Chapter 3 The Semiconductor Laser
3.4 Laser Beamwidth and the Fraunhofer Transform
In a laser such as the buried heterostructure type, the optical wave
inside the device is guided by the difference in indices of refraction be-
tw^een the active and surrounding regions. Even in the absence of an in-
dex step, the high gain tends to confine the wavefront to the vicinity of
the active region. Whether "index-guided" or "gain-guided," the beam
profile can be reasonably well described by a Gaussian, exp( -ax^-
the coefficients dependent on the height and width of the active region.
As the beam emerges from the laser, it propagates through free space,
obeying the electromagnetic wave equations, and we derive here what is
ihQ far-field distribution
produced by such a coherent source.
As shown in Figure 3.15, we ask for the electric field, Ep, at a long
distance from a plane containing a
^. If we
define E(t) =
then, from radiation theory
et a/., 1984, p.
we may write the contribution to
due to E^as
where fc, the wave vector, equals 2n/X. This expression is called the
"paraxial" approximation which assumes that the angle between r and
Figure 3.15 Far-field pattern
and near-field pattern E .