4.5 Summary
207
If a current pulse of amplitude I p is applied to an unbiased laser diode, show that the
time needed for the onset of stimulated emission is
t d = τln
I p
I p − I th
Assume the drive current I = JA, where J is the current density and A is the area of
the active region.
(b) If the laser is now prebiased to a current density J B = I B /A, so that the initial excess
carrier pair density is n B = J B τ/qd, then the current density in the active region during
a current pulse I p is J = J B + J p . Show that in this case Eq. (4.50) results.
4.20 A laser diode has a maximum average output of 1 mW (0 dBm). The laser
is to be amplitude-modulated with a signal x(t) that has a dc component of
0.2 and a periodic component of ± 2.56. If the current-input to optical-output
relationship is P(t) = i(t)/10, find the values of I 0 and m if the modulating
current is i(t) = I 0 [1 + mx (t)].
[Answer: i(t) = I 0 [1 + mx(t)] mA = 9.2 [1 + 0.42 x(t)] mA].
4.21 Consider the following taylor series expansion
of the optical-power-versus-drive-current relationship of an optical source
about a given bias point:
y(t) = a 1 x(t) + a 2 x
2
(t) + a 3 x
3
(t) + a 4 x
4
(t)
Let the modulating signal x(t) be the sum of two sinusoidal tones at frequencies ω 1
and ω 2 given by
x(t) = b 1 cos ω 1 t + b 2 cos ω 2 t
(a) Find the second-, third-, and fourth-order intermodulation distortion coefficients
B mn (where m and n = ±1, ±2, ±3, and ±4) in terms of b 1 , b 2 , and the a i .
(b) Find the second-, third-, and fourth-order harmonic distortion coefficients A 2 , A 3
and A 4 in terms of b 1 , b 2 , and the a i .
References
1. L.A. Coldren, S.W. Corzine, M.L. Mashanovitch, Diode Lasers and Photonic Integrated
Circuits, 2nd edn. (Wiley, 2012)
2. T. Numai, Fundamentals of Semiconductor Lasers, 2nd edn. (Springer, 2015)
3. D.J. Klotzkin, Introduction to Semiconductor Lasers for Optical Communications (Springer,
2020)
4. D.A. Neaman, 4th edn. Semiconductor Physics and Devices (McGraw-Hill, 2012)
207
If a current pulse of amplitude I p is applied to an unbiased laser diode, show that the
time needed for the onset of stimulated emission is
t d = τln
I p
I p − I th
Assume the drive current I = JA, where J is the current density and A is the area of
the active region.
(b) If the laser is now prebiased to a current density J B = I B /A, so that the initial excess
carrier pair density is n B = J B τ/qd, then the current density in the active region during
a current pulse I p is J = J B + J p . Show that in this case Eq. (4.50) results.
4.20 A laser diode has a maximum average output of 1 mW (0 dBm). The laser
is to be amplitude-modulated with a signal x(t) that has a dc component of
0.2 and a periodic component of ± 2.56. If the current-input to optical-output
relationship is P(t) = i(t)/10, find the values of I 0 and m if the modulating
current is i(t) = I 0 [1 + mx (t)].
[Answer: i(t) = I 0 [1 + mx(t)] mA = 9.2 [1 + 0.42 x(t)] mA].
4.21 Consider the following taylor series expansion
of the optical-power-versus-drive-current relationship of an optical source
about a given bias point:
y(t) = a 1 x(t) + a 2 x
2
(t) + a 3 x
3
(t) + a 4 x
4
(t)
Let the modulating signal x(t) be the sum of two sinusoidal tones at frequencies ω 1
and ω 2 given by
x(t) = b 1 cos ω 1 t + b 2 cos ω 2 t
(a) Find the second-, third-, and fourth-order intermodulation distortion coefficients
B mn (where m and n = ±1, ±2, ±3, and ±4) in terms of b 1 , b 2 , and the a i .
(b) Find the second-, third-, and fourth-order harmonic distortion coefficients A 2 , A 3
and A 4 in terms of b 1 , b 2 , and the a i .
References
1. L.A. Coldren, S.W. Corzine, M.L. Mashanovitch, Diode Lasers and Photonic Integrated
Circuits, 2nd edn. (Wiley, 2012)
2. T. Numai, Fundamentals of Semiconductor Lasers, 2nd edn. (Springer, 2015)
3. D.J. Klotzkin, Introduction to Semiconductor Lasers for Optical Communications (Springer,
2020)
4. D.A. Neaman, 4th edn. Semiconductor Physics and Devices (McGraw-Hill, 2012)