Biophotonics_Concepts_to_Applications

where the parameter m≥0 designates the number of rings. Given that the diameter
of an individualfiber is Dfiber, then the outer diameter of thefiber bundle Dbundleis
given by

Dbundle¼Dfiberð 1 þ2mÞð 7 : 2 Þ

The active end face area of the bundle depends on the core and cladding sizes.
Larger core diameters and thinner claddings result in smaller dead spaces between
fibers and thus give larger active areas.

Example 7.3Consider an opticalfiber that has a 100-μm core diameter and a

125-μm cladding diameter. (a) Find the number offibers in bundles that have

one and two rings. (b) What is the outer diameter of the bundle in each case?

Solution:(a) From Eq. (7.1) the number of opticalfibers Nhexthat can be

packaged hexagonally in a single ring (m = 1) around a centralfiber is

Nhex¼ 1 þ 6 ¼ 7

Similarly, for two rings offibers

Nhex¼ 1 þ

X^2

n¼ 0

6n¼ 1 þ 6 þ 12 ¼ 19

(b) From Eq. (7.2) for one ring offibers (m = 1) the outer diameter of the

fiber bundle Dbundleis given by

Dbundle¼Dfiberð 1 þ 2 Þ¼ 3 ð 125 lmÞ¼ 375 lm

Similarly, for two rings offibers (m = 2)

Dbundle¼Dfiberð 1 þ 2  2 Þ¼ 5 ð 125 lmÞ¼ 625 lm

Example 7.4Consider an opticalfiber that has a 100-μm core diameter and a

125-μm cladding diameter. (a) Find the size of the active area in a bundle

with one ring. (b) What is the ratio of the active area to the total cross

sectional area of the bundle?

Solution:(a) Sevenfibers can be packaged hexagonally in a single ring

around a centralfiber. Therefore the active area of this bundle is

7 fiber-core area¼ 7 pð 50 lmÞ^2 ¼ 5 : 50  104 lm^2 ¼ 0 :055 mm^2

7.2 Optical Fiber Probe Configurations 205