# Gaussian Beam Focusing

1. Dec 9, 2015

### Lemenks

A Gaussian beam has an intensity I(r,z), if the beam area at position Z is given by A(Z), then the beam gets focused by a lens of focal length f, what will the area of the beam be at the beam waist A(0) be?

So I have been trying to figure this out for ages, I had to replicate an experiment in which a student simply assumed the beam focused like a cone, in which case you say the beam is 0 at the beam waist and the beam is "close" to the beam waist and choose/measure a distance. This seemed like pretty poor experimental work to me as you can make the intensity become infinitely large by "choosing/measuring" a value closer to the beam waist. In this scenario I have taken position z from the beam waist to be the focal distance f:

A(f)/A(0) = (pi*w(f)^2)/(pi*w(0)^2) = (w(f)/(w(0))^2 = (f/x)^2

x is the distance from the beam waist that a person "chooses" or "measures". To see the above equation, I found it constructive to draw out a cone and put in the values.

I read several Gaussian optics manuals and a better expression seems to be

A(f)/A(0) = (f/ZR)

Where ZR is the Rayleigh length and is given by

ZR = pi*w(0)^2/gamma

However the problem with this is that I don't know w(0). I read a limit for w(0)>/= 2*gamma/pi, however this seems to result is nonsensical answers.

If anyone here knows or works with lasers, perhaps you could help explain it to me?

2. Dec 14, 2015

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Dec 15, 2015

### Andy Resnick

I'm a little unclear about your geometry: you seem to have a well-specified gaussian beam (do you know I(r,z) or not?) that is focused by a lens placed at a particular z = Z, and then you want to know the properties of the refracted beam?

4. Dec 23, 2015

### Lemenks

Yes I know the intensity at I(r,z) and need to calculate it at I(r,0) - sorry if I made it unclear. I was just a little confused as to the proper way of making this calculation, the beam focusing as a cone shape seemed too approximate and also to contain really large errors so I was trying to see if there was a batter method.

5. Dec 23, 2015

### Andy Resnick

Not sure what you have tried already- have you used these resources:

http://www.newport.com/Gaussian-Beam-Optics/144899/1033/content.aspx
http://uigelz.eecs.umich.edu/classes/pub/ece355/handouts/example_gaussian_beam_focused_lens.pdf