Fibre-Optic Communications.pdf

18
Fiber-Optic Communications
We again define the numerical aperture as with step-index fibers. However, n1 is
the core index only on the axis. Since the numerical aperture decreases the further
away from the axis we move, with equal conditions approximately half as much
power is coupled as in a step-index fiber.
The cladding does not occur in guiding itself, but plays an important spatial
filtering role by eliminating the most tilted rays.
Several “all silica” graded-index (GI) fiber standards have been normalized for
short distance telecommunications applications (50/125 fiber, now used for high
bandwidth local area networks), local computer networks (62.5/125) and first
generation video distribution (85/125, still not widely in use). Graded-index plastic
fibers appear for the Gigabit Ethernet.
1.4. Propagation in multimode optical fibers
1.4.1. Ray paths
Figure 1.9 and 1.10 diagrams only represent meridional rays, remaining in a
plane containing the optical fiber axis. In order to calculate all paths, we must switch
to 3 dimensions. Due to the symmetry of revolution of the optical fiber, we use
cylindrical coordinates (see Figure 1.11), by noting as:
– r, z, ψ coordinates from the path’s current point, P;
– u r, u z, u ψ local trihedral.
We must solve the ray equation:
d
ds
⎛ ⎞
⎜n.
dOP
⎟
⎝ ds ⎠
= grad n, with dOP ds
This vector has for components:
– over u r: dr/ds = sinθ cosφ;
– over u r: dz/ds = cosθ;
– over u ψ: r. dψ/ds = sinθ sinφ.
unitary vector tangent to the path
The resolution of this equation will result in the following wave vector:
k
= k0 n(P) dOP ds