensitivity of optical fiber [1,2,7]. The trenched bend insensitive fiber (BIF), which follows the ITU-T G.652 recommendations for the single mode optical fiber has been commercialized as a cost-effective solution to the bending problem. The bend insensitivity in optical fibers along with maintaining the ITU-T G.652 recommendations has been achieved by strongly confining the power in the optical fiber by means of a low-index ring (trench) in the cladding structure. Such structures have been already reported [3–5,8–10] and commercialized [11].

As BIFs have been recently developed, the ITU-T recommendations about BIFs don’t spell any standard method to measure the cutoff wavelength, and as it is well known, knowing cutoff wavelength is one of the most significant parameter about the optical fiber to employ it in the network [12]. A standard method to measure the cutoff wavelength of single mode optical fiber (SMF) is a bend reference method where a wavelength with an attenuation of 20 dB in the LP₁₁ mode is considered to be the effective cutoff wavelength [13]. For this, the spectral attenuation for the SMF with a loop of 6 cm diameter is measured in comparison with the straight fiber and the wavelength where the long wavelength edge of the bend induced loss is greater than the long wavelength baseline by 0.1 dB is considered as the effective cutoff wavelength [13,14]. There are standard experimental instruments available to determine the cutoff wavelength by using this method, which is widely used in optical fiber industries. However, when the new BIF is used instead of the commercial SMF, we need to give a huge number of loops (>100 loops) to estimate the cutoff wavelength, because the high order mode (LP₁₁) has a very low bending loss in the BIF, which is a real hindrance in the determination of the cutoff wavelength using the existing instrument. Because of this difficulty, several methods have been reported to determine the cutoff wavelength of the BIF. A multimode reference technique, where transmission powers are measured with the SMF and the multimode fiber are compared to estimate the cutoff wavelength [15], however this measurement method is affected by ripples due to leaky modes. A far field MFD method has also been reported to determine the cutoff wavelength of optical fibers with improved bending insensitivity in [16] where the spectral variation of the far field MFD is measured at different transverse offsets, which is a very complex method to carry out. Recently a method to determine a reliable cutoff wavelength of the BIF by using the commercial SMF as the reference has been reported [17], which is very useful to determine the cutoff wavelength of the BIF operating in the standard 1550 nm wavelength band, however for the BIF operating below the cutoff wavelength of the commercial SMF, it is the same as the multimode reference technique.

In the current communication, we report a transverse splice loss technique to determine the cutoff wavelength of the BIF. It is a very simple experimental method because no repositioning of fibers is needed, thereby preventing launching errors while repositioning the fibers. It also does not need complex MFD measurements that makes it very simple to perform, and finally, it can be used to determine the cutoff wavelength of the BIF operating at any nonstandard wavelength. In the next section, we prove theoretically how the transverse splice loss technique can be used to determine the cutoff wavelength of the BIF. Then we explain the experimental part where fabrication of BIFs operating at visible and IR bands is described; thereafter our splice loss measurement technique is discussed, and finally we conclude by comparing the performance of this method with theoretical predictions and a bend reference technique.

2. Splice loss and cutoff wavelength

In a weakly guiding approximation, the scalar wave equation satisfied by the transverse component of electric field can be expressed as [13,18]:

\nabla^{2} Ψ = ε_{0} μ_{0} n^{2} \frac{\partial^{2} Ψ}{\partial t^{2}}

where ε₀ is the permittivity of free space, μ₀ is the permeability of free space, n is the refractive index and t represents time. By adopting the method of separation of variables and by considering n² dependence only on transverse coordinates (

r, φ

), we may write:

Ψ (r, φ, z, t) = R (r) Φ (φ) e^{i (ω t - β z)}

where ω is the angular frequency, β is the propagation constant, and z is a coordinate along the fiber length. Further assuming n² dependency only on r and substituting Eq. (2) in Eq. (1) gives:

\frac{d^{2} R}{d r^{2}} + \frac{1}{r} \frac{d R}{d r} + [k_{0}^{2} n^{2} (r) - β^{2} - \frac{l^{2}}{r^{2}}] R = 0

where l is the constant (an azimuthal mode number) expressed as

- \frac{1}{Φ} \frac{d^{2} Φ}{d φ^{2}} = l^{2}

The φ dependency is of the form $\cos (l φ)$ or $\sin (l φ)$ . Modes with l > = 1 are four fold degenerate, while with l = 0 are φ independent and have two fold degeneracy (two independent states of polarization). It is known that intensity profiles of transverse electric fields belonging to the same LP mode have same distribution.

Now we develop mode field equations for the trenched SMF with the index profile shown in Fig. 1 ; for the current discussion, we are considering the optical fiber with one trench.

Fig. 1 Refractive index profile of the bend insensitive fiber with a single trench (solid line) and two trenches (solid line + dotted line). Refractive index difference, Δn_i = n_i – n_clad.

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The mode field at different regions of the single trenched BIF can be expressed as [13,18]

R_{1} (r) = A_{0} J_{l} (p_{1} r) r \leq a

R_{2} (r) = A_{1} I_{l} (q_{2} r) + A_{2} K_{l} (q_{2} r) a < r \leq b

R_{3} (r) = A_{3} I_{l} (q_{3} r) + A_{4} K_{l} (q_{3} r) b < r \leq c

R_{4} (r) = A_{5} K_{l} (q_{4} r) r > c

where R_i is the mode field in the i^th region along the radius r, J is the Bessel function of first kind, I and K are modified Bessel functions, A_i are constants and p_i and q_i are defined as follows:

p_{i} = \sqrt{k_{0}^{2} n_{i}^{2} - β_{l}^{2}}; q_{i}^{2} = - p_{i}^{2}

where k₀ is a propagation constant in the free space ( = 2π/λ, in which λ is the operating wavelength), n_i is the refractive index of optical fiber in the i^th region, and β_l is the propagation constant of l^th mode in the optical fiber.

It is noted that Eq. (5) to Eq. (8) are valid for β_l/k₀ > n₄, which is the case of the BIF of Fig. 1 that is operating without any bend. To solve Eq. (5) to Eq. (8), we use boundary conditions at i^th and (i + 1)^th interfaces, i.e., R_i(r) = R_i₊₁(r), and dR_i(r)/dr = dR_i₊₁(r)/dr and use r = radial distance at the interface under consideration. A characteristic equation in the form of a determinant to find mode field values can be expressed as:

| \begin{array}{l} J_{l} (p_{1} a) - I_{l} (q_{2} a) - K_{l} (q_{2} a) 0 0 0 \\ 0 I_{l} (q_{2} b) K_{l} (q_{2} b) - I_{l} (q_{3} b) - K_{l} (q_{3} b) 0 \\ 0 0 0 I_{l} (q_{3} c) K_{l} (q_{3} c) - K_{l} (q_{4} c) \\ X_{1} - X_{2} - X_{3} 0 0 0 \\ 0 X_{4} X_{5} - X_{6} - X_{7} 0 \\ 0 0 0 X_{8} X_{9} - X_{10} \end{array} | = 0

where

\begin{array}{l} X_{1} = l J_{l} (p_{1} a) - (p_{1} a) J_{l + 1} (p_{1} a); X_{2} = l I_{l} (q_{2} a) + (q_{2} a) I_{l + 1} (q_{2} a) \\ X_{3} = l K_{l} (q_{2} a) - (q_{2} a) K_{l + 1} (q_{2} a); X_{4} = l I_{l} (q_{2} b) + (q_{2} b) I_{l + 1} (q_{2} b) \\ X_{5} = l K_{l} (q_{2} b) - (q_{2} b) K_{l + 1} (q_{2} b); X_{6} = l I_{l} (q_{3} b) + (q_{3} b) I_{l + 1} (q_{3} b) \\ X_{7} = l K_{l} (q_{3} b) - (q_{3} b) K_{l + 1} (q_{3} b); X_{8} = l I_{l} (q_{3} c) + (q_{3} c) I_{l + 1} (q_{3} c) \\ X_{9} = l K_{l} (q_{3} c) - (q_{3} c) K_{l + 1} (q_{3} c); X_{10} = l K_{l} (q_{4} c) - (q_{4} c) K_{l + 1} (q_{4} c) \end{array}

By solving the characteristic equation given in Eq. (10), the propagation constant can be determined for a given value of mode number l. After that, the mode field variation along the radius can be calculated by using Eq. (5) to Eq. (8) with A₀ = 1. Field propagating at any time and at any distance in the optical fiber can be expressed from Eq. (2) as:

{LP}_{01} : Ψ_{x, y} = R_{01} (r) e^{[i (ω t - β_{01 x, y} z)]}

{LP}_{11} : Ψ_{x, y} = R_{11} (r) e^{[i (ω t - β_{11 x, y} z)]} \cos (φ)

{LP}_{11} : Ψ_{x, y} = R_{11} (r) e^{[i (ω t - β_{11 x, y} z)]} \sin (φ)

where suffixes y and x are for y-polarization and x-polarization, respectively and R’s are defined in Eq. (5) to Eq. (8). Normalization of Eq. (12) to Eq. (14) can also be carried out to get unity power for each mode [19].

The fundamental mode field diameter of the optical fiber can be determined from Eq. (5) to Eq. (8) by using the relationship [20]:

M F D = 2 {(\frac{2 \int_{0}^{\infty} \int_{0}^{2 π} {[R (r) r]}^{2} r d r d φ}{\int_{0}^{\infty} \int_{0}^{2 π} {[R (r)]}^{2} r d r d φ})}^{1 / 2}

For instance, when a = 4 μm, b = 8 μm, c = 12 μm, ∆n₁ = 0.006, and ∆n_T₁ = −0.003, theoretical cutoff wavelength of LP₁₁ mode (with l = 1) is about 1.3 μm. The LP₀₁ mode field and the LP₁₁ mode field at wavelengths below, above and at the cutoff wavelength are shown in Fig. 2 .

Fig. 2 Radial distribution of mode fields in the trenched fiber (a = 4 μm, b = 8 μm, c = 12 μm, ∆n₁ = 0.006, and ∆n_T₁ = −0.003) at different wavelengths. The LP₁₁ cutoff wavelength = 1.3 μm.

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Power in the fiber (in the core and the cladding) at a particular mode can be expressed as [13]

P = C \int_{0}^{\infty} \int_{0}^{2 π} | Ψ (r, φ) |^{2} r d r d φ

For a two mode fiber, the LP₀₁ modal power and the LP₁₁ modal power can be written as [from Eq. (15)]:

P_{01} = C_{1} (2 π) \int_{0}^{\infty} | R |^{2} r d r

P_{11} = C_{2} π \int_{r = 0}^{\infty} | R |^{2} r d r

P_{t o t a l} = \sum_{l} P_{l 1}

where C₁ and C₂ are constants, which can be determined from known power. It is noted that, if we launch equal power (p(λ)) in all degenerate modes then the fiber supporting two modes (LP₀₁, LP₁₁) will have 6 p(λ) power and the fiber supporting only one mode (LP₀₁) will have 2 p(λ) power. Thus, moving from the two-mode propagation to the fundamental mode propagation in the optical fiber will cause the loss of around 4.77 dB.

With regards to the transverse splice loss between two identical optical fibers, the overlap integration between two modes (ψ₁(x,y) in Fiber-1 and ψ₂(x,y) in Fiber-2) after the transverse misalignment of u (a movement with respect to aligned axes and which is parallel to end faces) can be expressed in Cartesian co-ordinates as:

T = \frac{{| \int_{- \infty}^{+ \infty} \int_{- \infty}^{\infty} Ψ_{1} (x, y) Ψ_{2}^{*} (x - u, y) d x d y |}^{2}}{(\int_{- \infty}^{+ \infty} \int_{- \infty}^{\infty} Ψ_{1}^{2} (x, y) d x d y) (\int_{- \infty}^{+ \infty} \int_{- \infty}^{\infty} Ψ_{2}^{2} (x - u, y) d x d y)}

where

Ψ_{}^{*}

is the complex conjugate of modal field. The splice loss, α (in dB) between two fibers with the transverse offset of u is expressed by

α (dB) = - 10 \log_{10} [T]

Now, if we consider the transverse misalignment (u) between two fibers in x-direction, the fundamental LP₀₁ mode ( $Ψ_{1}$ ) and two x, y LP₁₁ modes ( $Ψ_{2}$ , $Ψ_{3}$ ) will give total nine possibilities of overlap integrations for the transverse offset of u [21]:

\begin{array}{l} T_{11} = e^{- u^{2} / w^{2}}, T_{12} = {(- \frac{u^{2}}{2 w^{2}})}^{2} e^{- u^{2} / w^{2}} / 2, T_{13} = 0 \\ T_{22} = {(1 - \frac{u^{2}}{w^{2}})}^{2} e^{- u^{2} / w^{2}}, T_{21} = {(\frac{u^{2}}{2 w^{2}})}^{2} e^{- u^{2} / w^{2}} / 2, T_{23} = 0 \\ T_{33} = e^{- u^{2} / w^{2}}, T_{31} = 0, T_{32} = 0 \end{array}

where T_ij is the overlap integration between

Ψ_{i}

and

Ψ_{j}

and w is the fundamental mode spot size ( = MFD/2). The transverse splice loss is then expressed by:

α (d B) = - 10 \log_{10} [A (T_{11} + T_{12} + T_{13}) + B (T_{21} + T_{22} + T_{23}) + C (T_{31} + T_{32} + T_{33})

where A, B and C are constants; for equal power in all modes, A = B = C = 1/3. It is noted that in Eq. (22), LP₀₁ and LP₁₁ modes have been approximated by a Gaussian function and a Hermite-Gauss function, respectively, which are accurate within a few percent of exact field profiles [21].

The MFD and the splice loss determined for the above fiber are shown in Fig. 3 for equal power distributed in all modes. It can be observed that at the vicinity of the cutoff wavelength, the transverse splice loss is the lowest and jumps to the high value when only LP₀₁ mode propagates in the fiber. Thus, it can be stated that the wavelength where we get the lowest splice loss is the cutoff wavelength. Now, we use this idea to determine the cutoff wavelength of experimental BIFs.

Fig. 3 Spectral variations of the fundamental MFD and the transverse splice loss in the trenched fiber (a = 4 μm, b = 8 μm, c = 12 μm, ∆n₁ = 0.006, and ∆n_T₁ = −0.003). The LP₁₁ cutoff wavelength ~1.3 μm.

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3. Experiments

To determine the relationship between the cutoff wavelength and the splice loss, we used various optical fibers as follows: (i) single mode optical fiber (SMF, Fiber-1) [22], (ii) two bend insensitive optical fibers developed in the laboratory (Fiber-2 and Fiber-3), and (iii) commercial bend insensitive optical fiber (Fiber-4) [11]. The SMF (Fiber-1) was the commercial single mode fiber with the MFD of about 9-10 μm. For the laboratory made BIFs (Fiber-2 and Fiber-3), two optical fiber preforms with germano-silicate glass composition were fabricated by using the MCVD technique. Low index trenches were formed by boron doping during the fabrication of performs. Optical fibers with outer diameter of 125 µm were drawn at 2000 °C using the draw tower. Optical parameters of these two fibers are listed in Table 1 . It is noted that Fiber-2 had one trench while Fiber-3 had two trenches in the cladding region surrounding the core. Lastly, Fiber-4 was the commercial BIF; it had a single trench its MFD of about 9.8 μm at 1550 nm and its bending loss was less than 0.5 dB/loop of 15 mm diameter at 1550 nm [11].

Table 1. Various BIF parameters.

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For the splice loss measurements, the two identical fiber facets were separated less than 5 μm and one of the fibers was moved transversely (parallel to the end face). A broadband light source emitting at 350 nm to 1750 nm was used as the input at one part of the fiber (length = 0.5 m) and the optical power obtained at the end of other part of the fiber (length = 0.5 m) was measured by using the optical spectrum analyzer. Care was taken to avoid cladding modes in the fiber by stripping the polymer coating (~1 cm) and using the index matching oil at both ends, and additionally, other portion of fibers were coated by the high index polymer to eliminate cladding modes. The splice loss was measured with reference to the perfectly aligned fibers (u = 0). Typical measurements of splice loss for the SMF (Fiber-1) are shown in Fig. 4 and a linear curve fit at the central points of the transition curve (indicating a transition from the multimode to the single mode regime) was used to obtain transition values of the splice loss as shown in Fig. 5 . Subsequent splice loss measurements for bend insensitive fibers, Fiber-2, Fiber-3 and Fiber-4 are shown in Fig. 6 , Fig. 7 and Fig. 8 , respectively.

Fig. 4 Typical measurements for spectral variations of the bending loss at 60 mm of loop diameter and the transverse splice loss for the SMF (Fiber-1). For the splice loss measurement, two fibers facets were separated less than 5 μm.

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Fig. 5 Estimation of the cutoff wavelength of SMF. Vertical lines were drawn by the linear fit to central points. The wavelength value shown in the figure indicates that a pure LP₀₁ mode will be sustained after 1226.3 nm.

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Fig. 6 Typical measurements for spectral variations of the bending loss at 10 mm of loop diameter and the transverse splice loss for the BIF (Fiber-2). The effective LP₁₁ cutoff wavelength was at 599.33 nm. The bending loss was about 0.47 dB at 633 nm for one loop of 10 mm of diameter.

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Fig. 7 Typical measurements for spectral variations of the bending loss at 10 mm of loop diameter and the transverse splice loss for the BIF (Fiber-3). The effective LP₁₁ cutoff wavelength was at 1140.4 nm. The bending loss was negligible at 1550 nm for one loop of 10 mm of diameter.

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Fig. 8 Typical measurements for spectral variations of the bending loss at 10 mm of loop diameter and the transverse splice loss for the BIF (Fiber-4). The effective LP₁₁ cutoff wavelength was at 1169.5 nm.

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The effective cutoff wavelength of the SMF was measured by a normal bend reference technique where a loop of 6 cm diameter was involved. However, the same method could not be used for BIFs because bending losses for BIFs were almost negligible at the standard loop diameter of 6 cm, (for instance, the bending loss of Fiber-2 was about 0.47 dB/loop of 10 mm diameter at 633 nm and that of Fiber-3 was about 0.01 dB/loop of 10 mm diameter at 1550 nm). Therefore, we used 10 loops of 10 mm diameter and determined the cutoff wavelength by considering the attenuation above 0.1 dB of the baseline after LP₁₁ mode attenuation peak. Bending loss measurements for Fiber-1, Fiber-2, Fiber-3 and Fiber-4 are shown in Fig. 4, Fig. 6, Fig. 7 and Fig. 8, respectively.

It is also worth mentioning that measurements for in-house made BIFs (Fiber-2 and Fiber-3) were somewhat noisy possibly due to increased absorption caused by the boron doping. In fact, the transmission loss of Fiber-2 and Fiber-3 was about 5 times more than that of the SMF.

4. Results and discussion

By adopting the procedure of measuring the splice loss as described in a Section 3, we obtained spectral variations of transverse splice loss characteristics of various optical fiber samples for different offsets as illustrated in Fig. 4 to Fig. 8. In the case of the single mode optical fiber where the mode field is loosely confined in the core region, small bending of 6 cm diameter causes the field to leak into the cladding. When scanned from low wavelength to high wavelength, the LP₁₁ mode field starts to suffer attenuation much before the cutoff wavelength due to spreading and leakage of the mode field and the pure single mode operation starts earlier than the cutoff wavelength; the wavelength where single mode starts before the theoretical cutoff is known as an effective cutoff wavelength. In contrast to this, increase in the spreading of the LP₁₁ mode decreases the splice loss as the operating wavelength approaches the LP₁₁ mode field cutoff wavelength. Because no bending is applied to leak the LP₁₁ mode field, the splice loss where it again reaches a high value nearly represents a pure single mode operation that is predicted by theory. We obtained the pure single mode regime for the SMF at about 1226.3 nm as illustrated in Fig. 5.

For the bend insensitive fiber, where the mode field (including the high order mode field) is strongly confined due to surrounding low index trench, bending actually does not cause the mode field to spread much to reduce the bending loss. But if forced to undergo leakage due to successive sharp bends, it also undergoes a similar action as described for the SMF to cause high bending loss at a much lower wavelength than the theoretical cutoff (See Fig. 6 to Fig. 8 and Table 2 ). It can be observed in Table 2 that mean splice loss measured for the BIF shows good match with the effective cutoff wavelength measured by using the bend reference technique. Only difficulty faced in this technique was the determination of transition points of minimum and maximum splice loss at the cutoff wavelength and it can be solved by a linear fit approach we adopted in Fig. 5.

Table 2. Comparison of estimated cutoff wavelengths by using different techniques.

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As we measured the transverse splice loss at various transverse offset values, it is worth mentioning the possible optimum value of the offset to determine the cutoff wavelength of BIF. As listed in Table 2, as the transverse offset is changed from 8 μm to 2 μm, the cutoff wavelength values match more and more with the cutoff wavelength determined by using the bending reference technique. For the offset of 2 μm and 4 μm, measured cutoff wavelengths were nearly same. If compared with the cutoff wavelength determined from the bending loss technique, it can be stated that the offset value of less than 4 μm can be conveniently used to determine the LP₁₁ cutoff wavelength.

5. Summary

We proposed a simple method to determine the cutoff wavelength of bend-insensitive fiber. The effective cutoff wavelength of the bend insensitive optical fiber obtained by the proposed transverse splice loss measurement showed very good match with that obtained by the bend reference technique. The method was proven very simple and can be adopted effectively to estimate the effective cutoff wavelength.

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, and by the GIST Top Brand Project (Photonics 2020), Ministry of Science and Technology.

References and links

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4. I. Sakabe, H. Ishikawa, H. Tanji, Y. Terasawa, M. Ito, and T. Ueda, “Enhanced bending loss insensitive fiber and new cables for CWDM access networks,” Proceeding of 53rd International Wire and Cable Symposium, Philadelphia, USA, November 14–17, 2004, 112–118, (2004).

5. K. Himeno, S. Matsuo, Ning Guan, and A. Wada, “Low bending loss single mode fibers for Fiber-to-the-Home,” J. Lightwave Technol. 23(11), 3494–3499 (2005). [CrossRef]

6. 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).

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

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9. P. R. Watekar, S. Ju, and W.-T. Han, “Near zero bending loss in a double-trenched bend insensitive optical fiber at 1550 nm,” Opt. Express 17(22), 20155–20166 (2009). [CrossRef] [PubMed]

10. P. R. Watekar, S. Ju, and W.-T. Han, “Design and development of a trenched optical fiber with ultra-low bending loss,” Opt. Express 17(12), 10350–10363 (2009). [CrossRef] [PubMed]

11. Draka BendBright Fiber data-sheets (2010). (http://communications.draka.com/sites/eu/Datasheets/SMF%20-%20BendBright-XS%20Single-Mode%20Optical%20Fiber.pdf)

12. ITU-T recommendation G.652.

13. A. Ghatak, and K. Thyagarajan, Introduction to Fiber Optics, Cambridge University Press, USA (1998).

14. D. Pagnoux, J.-M. Blondy, P. Roy, and P. Facq, “Cutoff wavelength and mode field radius determinations in monomode fibers by means of a new single measurement device,” Pure Appl. Opt. 6(5), 551–556 (1997). [CrossRef]

15. International Standard IEC 60793–1-42, 2007–04 (2007).

16. K. Nakajima, J. Zhou, K. Tajima, C. Fukai, K. Kurokawa, and I. Sankawa, “Cutoff wavelength measurement in a fiber with improved bending loss,” IEEE Photon. Technol. Lett. 16(8), 1918–1920 (2004). [CrossRef]

17. T. Nakanishi, M. Hirano, and T. Sasaki, “Proposal of reliable cutoff wavelength measurement for bend insensitive fiber,” Proceedings of European Conference on Optical Communications (ECOC), Vienna, Austria, Sept. 20–24, 2009, P1.14 (2009).

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22. Samsung single mode fiber data-sheets (2010).

	a (μm)	b (μm)	c (μm)	d (μm)	e (μm)	Δn₁	Δn_T₁	Δn_T₂
Fiber-2	2.95	7.9	11.3	–	–	0.0025	−0.007	–
Fiber-3	2.02	10.79	17.89	22.49	28.19	0.00484	−0.005	−0.0046

Cutoff wavelength estimation		Fiber-1 [22]	Fiber-2	Fiber-3	Fiber-4 [11]
Theoretical		<1240 nm**	630 nm	1205 nm	<1280**
Bending loss technique		1197.5 nm	599.3 nm	1140.4 nm	1169.5 nm
Splice loss technique [present]	Offset = 2 μm	1182.1 nm	601.7 nm	1143.6 nm	1169.9 nm
	Offset = 4 μm	1176.8 nm	598.1 nm	1144.2 nm	1168.6 nm
	Offset = 6 μm	1178.5 nm	595.9 nm	1151.4 nm	1165.5 nm
	Offset = 8 μm	1179.2 nm	594.8 nm	1155.3 nm	1163.7 nm
	Mean	1179.2 nm	597.6 nm	1148.6 nm	1166.9 nm

	a (μm)	b (μm)	c (μm)	d (μm)	e (μm)	Δn₁	Δn_T₁	Δn_T₂
Fiber-2	2.95	7.9	11.3	–	–	0.0025	−0.007	–
Fiber-3	2.02	10.79	17.89	22.49	28.19	0.00484	−0.005	−0.0046

Cutoff wavelength estimation		Fiber-1 [22]	Fiber-2	Fiber-3	Fiber-4 [11]
Theoretical		<1240 nm**	630 nm	1205 nm	<1280**
Bending loss technique		1197.5 nm	599.3 nm	1140.4 nm	1169.5 nm
Splice loss technique [present]	Offset = 2 μm	1182.1 nm	601.7 nm	1143.6 nm	1169.9 nm
	Offset = 4 μm	1176.8 nm	598.1 nm	1144.2 nm	1168.6 nm
	Offset = 6 μm	1178.5 nm	595.9 nm	1151.4 nm	1165.5 nm
	Offset = 8 μm	1179.2 nm	594.8 nm	1155.3 nm	1163.7 nm
	Mean	1179.2 nm	597.6 nm	1148.6 nm	1166.9 nm

A simple and reliable method to determine LP₁₁ cutoff wavelength of bend insensitive fiber

Abstract

1. Introduction

2. Splice loss and cutoff wavelength

3. Experiments

4. Results and discussion

5. Summary

Acknowledgments

References and links

Cited By

Figures (8)

Tables (2)

Equations (23)

Optics Express