Ray Transfer Matrices For Gaussian Beams
The matrix formalism is also useful to describe Gaussian beams. If we have a Gaussian beam of wavelength, radius of curvature R, beam spot size w and refractive index n, it is possible to define a complex beam parameter q by:
- .
This beam can be propagated through an optical system with a given ray transfer matrix by using the equation:
- ,
where k is a normalisation constant chosen to keep the second component of the ray vector equal to 1. Using matrix multiplication, this equation expands as
and
Dividing the first equation by the second eliminates the normalisation constant:
- ,
It is often convenient to express this last equation in reciprocal form:
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