as it passes through the medium:
is the coordinate in the direction of propagation.
This equation neglects the effects of the transversal profile of beam.
is variation of index of refraction (Which is supposed to be small),
is complex field, related to the physical electric field
with relation
, where
is vector of polarization,
is wavenumber,
is frequency,
is transversal Laplacian;
means real part.
and
of lower and excited states:
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