444
11 Basics of Optical Amplifiers
N ph =
1 × 10
−6 W
2 × 10
8 m/s
(6.626×10
−34 J·s)(3×10
8 m/s)
(1.55×10
−6 m)
(5 μm)(0.5 μm)
= 1.56 × 10
6 photons/m
3
Example 11.2 Consider the following parameters for a 1300-nm InGaAsP SOA:
Symbol
Parameter
Value
w
Active area width
3 μm
d
Active area thickness
0.3 μm
L
Amplifier length
500 μm
Γ
Confinement factor
0.3
τ r
Time constant
1 ns
a
Gain coefficient
2 × 10 –20 m 2
n th
Threshold density
1 × 10 24 m −3
(a) What is the pumping rate for the SOA?
(b) What is the zero-signal gain?
Solution:
(a) If a 100-mA bias current is applied to the device, then from Eq. (11.2) the
pumping rate is
R p =
J
qd
=
i
qdwL
=
0.1 A
1.6 × 10 −19 C
(0.3 μm)(3 μm)(500 μm)
= 1.39 × 10
33
(electrons/m
3
)/s
(b) From Eq. (11.7b), the zero-signal gain is
g 0 = 0.3
2.0 × 10
−20 m
2
(1 ns)
1.39 × 10
33 m
−3 s
−1
−
1.39 × 10
24 m
−3
1.0 ns
= 2340 m
−1
= 23.4 cm
−1
Drill Problem 11.1 Consider an InGaAsP SOA that has cavity dimensions w
= 5 μm, d = 0.5 μm, and L = 200 μm. Assume the SOA has a gain coefficient
a = 1.0 × 10
−20 m
2 , a confinement factor = 0.3, a 1-ns time constant,
and a threshold carrier density n th = 1.0 × 10
24 m
−3 . (a) If a 100-mA bias