Biophotonics_Concepts_to_Applications

dental diseases, and intracavity or superficial tumors in arteries or veins, in the
esophagus, in gastrointestinal tracts, in urinary tracts, or in bronchi in the lungs.
As an alternative to using an angle-polishedfiber tip, aflat-polished tip can be
used in conjunction with a micro-optic 45° prism. An example of this configuration
used within a needle probe is described in Chap. 11.

Example 7.6 Consider an opticalfiber that has a core refractive index

n 1 = 1.450 at a wavelengthλ= 680 nm. At what angle should the end face

be polished in order to have 680-nm light rays that are traveling parallel to the

fiber axis be reflected sideways at thefiber end?

Solution:The end face must be oriented at angle that causes total reflection of

the rays at a glass-air interface. Ifφcis the angle between the incident ray and

the normal to thefiber end face as shown in Fig.7.11b, then from Eq. (3.1)

this angle is given byφc= sin−^1 (n 2 /n 1 ). Here n 2 = 1.000 is the refractive

index of air and n 1 = 1.450 is the refractive index of glass at 680 nm. Thus,

from Eq. (3.2) the critical angleθc=π/2−φcat which the end face should be

polished is

hc¼p= 2 sin^1 ðÞ¼ 10 : 000 = 1 : 450 90  43 : 6 ¼ 46 : 4 

Probe designs with two or morefibers can be used to increase the light illu-
mination or collection efficiency. Figure7.12shows a probe design that is based on
using twofibers that haveflat-polished end faces. In this specific configuration, one
fiber is used for illumination and the otherfiber is used for light collection.

Critical

angle c

Illumination

area

Optical

fiber core

(a)

Fiber end face

Incident ray

Reflected ray

Normal to the

fiber end face

c

c

(b)

Fig. 7.11 Polishing the end face at the critical angle creates a side-firingfiber

208 7 Optical Probes and Biosensors