Propagation of a gaussian beam through free space and an arbitrary configuration thin lenses using the ABCD formalism1.
Maxwell's equations give us the equation of motion for a propagatin gelectric field:
Under the assumption that and
we arrive at the Helmholtz equation
From which, we find the field:
We define the 'complex-q' parameter as
When the beam propagates through free space or a thin lens, it transforms according to
where
for propagation by a distance and
for transmission through a thin lens with focal length
The thick lens implementation is taken from2
- numpy
- matplotlib
References