Biophotonics_Concepts_to_Applications

second movablefiber that is located an axial distancesfrom thefixedfiber [ 3 ]. The
secondfiber can move axially due to a variation in an external parameter, thus
changing the distancesbetween the twofiber ends. If there is an increase in the
distances, then less light will enter the secondfiber and vice versa. The optical
power variation at the photodetector thus can be used to measure the change in an
external parameter.
When light is coupled from one optical fiber to another, not all of the
higher-mode optical power emitted in the ring of width x shown in Fig.7.10will be
intercepted by the receivingfiber. The fraction of optical power coupled into the
receivingfiber is given by the ratio of the cross-sectional area of the receivingfiber
(πr^2 ) to the areaπ(a+x)^2 over which the emitted power is distributed at a distance
s. From Figs.7.10and7.15it follows that x = s tanθA, whereθAis the acceptance
angle of thefibers, as defined in Eq. (2.2). From this ratio the loss in dB for an
offset joint between two identical step-indexfibers is found to be [ 28 ]

Lgap¼10 log

a

aþx

 2

¼10 log

a

aþs tanhA

 2

¼10 log 1þ

s

a

sin^1

NA

n

 2

ð 7 : 3 Þ

whereais thefiber radius, NA is the numerical aperture of thefiber, and n is the
refractive index of the material between thefiber ends (usually either air or an index
matching gel).

Example 7.7 Suppose two identical step-indexfibers each have a 25-μm

core radius and an acceptance angle of 14°. Assume the twofibers are per-

fectly aligned axially and angularly. What is the variation in the insertion loss

when the longitudinal separation changes from 0.020 to 0.025 mm?

Solution:The insertion loss due to a gap betweenfibers can be found by

using Eq. (7.3).

Pressure-induced

fiber movement

Cladding

Cladding

Core

Fixed fiber Separation s

Captured area of

emitted light

Cladding

Cladding

Core

Movable fiber

Incident

light

Fig. 7.15 Simple opticalfiber-based pressure sensor based on using a moving acceptorfiber
(J. Biomed. Opt. 19(8), 080902 (Aug 28, 2014). doi:10.1117/1.JBO.19.8.080902)

212 7 Optical Probes and Biosensors