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:
“The reality is that zero defects in products plus zero pollution plus zero risk on the job is equivalent to maximum growth of government plus zero economic growth plus runaway inflation.”
—Dixie Lee Ray (b. 1924)
“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)
“If we reason, we would be understood; if we imagine, we would that the airy children of our brain were born anew within another’s; if we feel, we would that another’s nerves should vibrate to our own, that the beams of their eyes should kindle at once and mix and melt into our own, that lips of motionless ice should not reply to lips quivering and burning with the heart’s best blood. This is Love.”
—Percy Bysshe Shelley (1792–1822)