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:
“Colleges, in like manner, have their indispensable office,—to teach elements. But they can only highly serve us, when they aim not to drill, but to create; when they gather from far every ray of various genius to their hospitable halls, and, by the concentrated fires, set the hearts of their youth on flame.”
—Ralph Waldo Emerson (1803–1882)
“I have proceeded ... to prevent the lapse from ... the point of blending between wakefulness and sleep.... Not ... that I can render the point more than a point—but that I can startle myself ... into wakefulness—and thus transfer the point ... into the realm of Memory—convey its impressions,... to a situation where ... I can survey them with the eye of analysis.”
—Edgar Allan Poe (1809–1849)
“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)