Page 149 - Fiber Optic Communications Fund

130 Fiber Optic Communications

10 24 10 24
4 4

3.5 3.5
3 3
Electron density, m *3 2.5 2 Electron density, m *3 2.5 2

1.5
1.5
1 1
0.5 0.5

0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
Time (ns) Time (ns)
(a) (b)

Figure 3.36 Numerical solution of the rate equation using typical parameters of an InGaAsP laser diode: (a) I = 50 mA;
(b) I = 100 mA.

The next step is to develop an expression for the optical power generated as a function of the current. Since
the energy of a photon is equal to ℏ, the mean photon density of N ph corresponds to the energy density,
u = N ℏ. (3.134)
ph
The relation between energy density and optical intensity is given by Eq. (3.50),

 = u = N ℏ. (3.135)
ph
Since optical intensity is power per unit area perpendicular to photon flow, the mean optical power generated
can be written as
P gen = A = N ℏA, (3.136)
ph
where A is the effective cross-section of the mode. Using Eq. (3.133) in Eq. (3.136), we finally obtain
(I − I ) ℏA
ph
th
P = . (3.137)
gen
qdL
Note that the above equation is valid only when I > I .If I ≤ I , P = 0 under our approximations.
th th gen
Example 3.7
A 1300-nm InGaAs semiconductor laser has the following parameters:

Active area width = 3 μm
Active area thickness d = 0.3 μm