I have a question on how peak fluence is calculated. For a Gaussian circular beam, the peak fluence is the total pulse energy divided by πω2/2, where ω is the Gaussian beam radius. Now my question is about a Gaussian elliptical beam with a 10um x 500um beam spot size, is there a way to calculate the peak fluence? Thanks for the inputs!
You need to find an expression for your elliptical beam. I am assuming it is a simple product of a Gaussian beam in the x-direction and the y-direction. You want to have this normalized so that you know that the total integral of your beam profile is equal to 1. Once you have this normalized you know that the power distribution is the total power times this normalized distribution.
In brief, I think you want the normalization constant. In your case this appears to be \pi*w_x*w_y
https://www.wolframalpha.com/input/?i=integral_%7B-infty%7D%5E%5Cinfty+integral_%7B-infty%7D%5E%5Cinfty+exp%28-%28x%2Fa%29%5E2%29++exp%28-%28y%2Fb%29%5E2%29+dx+dy
Note: there is a factor 2 in your equation compared to mine. Will you be careful with the definition of 'beam radius'? Is this at half intensity? 1/e intensity? 1/e for the field? etc? etc?
Hello Michiel, I am using the definition of peak fluence from here https://www.rp-photonics.com/fluence.html where the beam radius is defined at 1/e2 of intensity
Can't you divide the pulse energy by (pi)ab where a and b are the semi-major and semi-minor axis lengths of an ellipse?
Hello Srini, I think that will give you the average fluence, not the peak fluence.
Hi Michael
Michiel's answer is correct and complete, but both he and Srini Vasan have used a different definition of the beam radius from yours (as Michiel pointed out in his answer). The quick answer is that since an elliptical Gaussian beam is separable into a product of one dimensional Gaussian beams with axes oriented along the ellipse's major and minor axes, you just need to replace the factor w^2 in the circular Gaussian result by the product (w_major)*(w_minor). This will work regardless of how you define your beam radii (as long as you are consistent ).
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