Page 1

Design of a trenched bend insensitive single

mode optical fiber using spot size definitions

Pramod R. Watekar1, Seongmin Ju1, Young Sik Yoon2, Yeong Seop Lee2 and

Won-Taek Han1,3

1Department of Information and Communications, 3School of Photon Science and Technology

Gwangju Institute of Science and Technology (GIST), 1 Oryong-dong, Buk-gu, Gwangju 500-712, South Korea

2Samsung Electronics Hainan Fiberoptics-Korea Co. Ltd.

#94-1, Imsoo-Dong, Gumi, Gyeong-Buk, Seoul 730-350, South Korea.

wthan@gist.ac.kr

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

OCIS codes: (060.2310) Fiber optics, (060.2330) Fiber optics communication.

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).

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).

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).

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).

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).

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

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Received 6 Jun 2008; revised 3 Aug 2008; accepted 5 Aug 2008; published 19 Aug 2008

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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.

Table 1. Typical optical parameters of the SMF under consideration in the current communication.

Core diameter =

8.18 µm

Core-cladding

refractive index

difference =

0.00467

Bending loss (32

mm bend

diameter) = 9778

dB/km

at 1550 nm

Cutoff wavelength

= 1246 nm

MFD = 9.1 µm

at 1310 nm

MFD = 10.3 µm

at 1550 nm

Bending loss (10

mm bend

diameter) = 1.3

×106 dB/km

at 1550 nm

Zero dispersion

Wavelength*

= 1316.5 nm

Dispersion slope

=0.083

ps/(km.nm2)

Dispersion at:

1310 nm = 1.16

(ps/km.nm)

1550 nm = 15.94

(ps/km.nm)

1625 nm = 21.44

(ps/km.nm)

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

(MFDeff), which is defined as [8, 9]

(

∫

eff

MFD

22

)

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

∫

r

r

rdrErdrE

4

2

2

/

ππ

(1)

where E is the mode field, which can be computed from its evolution in the optical fiber using

a scalar wave equation [8, 9]:

E

r

L

Ernk

dr

dE

r

dr

E

2

d

2

2

222

0

2

))((

1

+−+=β

(2)

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1 September 2008 / Vol. 16, No. 18 / OPTICS EXPRESS 13546

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where E is an electric field along a radius r, k0 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.

-60-40-20020 40 60

-0.004

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

Δntrench

Δncore

c

b

Δn

Radial distance (μm)

2a

Fig. 1. Refractive index profile of the trenched SMF.

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

)(

2

min0 max

nnkn

MFD

eff−

=

∞

π

λ

(3)

where nmax and nmin are maximum and minimum values of the refractive index, neff (=

0

/k

β

λ

)

is an effective refractive index, λ is a wavelength of operation and

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

π /2

0=

k

. A

∫

0

∫

0

∞∞

⎥

⎦

⎤

⎢

⎣

⎡

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

Δ

V

c

−

=

2

0

2

0

2

3

3

8

/)1 (

3

4

exp

1610log

10

rdrFrdrFg

R

WR

W

b

RR

V

b

ce

macro

π

α

(4)

where F0 is a radial field of fundamental mode, Rc denotes the fiber core radius, Rb is a bend

radius and other parameters appearing in Eq. (4) are given by:

2

min

2

max

n

2

min

2)(

n

nrn

g

−

−

=

;

2

min

2

max0

nnrkV

c

−=

;

2

min0

2

)( nkrW

c

−=β

;

2

max

2

min

2

max

n

2n

n

−

=Δ

(5)

The Petermann-3 spot size (

∞

MFD ) is directly related to the bending loss. Earlier in the

MFDMFD /

∞

case of dispersion shifted fibers, the MFD ratio (

splicing and bending losses [7]. For the BI-SMF (if MFDs are determined using Eq. (1) and

Eq. (3)), when

∞

MFD <

eff

MFD

, the bending loss reduces as the MFD ratio approaches 1

and when

∞

MFD >

eff

MFD

, the bending loss reduces as the MFD ratio increases beyond 1.

eff

) was used to optimize

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Therefore, one has to optimize the MFD ratio carefully considering

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 (b), the trench width (c) and the trench

index (∆nTrench). To understand relationships among different trench parameters, the MFD

ratio and the bending loss, bending losses with respect to b, c and ∆nTrench are shown in Figs.

2(a), 2(b) and 2(c), respectively at typical dimensions shown in figures (where

MFD <

eff

MFD

). In Fig. 2(a), it is noted that there exists minimum bending loss at an

optimum value of b and increasing b far beyond the optimum value does not produce any

significant change in the bending loss. For c and ∆nTrench, the bending loss decreases with

increase in the MFD ratio (Figs. 2(b) and 2(c)).

∞

MFD and

eff

MFD

∞

02468 1012 14 16

0.0016

0.0018

0.0020

0.0022

0.0024

0.0026

0.0028

b (μm )

Bending loss (dB/turn)

c=8.18 μm

ΔnTrench= -0.004

0.75

0.78

0.81

0.84

0.87

MFD ratio

02468 10 12 14 16 18 20 22

c (μm)

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0.0022

0.0024

b=4.09 μm

ΔnTrench= -0.004

MFD ratio

Bending loss (dB/turn)

0.784

0.786

0.788

0.790

0.792

0.794

0.796

(a) (b)

-0.004 -0.003 -0.002

ΔnTrench

-0.001 0.000

-10

0

10

20

30

40

50

60

70

Bending loss (dB/turn)

b=4.09 μm

c=8.18 μm

0.762

0.768

0.774

0.780

0.786

0.792

0.798

MFD ratio

(c)

Fig. 2. Effect of variations of design parameters of the trenched SMF on bending loss.

To design the BI-SMF, initially we fixed the design criteria so as to follow ITU-T

recommendations at 1550 nm: MFDeff >= 9.6 µm, dispersion <=18.5 ps/km.nm and dispersion

slope <= 0.095 ps/km.nm2; 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<=4a, c<=4a and ∆nTrench >= -0.004. The

scalar wave equation of the optical fiber was solved at each set of b, c and ∆nTrench 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.

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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 ∆nTrench 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=1.1a, c=4a

and ∆nTrench = -0.003 from the figure, where a is the core radius.

1.062 1.0651.068

MFD ratio

1.0711.0741.077

0

2

4

6

8

10

ΔnTrench= -0.001

b/a

Minimum bending loss (dB/turn)

c/a

b/a

c/a

1.0

1.1

1.2

1.3

1.4

1.5

Bending loss

0.984 0.9870.990

MFD ratio

0.9930.9960.999

0

1

2

3

4

5

ΔnTrench= -0.0015

b/a

Minimum bending loss (dB/turn)

c/a

b/a

c/a

1.0

1.1

1.2

1.3

1.4

1.5

Bending loss

(a) (b)

0.9210.9240.9270.9300.933

0

1

2

3

4

5

ΔnTrench= -0.002

b/a

MFD ratio

Minimum bending loss (dB/turn)

c/a

b/a

c/a

1.1

1.2

1.3

1.4

Bending loss

0.8250.828 0.8310.8340.837

0

1

2

3

4

5

x50

ΔnTrench= -0.003

b/a

MFD ratio

Minimum bending loss (dB/turn)

c/a

b/a

c/a

1.1

1.2

1.3

1.4

Bending loss

(c) (d)

0.7770.7800.783

MFD ratio

0.786 0.7890.792

0

1

2

3

4

5

x500

ΔnTrench= -0.004

b/a

Minimum bending loss (dB/turn)

c/a

b/a

c/a

1.1

1.2

1.3

1.4

Bending loss

(e)

Fig. 3. (a). to 3. (e). Optimized design parameters of the BI-SMF. (Wavelength = 1550 nm,

bending radius = 5 mm). x50 and x500 in the figures indicate that original bending loss values

have been multiplied by 50 and 500 times, respectively.

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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.

Table 2. Optical parameters of the typical BI-SMF.

At 1550 nm: Dispersion = 18.48 ps/km.nm, MFDeff=10µm

Zero dispersion: Wavelength = 1302 nm, Slope = 0.085 ps/km.nm2

Bending loss = 0.043 dB/turn at 1550 nm for 5 mm of bending radius

-10

0

10

20

30

40

1200 1300 1400 1500 1600 1700 1800

Wavelength (nm)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Bending loss

Dispersion

Dispersion (ps/km.nm)

MFDeff (μm)

MFDeff

Bending loss (dB/turn)

Dispersion slope (ps/km.nm2)

x10

Dispersion

slope

Fig. 4. Spectral variations of the dispersion, the MFDeff and the bending loss of the single

trenched BI-SMF (b=1.1a, c=4a and ∆nTrench = -0.003). ‘x10’ in the figure indicates that

original dispersion slope values have been multiplied by 10 times.

120013001400

Wavelength (nm)

15001600 17001800

-10

0

10

20

30

40

x10

Bending loss

Bending lossBending loss Bending loss

Dispersion

Dispersion (ps/km.nm)

MFDeff (μm)

MFDeff

Dispersion slope

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Bending loss (dB/turn)

Dispersion slope (ps/km.nm2)

Fig. 5. Spectral variations of the MFDeff, the dispersion and the bending loss of the double

trenched BI-SMF (b=1.1a, c=4a and ∆nTrench = -0.003. Additional trench: separation=1.1a,

width=4a and refractive index difference = -0.003). ‘x10’ in the figure indicates that original

dispersion slope values have been multiplied by 10 times.

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

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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.

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