### 7.6 The Gaussian beam parameter

For a more compact description of the interaction of Gaussian modes with optical components we will
make use of the Gaussian beam parameter [34]. The beam parameter is a complex quantity defined as
It can also be written as
Using this parameter, Equation (119) can be rewritten as
Other parameters, like the beam size and radius of curvature, can also be written in terms of the beam
parameter :
and
The Hermite–Gauss modes can also be written using the Gaussian beam parameter
as