Determine the intensity profile and fwhm for gaussian beam.

[Aerozeppelin]

Homework Statement

A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a
fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.

Homework Equations

FWHM = λ/(2NA√(1 + I/Is))

The Attempt at a Solution

[/B]
FWHM₁ = 1mm = 600 nm/(2NA√(1 + I/Is))

(2NA√(1 + I/Is)) = 0.0006m
NA²(1+ I/Is) = 0.00015

10meters away :

NA²(1+ I/Is) = (0.00015)/10 = 0.000015

 

[blue_leaf77]

Where is the initial information are given? Is it at the beam waist?

 

[Aerozeppelin]

This is all the information given!

 

[blue_leaf77]

You have to know either the beam waist diameter or the distance between the initial plane and the beam waist. Without these information you can only guess what the question maker means with "initially" in the question's wording.

 

[Aerozeppelin]

There must be a solution as it was on an exam?

 

[blue_leaf77]

If I were to face such a problem in an exam, exactly worded as you have written, I would be most likely not overwhelmed by shyness to ask the prof for a greater detail about the initial plane.