Page 156 - Fiber Optic Communications Fund

Lasers 137

3.10 The wavelength separation between longitudinal modes of a 1300-nm Fabry–Perot laser is 0.8 μm.
Calculate the cavity length. Assume that the refractive index n = 3.5.
(Ans: 300 μm.)
3.11 The two cleaved facets of a 350-nm long semiconductor laser act as mirrors of reflectivity,

( n − 1 ) 2
R = R = , (3.146)
1 2
n + 1
−1
where n is the refractive index of the gain medium. If the internal loss coefficient is 15 cm , calculate
the gain coefficient required to offset the loss.
−1
(Ans: 50.75 cm .)
3.12 Explain the difference between direct and indirect band-gap materials.

3.13 In a direct band-gap material, an electron in the conduction band makes transition to the valence band,
14
emitting a light wave of frequency 75 × 10 Hz. The band-gap energy is 1.8 eV. Calculate the crystal
momentum of the electron. Assume that the effective mass of an electron in the conduction band and
the valence band is 0.07m and 0.5m, respectively, where m is the rest mass of an electron = 9.109 ×
10 −31 kg.
(Ans: 7.23 ×10 −25 kg ⋅ m/s.)
−3
23
3.14 The threshold electron density in a 800-nm Fabry–Perot laser diode is 4.2 × 10 m , the electron
−3
lifetime is 1.5 ns, and the volume of the active region is 5 × 10 −16 m . Calculate (a) the photon
e
lifetime and (b) the threshold current. Assume that the gain can be modeled as G = G (N − N ),
e0
e
0
−3
23
3
with G = 2 × 10 −12 m ∕s and N e0 = 3.2 × 10 m .
0
(Ans: (a) 5 ps; (b) 22.4 mA.)
3.15 A semiconductor laser diode has the following parameters:
Active area width = 4 μm
Active area thickness d = 0.5 μm
Length L = 400 μm
Electron lifetime = 1.5ns
Internal cavity loss = 10 cm −1
Reflective index = 3.3
Reflectivity R = 0.32
1
Reflectivity R = 0.92
2
3
G = 1.5 × 10 −12 m /s
0
23
N = 3.4 × 10 m −3
0
The bias current is 65 mA. Under steady-state conditions, calculate (a) the photon lifetime, (b) the
threshold electron density, (c) the threshold current, (d) the photon density, and (e) the optical intensity.
23
2
23
−3
10
−3
(Ans: (a) 4.35 ps, (b) 4.93 ×10 m , (c) 42.1 mA, (d) 7.75 ×10 m , (e) 1.75 ×10 W/m .