The beam parameters can then be split into two respective parameters: ,
for the sagittal
plane and
and
for the tangential plane so that the Hermite–Gauss modes can be written as
Remember that these Hermite–Gauss modes form a base system. This means one can use the separation
into sagittal and tangential planes even if the actual optical system does not show this special type of
symmetry. This separation is very useful in simplifying the mathematics. In the following, the term beam
parameter generally refers to a simple case where and
but all the results can also
be applied directly to a pair of parameters.
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