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:
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)
“If it had not been for storytelling, the black family would not have survived. It was the responsibility of the Uncle Remus types to transfer philosophies, attitudes, values, and advice, by way of storytelling using creatures in the woods as symbols.”
—Jackie Torrence (b. 1944)
“When Gabriel’s trumpet ends all life’s 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 (1899–1979)