Can Someone Help with Gaussian Beams?

[Green Lantern]

Homework Statement

3. A laser scientist tells you that her He-Ne laser can be focused to a spot size of 5.00 microns. When pressed for details, she tells you that she got this number by measuring the Full Width Half Maximum (FWHM) of the intensity profile of the laser waist.

a) What is w(0) for this laser?

b) What fraction of the laser intensity is contained within the FHWM?

c) At what (full) angle will the beam spread over large distances, if one continues to measure the width of the laser beam to be the FHWM of the intensity?

Homework Equations

[PLAIN]http://www.zemax.com/kb/content_images/fwhm/Equation1.jpg

The Attempt at a Solution

[URL]http://upload.wikimedia.org/wikipedia/commons/thumb/5/53/GaussianBeamWaist.svg/350px-GaussianBeamWaist.svg.png[/URL]

From previous experience in a laboratory I know that the wavelength of a He-Ne laser is about 633 nm. I don't know if I can assume that for the purposes of this question. I'm using Laser Electronics 3E by Joseph Verdeyen and the book doesn't do a good job of explaining full width half maximum intensity. There's also no sample problems in the book or examples so I really can't tell if I'm doing it right. I don't know either z or z(R), although I can express z(R) in terms of w(0), but I don't know that quantity either. The equation for intensity above didn't come from my book. At least I didn't see it there. Am I supposed to use the 0.5 microns as w(z) for the intensity equation here?

 

[Green Lantern]

I'm just going to bump this topic.

 

[vela]

What does w(z) represent? I assume it's some sort of measure of the width of the beam, but how is it defined exactly?

 

[Green Lantern]

The book here gives w(z) as the spot size. There is a minimum spot size at a certain point along the z-axis defined as z=0.

 

[Redbelly98]

What does w(z) represent? I assume it's some sort of measure of the width of the beam, but how is it defined exactly?

It's defined by this equation given in the OP:

[PLAIN]http://www.zemax.com/kb/content_images/fwhm/Equation1.jpg[/INDENT]

where I₀ is the intensity at r=0. I₀ and w are both functions of z. At the beam's focus, w takes on it's minimum value, denoted by w₀.

Green Lantern, if you set I=I₀/2 in that equation, you can determine what r is at the half-maximum points.

From previous experience in a laboratory I know that the wavelength of a He-Ne laser is about 633 nm. I don't know if I can assume that for the purposes of this question.

Yes, that is a reasonably valid assumption.​

 

[Green Lantern]

Great. Thanks for the help.