Page 33 - Fiber Optic Communications Fund

14 Fiber Optic Communications

A rect (t/T 0 ) A 0 rect (t/T 0 – 0.33E-8 s/T 0 )
0

1 ns t
z/c = 0.33E-8 s
At flash light At screen

Figure 1.11 The electric field envelopes at the flash light and at the screen.

where {
1, if |x| < 1∕2
rect(x)= (1.80)
0, otherwise
8
and T = 1 ms. The speed of light in free space = c ≃ 3 × 10 m/s. Therefore, it takes 0.33 × 10 −8 s to get
0
the light pulse on the screen. At z = 1 m (see Fig. 1.11),
( )
( z ) t − 0.33 × 10 −8
E (t, z)= f t − = A rect . (1.81)
x 0
T
0
Example 1.2
A laser shown in Fig. 1.12 operates at 191 THz. Under ideal conditions and ignoring transverse distributions,
the laser output may be written as
E (t, 0)= f(t)= A cos (2f t), (1.82)
x 0 0
where f = 191 THz. The laser output arrives at the screen after 0.33 × 10 −8 s (see Fig. 1.12). The electric
0
field intensity at the screen may be written as
( z )
E (t, z)= f t −
x

[ ( z )]
= A cos 2f 0 t −

−8
= A cos [2f (t − 0.33 × 10 )]. (1.83)
0
Screen

Laser

1 m

Figure 1.12 The propagation of laser output in free space.