Page 188 - Introduction to Information Optics

3.2. Light Propagation in Optical Fibers I '3

n = f}/k 0 is defined as the effective refractive index of the fiber for a light
field with propagation constant /?. From Eq. (3.31), it can be seen that
this refractive index is larger than the cladding refractive index n 2 and
smaller than the core refractive index n l.
4. For a given m, we may get a set of solutions for /?, denoted by n
(n — 1,2,3,...). Thus, we may get many possible propagation constants
f$ mn corresponding to different m and n. Since m and n are integers, ft mn
are discrete numbers. Each /? mn corresponds to one possible propagation
mode. For example, /i ()l represents one mode and /?, j represents another
mode.
5. To find out the number of modes that propagate in the fiber, first iet us
define an important parameter — normalized frequency, K
2
V = vOy 2 )^ = X = k 0a v'« = k 0a • NA.
(3.32)

There is only one solution of /? in Eq. (3.29) when V < 2.405. In other words,
there is only one possible propagation mode in the fiber in this case. This
is the so-called single mode fiber case. Since there is only one mode
propagating in the fiber, there is no intermodal dispersion in this type of
fiber, so that much higher bandwidth can be achieved in a single mode
fiber for long-haul communications. When V is larger, it can also be
shown that the number of modes existing in the fiber is about

(3.33)

This corresponds to the multimode fiber case.

Example 3.4. Compute the number of modes for a fiber the core diameter of
which is 50jum. Assume that n } — 1.48, n 2 = 1-46, and operating wavelength
A - 0.82 urn.
Solve:

27i • 50 /iw/2 2 2
ii = ^^^ N/1.48 -1.46 = 46.45.
"O82^m~
2
Since V » 1, we can use the approximation formular N — V /2 to calculate the
number of modes in the fiber.