Page 198 - Introduction to Information Optics

3.2. Light Propagation in Optical Fibers ! 83

3,2.3.4.2. Waveguide Dispersion for Single Mode Fiber
Besides material dispersion, we also have waveguide dispersion. Waveguide
dispersion comes from the fact that the propagation constant /? depends on
normalized frequency V that depends on / even when n(A] is a constant. The
waveguide dispersion, D w, can be written as

where
A — (n l ~ n 2)/n 2,
\ _ n
~ (normalized propagation constant),

2
0.08 + 0.549-(2.834 - V} .

Example 3.9. For a single mode step index fiber, we have n v — 1.4508,
1.446918, a = 4.1 n™, A = 1560nm, A/ = 1 nm, and L - 1 km.
Solve:

Step 1: Calculate the normalized frequency

K = ^! V /«F:^= 1.751.

Step 2: Calculate

2
y—j-^- « 0.08 + 0.549-(2.834 - V} = 0.724.
Step 3: Calculate

L

The total dispersion for the single mode fiber is the summation of material and
waveguide dispersions. Figure 3.10 shows the total dispersion as a function of
operating wavelength for the standard silica fiber under the conditions of
A/I = 1 nm and L = 1 km. For the pure silica single mode fiber, the dispersion
is on the order of tens of ps/nm-km, which is much smaller than that of
multimode fiber (tens of ns/nm-km). When A as 1.31 /mi, we have zero disper-