Page 180 - Introduction to Information Optics

3.2. Light Propagation in Optical Fibers 165

Cladding n 2

Core n 1 Jacket

Fig. 3.1. Basic structure of optical fiber.

ensure light propagation in the fiber, the core must have a refractive index
larger than that of the cladding so that the total internal reflection can happen.
Let us look at a simple step index fiber, as shown in Fig. 3.2, where the core
has a refractive index n t, the cladding has a refractive index n 2, the outside has
a refractive index n 0, the incident angle from the outside to the fiber is $,, the
refractive angle of 0,- is d r, and the internal incident angle from the core to the
cladding is (f). Assume that the light is coupled into the fiber at point A and
reaches to the intersection point between the core and the cladding at point B.
The minimum angle that can result in total internal reflection at point B, $ c, is

(3.2)

In this critical angle case, the incident angle 0,, denoted as 0 fc, can be described
in terms of n v and n 2 from the following geometric relationship (as shown in
Fig. 3.2),

+ 0, (3.3)

Fig. 3. 2. Basic principle of light propagation in optical fiber: total internal reflection.