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:
Read more about this topic: Ray Transfer Matrix Analysis
Famous quotes containing the words ray, transfer and/or beams:
“It has never been my object to record my dreams, just the determination to realize them.”
—Man Ray (18901976)
“No sociologist ... should think himself too good, even in his old age, to make tens of thousands of quite trivial computations in his head and perhaps for months at a time. One cannot with impunity try to transfer this task entirely to mechanical assistants if one wishes to figure something, even though the final result is often small indeed.”
—Max Weber (18641920)
“When Gabriels trumpet ends all lifes delay,
Will crash the beams of firmamental woe:
Not nature will sustain the even crime
Of death, though death sustains all nature, so.”
—Allen Tate (18991979)