Page 441 - Fiber Optic Communications Fund

422 Fiber Optic Communications

Area A

dx

Figure 10.2 A slice of atomic system consisting of N atoms per unit volume.

If we define P = Np as the polarization, Eq. (10.18) can be written as

dP
J = . (10.19)
dt
From Eq. (10.11), it follows that
Nq 2 e
P = 2 E. (10.20)
2
m( − )
0
Polarization is directly proportional to electric field intensity, and is often written as
(1)
P = E, (10.21)
0
where (1) is known as the first-order susceptibilty or linear susceptibility. Comparing Eqs. (10.20) and
0
(10.21), we find
Nq 2
(1) e
= . (10.22)
2
2
m( − )
0 0
Substituting Eq. (10.19) in Eq. (10.12), we find
( E + P)
0
∇× H = . (10.23)
t
If we define the electric flux density D as
D = E + P, (10.24)
0
Eq. (10.23) becomes
D
∇× H = , (10.25)
t
which is the same as Maxwell’s equation in a medium (Eq. (1.51)) in the absence of current source. In fact,
the induced current and charge due to applied electromagnetic field are taken into account by using electric