Page 150 - Fiber Optic Communications Fund

Lasers 131

Length L = 500 μm
Electron lifetime = 1 ns (associated with spontaneous and non-radiative recombination)
24
Threshold electron density = 0.8 × 10 m −3
Internal cavity loss = 46 cm −1
Refractive index = 3.5
Reflectivity R = R = 0.65
2
1
Under steady-state conditions, calculate (a) the photon lifetime, (b) the threshold current, and (c) the current
−3
21
required to generate a mean photon density of 8.5 × 10 m .
Solution:
(a) The photon lifetime is given by Eq. (3.79),

1
= , (3.138)
p
( + )
int mir
−1
2
int = 46 cm −1 = 46 × 10 m . (3.139)
The mirror loss is, by Eq. (3.38),
( )
1 1
= ln
mir
2L R R
1 2
1 ( 1 )
= ln
2 × 500 × 10 −6 0.65 2
2 −1
= 8.61 × 10 m , (3.140)
c 3 × 10 8 7
= = = 8.57 × 10 m/s. (3.141)
n 3.5
Using Eqs. (3.139), (3.140), and (3.141) in Eq. (3.138), we find
1
= = 2.13 ps.
p
8.57 × 10 (46 × 10 + 8.61 × 10 )
2
7
2
(b) The threshold current I is related to the threshold electron density by Eq. (3.130),
tn
N e,th qV
I = ,
th

e
where V is the active volume,
V = dL
= 0.3 × 10 −6 × 3 × 10 −6 × 500 × 10 −6 m 3
3
= 4.5 × 10 −16 m .
−3
24
The electron lifetime = 1 × 10 −9 s and N = 0.8 × 10 m ,
e e,th
24
0.8 × 10 × 1.602 × 10 −19 × 4.5 × 10 −16
I = A
th
1 × 10 −9
= 52.7 mA.