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Energy density expression of a Gaussian pulse

  1. Nov 14, 2009 #1
    Hi,

    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
     
  2. jcsd
  3. Nov 20, 2009 #2
    The question can be misunderstood.
    I know I = I0*(w/w0)^2*int(r*exp(-2r^2/w^2)*int(-2t^2/tho_laser) and
    F = I*tho_laser.

    My question is how or.. can I find F(r) from F(r_i, r_i+1) [the equation above] ?
     
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