Biophotonics_Concepts_to_Applications

In this case, approximately 5 % of the optical power propagates in the

cladding. IfΔis decreased to 0.03 in order to lower the signal dispersion

effects, then there are 242 modes in thefiber and about 9 % of the power

propagates in the cladding.

3.1.3 Mode Field Diameter

The geometric distribution of optical power in the fundamental mode in a SMF is
needed when predicting performance characteristics such as splice loss between
twofibers, bending loss, and cutoff wavelength. The parameter describing this
optical power distribution is themodefield diameter(MFD), which is analogous to
the core diameter in a MMF. The MFD is a function of the optical wavelength, the
fiber core radius, and the refractive index profile of thefiber.
A standard method tofind the MFD is to measure the far-field intensity distri-
bution E^2 (r) at thefiber output and then calculate the MFD using the equation [ 6 ]

MFD¼2w 0 ¼ 2

2

R^1

0

E^2 ðrÞr^3 dr

R^1

0

E^2 ðrÞrdr

2

6

6

6

4

3

7

7

7

5

1 = 2

ð 3 : 7 Þ

where the parameter 2w 0 (with w 0 being called thespot sizeor themodefield
radius) is the full width of the far-field distribution. For calculation simplicity for
values of V lying between 1.8 and 2.4 thefield distribution can be estimated by a
Gaussian function [ 6 ]

E(r)¼E 0 expr^2 =w^20



ð 3 : 8 Þ

where r is the radius and E 0 is the electricfield at zero radius, as shown in Fig.3.5.
Then the MFD is given by the 1/e^2 width of the optical power. An approximation to

Fiber

core

Fiber

cladding

Fiber

cladding

r

E(r)

Fig. 3.5 Distribution of light
in a single-modefiber above
its cutoff wavelength; for a
Gaussian distribution the
MFD is given by the 1/e^2
width of the optical power

3.1 Light Guiding Principles in Conventional Optical Fibers 63

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