Page 188 - Photonics Essentials an introduction with experiments

Direct Modulation of Laser Diodes

182 Advanced Topics

where
B 21 = stimulated recombination rate
N = photon density
f = photon frequency
K th = optical gain coefficient a N
r = effective recombination time

In this equation, we have isolated the stimulated recombination rate,
which depends on the photon density from the spontaneous and non-
radiative parts, which depend only on N. They have been grouped to-
gether with an effective recombination time, r .
We assume that NP n i , and N n D .
2
dN J N
= – B 21 N · f·K th – (8.3)
dt qd r

gain due to loss due to loss due to all other
electrical pumping stimulated emission recombination
On the other hand, the equation for the photon density can be writ-
ten as

dN N – spont N A 21
= +B 21 N · f·K th – 2 (8.4)
dt

gain due to loss due to gain due to fraction
stimulated emission emission from cavity of spontaneous
and absorption emission that falls in
the laser mode

These equations are complicated to solve, and we will not attempt a
comprehensive solution. Instead, we will look at some of the features
that appear in transient behavior.

Part 1. Before the laser reaches threshold: 0 < t < d
First, let us suppose that the laser is “off.” This means that there may
be some spontaneous emission coming out of the laser, but that the
stimulated term is turned off. In this state, the current density is J 1
and the carrier density is N 1 . Then we will turn the laser on by step-
ping the current to J 2 , which is well above the threshold current. At
some time, d , after the current is stepped, the laser will turn on.
However, before this time the stimulated emission is zero, even
though the current is already at J 2 . Setting the stimulated emission
term = 0 in Eq. 8.3 gives

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