Page 184 - Photonics Essentials an introduction with experiments

Direct Modulation of Laser Diodes

178 Advanced Topics

population of excited carriers in the laser structure. The presence of
self-pulsations or relaxation oscillations puts a limit on the modula-
tion bandwidth of the laser.
This chapter is somewhat different from the others in this book.
There are no suggested laboratory experiments because they are
sometimes difficult to set up and involve specialized equipment. In
addition, the ultimate bandwidth that can be obtained by direct mod-
ulation of laser emission is a subject of current research. Less than a
decade ago, it was felt that modulation rates above 2 GHz would be
quite difficult to achieve based on the theoretical understanding of
laser dynamics. At the time of this writing, the state of the art modu-
lation bandwidth exceeds 10 GHz. Existing understanding is based
entirely on the properties of the materials used to make these lasers.
Yet, knowledge about the electronic properties of these materials has
not changed during this time. Clearly, there is room for improvement
in the theory, and perhaps one of you will bring this contribution to
the field soon.
Like the case of the LED, laser modulation properties are based on
the change in the carrier concentration that is caused by a change in
the drive current. An increase in the carrier concentration will cause
an increase in the photon density. However, in the case of the laser,
this increase in the photon density will cause a decrease in the free
carrier density by stimulating recombination of excess carriers. The
most significant difference between the transient properties of a laser
and the properties of the LED is directly related to this coupling be-
tween the carrier density and the photon density that is fundamental
to laser action.
Our approach in this chapter will be to examine this coupled inter-
action. The coupled equations that describe the electron density and
the photon density can be solved only numerically. However, we will
be able to extract the delay time for light emission and the frequency
of the self-pulsations of the light emission. The materials parameter
that plays a determining role in the model of rise time is the carrier
lifetime, r . This is the amount of time an excess electron can last in
the conduction band before recombining. In our treatment, we assume
that this is a constant in order to proceed toward a solution of the
equations describing the time dependence of light emission. This as-
sumption is convenient, but not realistic. It would be more realistic to
recognize that the relaxation time will be a function of both the excess
carrier density and the coupling between the photon density and the
excess carrier density.
The current models for modulation rate of laser diodes have been
developed during the last decade by looking for closed-form solutions
to the modulation rate equations, so that the role of physical parame-

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