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Energy density of the ith annular section of a Gaussian pulse is written as

F(r_i, r_i+1)=2*totalEnergy/[(r_i+1^2-r_i^2)*w^2]*integral(r*exp(-r^2/w^2),from r_i to r_i+1)

where r spans from r=0 to r=r_n (theoretically infinity) in n steps, w is the waist size of the beam.

This equation is for i. annular part. How can I write the whole energy density of a Gaussian pulse?

I know F_average = 2*totalEnergy/[pi*w^2]

What is the equivalance of F_average in its exact form considering Gaussian spatial profile?

Any answer will be highly appreciated!

Fulya

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# Energy density expression of a Gaussian pulse

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