I have the following situation to evaluate:
A laser emitting a Gaussian beam having d63=5mm, a small divergence θ and power P0.
d63 is the diameter in which my beam has 63% of its power.
I need to compute the power through a circular aperture of diameter ϕ=7mm placed at a distance z=100mm from the laser.
I would apply the formula for finding the % of power which pass the aperture: T=1−e−(ϕd100mm)2
Where d100mm is the diameter of the beam computed as d100mm=d63+rθ
And after
Pout=T∗P0
Heres my biggest doubt: in the formula for finding d100mm is supposed I know the waist of my beam at the origin (z=0, the laser aperture in this case) but I don't actually know it. I only know the diameter where the power is 63%. So I think it's wrong. How do you think about that? There is a way to correctly apply this formula in my case? Also, which are the differences if I know the 86% diameter instead of 63%? Many thanks.
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