24 CHAPTER 2. OPTICAL FIBERS
Figure 2.1: Cross section and refractive-index profile for step-index and graded-index fibers.properties of optical fibers can be gained by using a ray picture based on geometrical
optics [22]. The geometrical-optics description, although approximate, is valid when
the core radiusais much larger than the light wavelengthλ. When the two become
comparable, it is necessary to use the wave-propagation theory of Section 2.2.
2.1.1 Step-Index Fibers
Consider the geometry of Fig. 2.2, where a ray making an angleθiwith the fiber axis
is incident at the core center. Because of refraction at the fiber–air interface, the ray
bends toward the normal. The angleθrof the refracted ray is given by [22]
n 0 sinθi=n 1 sinθr, (2.1.1)wheren 1 andn 0 are the refractive indices of the fiber core and air, respectively. The re-
fracted ray hits the core–cladding interface and is refracted again. However, refraction
is possible only for an angle of incidenceφsuch that sinφ<n 2 /n 1. For angles larger
than acritical angleφc, defined by [22]
sinφc=n 2 /n 1 , (2.1.2)wheren 2 is the cladding index, the ray experiences total internal reflection at the core–
cladding interface. Since such reflections occur throughout the fiber length, all rays
withφ>φcremain confined to the fiber core. This is the basic mechanism behind light
confinement in optical fibers.