4.3 Principles of Laser Diodes
181
reflectivity is R 1 = R 2 = R = 0.32 for each end face. Find (a) the threshold current
density and (b) the threshold current for this device.
Solution (a) From Eqs. (4.28) and (4.29)
J th =
1
β th
α mat +
1
L
ln
1
R
=
1
21 × 10 −3
10 +
1
300 × 10 −4 ln
1
0.32
= 2.28 × 10
3 A/cm
2
(b) The threshold current I th is given by.
I th = J th × cross-sectional area of the optical cavity = (2.28 × 10
3 A/cm
2 ) ×
(300 × 10
−4 cm) × (100 × 10
−4 cm) = 684 mA.
Drill Problem 4.6 Consider a Fabry-Perot laser cavity in which the absorption
loss coefficient is 20 cm
−1 . If the cavity mirror reflection coefficient is 0.33 at
both ends, use Eq. (4.28) to verify that the cavity length at which the absorption
loss and the cavity loss become equal is L = 554 μm.
4.3.2 Laser Diode Rate Equations
The relationship between optical output power and the diode drive current can be
determined by examining the rate equations that govern the interaction of photons and
electrons in the active region. As noted earlier, the total carrier population is determined by carrier injection, spontaneous recombination, and stimulated emission. For
a pn junction with a carrier-confinement region of depth d, the rate equations are
given by
d
dt
= Cn + R sp −
τ ph
= stimulated emission + spontaneous emission + photon loss
(4.30)
which governs the number of photons , and
dn
dt
=
J
qd
−
n
τ sp
− Cn
= injection + spontaneous recombination + stimulated emission
(4.31)
which governs the number of electrons n. Here, C is a coefficient describing the
strength of the optical absorption and emission interactions, R sp is the rate of
181
reflectivity is R 1 = R 2 = R = 0.32 for each end face. Find (a) the threshold current
density and (b) the threshold current for this device.
Solution (a) From Eqs. (4.28) and (4.29)
J th =
1
β th
α mat +
1
L
ln
1
R
=
1
21 × 10 −3
10 +
1
300 × 10 −4 ln
1
0.32
= 2.28 × 10
3 A/cm
2
(b) The threshold current I th is given by.
I th = J th × cross-sectional area of the optical cavity = (2.28 × 10
3 A/cm
2 ) ×
(300 × 10
−4 cm) × (100 × 10
−4 cm) = 684 mA.
Drill Problem 4.6 Consider a Fabry-Perot laser cavity in which the absorption
loss coefficient is 20 cm
−1 . If the cavity mirror reflection coefficient is 0.33 at
both ends, use Eq. (4.28) to verify that the cavity length at which the absorption
loss and the cavity loss become equal is L = 554 μm.
4.3.2 Laser Diode Rate Equations
The relationship between optical output power and the diode drive current can be
determined by examining the rate equations that govern the interaction of photons and
electrons in the active region. As noted earlier, the total carrier population is determined by carrier injection, spontaneous recombination, and stimulated emission. For
a pn junction with a carrier-confinement region of depth d, the rate equations are
given by
d
dt
= Cn + R sp −
τ ph
= stimulated emission + spontaneous emission + photon loss
(4.30)
which governs the number of photons , and
dn
dt
=
J
qd
−
n
τ sp
− Cn
= injection + spontaneous recombination + stimulated emission
(4.31)
which governs the number of electrons n. Here, C is a coefficient describing the
strength of the optical absorption and emission interactions, R sp is the rate of