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4 Light Sources for Fiber Links
0.32 at each end. What is the optical gain at the lasing threshold?
(b) If one end of the laser is coated with a dielectric reflector so that its reflectivity is now 90%, what is the optical gain at the lasing threshold?
(c) If the internal quantum efficiency is 0.65, what is the external quantum
efficiency in cases (a) and (b)? [Answers: (a) 55.6 cm
–1 ; (b) 34.9 cm
–1 ; (c) η ext
= 0.53 and 0.46, respectively.]
4.10 Find the external quantum efficiency for a Ga 1−x Al x As laser diode (with x
= 0.03) that has an optical-power-versus-drive-current relationship of 0.5
mW/mA. [Hint: Use Eq. (4.3) to find E g = 1.462 eV and then find λ =
848 nm. Then from Eq. (4.38) η ext = 0.342.]
4.11 Approximate expressions for the transverse and lateral optical-field confinement factors T and L , respectively, in a Fabry-Perot lasing cavity are
T =
D
2
2 + D 2 with D =
2π d
λ
n
2
1 − n
2
2
1/2
and
L =
W
2
2 + W 2 with W =
2πw
λ
n
2
e f f − n
2
2
1/2
where
n
2
e f f = n
2
2 + T
n
2
1 − n
2
2
Here w and d are the width and thickness, respectively, of the active layer, and n 1
and n 2 are the refractive indices inside and outside the cavity, respectively.
(a) Consider a 1300-nm InGaAsP laser diode in which the active region is 0.1 μm
thick, 1.0 μm wide, and 250 μm long with refractive indices n 1 = 3.55 and n 2 =
3.20. What are the transverse and lateral optical-field confinement factors?
(b) Given that the total confinement factor is.
= T L , what is the gain threshold if the effective absorption coefficient is α mat
= 30 cm
−1 and the facet reflectivities are R 1 = R 2 = 0.31?
[Answer: (a) T = 0.216 and L = 0.856; (b) = 0.185].
4.12 A GaAs laser emitting at 800 nm has a 400-μm cavity length with a refractive
index n = 3.6. If the gain g exceeds the total loss α t throughout the range
750 nm < λ < 850 nm, how many modes will exist in the laser? [Answer:
λ = 0.22 nm yielding 455 modes].
4.13 A laser emitting at λ 0 = 850 nm has a gain-spectral width of σ = 32 nm and
a peak gain of g(0) = 50 cm
−1 . Plot g(λ) from Eq. 4.41. If α t = 32.2 cm
−1 ,
show the region where lasing takes place. If the laser is 400 μm long and n =
3.6, how many modes will be excited in this laser? [Answer:
λ = 0.25 nm yielding 240 modes].
4 Light Sources for Fiber Links
0.32 at each end. What is the optical gain at the lasing threshold?
(b) If one end of the laser is coated with a dielectric reflector so that its reflectivity is now 90%, what is the optical gain at the lasing threshold?
(c) If the internal quantum efficiency is 0.65, what is the external quantum
efficiency in cases (a) and (b)? [Answers: (a) 55.6 cm
–1 ; (b) 34.9 cm
–1 ; (c) η ext
= 0.53 and 0.46, respectively.]
4.10 Find the external quantum efficiency for a Ga 1−x Al x As laser diode (with x
= 0.03) that has an optical-power-versus-drive-current relationship of 0.5
mW/mA. [Hint: Use Eq. (4.3) to find E g = 1.462 eV and then find λ =
848 nm. Then from Eq. (4.38) η ext = 0.342.]
4.11 Approximate expressions for the transverse and lateral optical-field confinement factors T and L , respectively, in a Fabry-Perot lasing cavity are
T =
D
2
2 + D 2 with D =
2π d
λ
n
2
1 − n
2
2
1/2
and
L =
W
2
2 + W 2 with W =
2πw
λ
n
2
e f f − n
2
2
1/2
where
n
2
e f f = n
2
2 + T
n
2
1 − n
2
2
Here w and d are the width and thickness, respectively, of the active layer, and n 1
and n 2 are the refractive indices inside and outside the cavity, respectively.
(a) Consider a 1300-nm InGaAsP laser diode in which the active region is 0.1 μm
thick, 1.0 μm wide, and 250 μm long with refractive indices n 1 = 3.55 and n 2 =
3.20. What are the transverse and lateral optical-field confinement factors?
(b) Given that the total confinement factor is.
= T L , what is the gain threshold if the effective absorption coefficient is α mat
= 30 cm
−1 and the facet reflectivities are R 1 = R 2 = 0.31?
[Answer: (a) T = 0.216 and L = 0.856; (b) = 0.185].
4.12 A GaAs laser emitting at 800 nm has a 400-μm cavity length with a refractive
index n = 3.6. If the gain g exceeds the total loss α t throughout the range
750 nm < λ < 850 nm, how many modes will exist in the laser? [Answer:
λ = 0.22 nm yielding 455 modes].
4.13 A laser emitting at λ 0 = 850 nm has a gain-spectral width of σ = 32 nm and
a peak gain of g(0) = 50 cm
−1 . Plot g(λ) from Eq. 4.41. If α t = 32.2 cm
−1 ,
show the region where lasing takes place. If the laser is 400 μm long and n =
3.6, how many modes will be excited in this laser? [Answer:
λ = 0.25 nm yielding 240 modes].