Page 189 - Introduction to Information Optics

174 3. Communication with Optics

Thus, there are over a thousand modes propagating in the common multimode
fiber.
Example 3.5. What is the maximum core radius allowed for a glass liber
having /i t = 1.465 and n 2 = 1.46 if the fiber is to support only one mode at a
wavelength of 1250 nm?
Solve: The single mode operating condition is V — 2nal/.(^/n\ — n\ < 2.405).
Thus, the maximum radius, a max , is
2.405-1 2.405 x 1.25 pm
/, = _ , __ — _ , _ , ___ — . ,. /.,.. __ = 3 96 //m
*"*rn'*Y ^^ r ---- ~ - f / — ™ -- ' 2 --- ' ------ : — - »J • s \J £/tJ.iJ«
2
~ n\ 2n^ \A65 - 1.46
This result tells us that the radius of a single mode fiber is very small.

Example 3.6. An optical fiber has a radius a = 2/mi, n 2 = 1.45, relative refrac-
tive index difference A = 0.01, and operating wavelength A= 1.288 jum. Calculate
the propagating constant, /?, and effective refractive index of the fiber, n.
Solve: Based on the definition of relative refractive index difference A =
(M[ — n 2)/n 1, we get

n L4S

The wave number

2n 2n
= 4.878
A 1.288/im

The normalized frequency

2n • 2 /im 2 2
n\ ^^^-^-JlM46 - 1.45 = 2.016 < 2.405.
1.288jum

Thus, there is only one mode propagating in the fiber. This is the single mode
fiber case. The propagating constant /? can be found by solving Eq. (3.29); i.e.,

l a)

Our fiber is a single mode fiber, which has only a fundamental mode