Biophotonics_Concepts_to_Applications

the relative spot size w 0 /a, with an accuracy better than 1 % for a SMF, is given by
[ 6 ]

w 0

a

¼ 0 : 65 þ 1 :619V^3 =^2 þ 2 :879V^6 ð 3 : 9 Þ

SMFs typically are designed with V > 2.0 to prevent high cladding losses but
somewhat less than 2.4 to ensure that only one mode propagates in thefiber.

Example 3.7Suppose a certain single-mode step-index fiber has an

MFD = 11.2μm and V = 2.25. What is the core diameter of thisfiber?

Solution: From Eq. (3.7)w 0 = MFD/2 = 5.6μm. Using Eq. (3.9) then yields

a¼w 0 = 0 : 65 þ 1 :619V^3 =^2 þ 2 :879V^6



¼

5 : 6 lm

0 : 65 þ 1 : 619 ð 2 : 25 Þ^3 =^2 þ 2 : 879 ð 2 : 25 Þ^6

¼

5 : 6 lm

1 : 152

¼ 4 : 86 lm

Thus the core diameter is 2a= 9.72μm.

3.2 Graded-Index Optical Fibers

3.2.1 Core Index Structure

As Fig.3.2illustrates, in a graded-indexfiber the core refractive index decreases
continuously with increasing radial distance r from the center of thefiber but is
generally constant in the cladding [ 5 ]. The most commonly used construction for
the refractive-index variation in the core is the power law relationship

nðrÞ¼n 1 1  2 D

r

a

hia 1 = 2

for 0ra

¼n 1 ðÞ 1  2 D^1 =^2 n 1 ðÞ¼ 1 D n 2 for ra

ð 3 : 10 Þ

Here, r is the radial distance from thefiber axis,ais the core radius, n 1 is the
refractive index at the core axis, n 2 is the refractive index of the cladding, and the
dimensionless parameterαdefines the shape of the index profile. The index dif-
ferenceΔfor the graded-indexfiber is given by [ 5 ]

64 3 Optical Fibers for Biophotonics Applications