Page 189 - Photonics Essentials an introduction with experiments

Direct Modulation of Laser Diodes

Direct Modulation of Laser Diodes 183

dN J 2 N
= – (8.5)
dt qd r
During the time 0 < t < d , we will assume that r remains constant.
This is probably not an accurate assumption, but it is necessary in or-
der to obtain an analytic solution. This equation is now the same as
Eq. 6.18, and we can write down the solution right away:

J 2 r
N(t) = · (1 – e –t/ r ) + N 1 e –t/ r (8.6)
qd
At time d , the laser turns on because threshold has been reached, so,
by definition, the carrier concentration at threshold is

J 2 r
N th ( d ) = · (1 – e – d / r ) + N 1 e – d / r
qd
Combining terms:
– N 1 e – d / r =
J 2 r
J 2 r
qd qd – N th
Solving for d :

N 1
J 2
–
qd
r
d = r ·ln (8.7)
N th
J 2
–
qd r
Remember that we can write
N 1 J 1 N th J th
= and =
r qd r qd
so,
J 2 – J 1
d = r ·ln (8.8)
J 2 – J th
where J 2 > J th > J 1 .
This result is an estimate that shows that there is a time delay be-
tween the electrical pulse and the appearance of light. This delay lim-
its the maximum bit rate for the laser when it is used in a communi-
cation system, even though the ac modulation bandwidth of the laser
may be higher. The delay is caused by the time needed to build up the
carrier concentration to threshold. The delay time can be reduced by
prebiasing the laser closer to threshold.
The space of time between the build-up of the carrier concentration

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