Page 283 - Fiber Optic Communications Fund

264 Fiber Optic Communications

6.6.1 Cavity-Type Semiconductor Optical Amplifiers
Let the power reflectivities of mirrors M and M , shown in Fig. 6.8, be R and R , respectively. Assuming
2
1
2
1
that the power is conserved at each mirror, the corresponding power transmittivities at mirror M are given by
j
T = 1 − R , j = 1, 2. (6.111)
j
j
√ √
The optical field transmitted at A is t , where = P and |t | = T , j = 1, 2. Let g be the gain
in
1 in
in
j
j
coefficient and int be the cavity internal loss. The net gain coefficient is g =Γg − , where Γ is the overlap
int
s
factor introduced in Eq. (3.109). As shown in Fig. 6.9, the partial optical field at B after a single pass is
0
√
= t t G exp(i ), (6.112)
0 in 1 2 s 0
where = 2nL∕ is the phase-shift due to propagation, n is the refractive index of the gain medium, and
0
is the free-space wavelength. In the small-signal limit, the single-pass gain is
G = exp(g L). (6.113)
s s
A fraction of the optical field is reflected at the mirror M and then at M . After one round trip, the partial
2
1
field at B is (see Fig. 6.9)
√ 3
= t r r t [ G exp(i )] , (6.114)
1 in 1 2 1 2 s 0
L
M 1 M 2
ψ in A B ψ out
Gain medium
R 1 R 2
Figure 6.8 Cavity-type semiconductor optical amplifier.

A B A B B
ψ in
t 1 G s e iφ 0 r 2 G s e iφ 0 r 1 G s e iφ 0 r 2 … ... G s e iφ 0 r 2

t 2 t 2 t 2
… ... … ...
ψ 0 ψ 1 ψ n

∑

ψ out
Figure 6.9 The optical signal output of the amplifier is the sum of the partial fields due to repeated reflections.