Page 152 - Fiber Optic Communications Fund

Lasers 133

modes do not satisfy the Bragg condition given by Eq. (3.142) and, therefore, they suffer huge losses.
One drawback of the DBR is that the corrugated region is part of the cavity and it is somewhat lossy, which
lowers the efficiency of the device. Instead, the corrugated region can be fabricated above the active region
as shown in Fig. 3.37(c). Such a laser is known as a distributed-feedback (DFB) laser [18, 19]. The grating
placed above the waveguide changes the effective index periodically and is equivalent to the waveguide
with periodic index variation in the core region. This grating provides coupling between forward- and
backward-propagating waves and maximum coupling occurs for frequencies satisfying the Bragg condition,
Eq. (3.142). The advantage of a DFB laser is that the corrugated region is not part of the cavity and, therefore,
cavity loss does not increase because of the grating. DFB lasers are widely used in applications such as CD
players, transmitters in fiber-optic communications, and computer memory readers.

3.9 Additional Examples

Example 3.8
For an atomic system under thermal equilibrium conditions, the ratio of spontaneous emission rate to stimu-
∘
14
lated emission rate is 2 × 10 . Find the wavelength of the light emitted. Assume that the temperature is 30 C.
Solution:
From Eq. (3.16), we have

R ( )
spont ℏ
= exp − 1,
R k T
stim B
( )
ℏ
14
2 × 10 = exp − 1,
k T
B
( )
14
2 × 10 ≈ exp ℏ ,
k T
B
ℏ 14
= ln(2 × 10 ).
k T
B
∘
With T = 30 C = 303 K, k = 1.38 × 10 −23 J/K, and ℏ = 1.054 × 10 −34 J ⋅ s,
B
15
= 1.3 × 10 rad/s.
The wavelength is
c 2c 2 × 3 × 10 8
= = = = 1.44 μm.
f 1.3 × 10 15
Example 3.9
A laser diode operating at 1.3 μm has a cavity length of 300 μm and the refractive index n of the active region
is 3.5. (a) What is the frequency separation between modes? (b) What is the wavelength separation between
modes?