Ultrafast Physics

Imlau Research Group


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Gaussian Beam Calculators

Gaussian Beam Radius

\(w_0=\) mm \(z=\) mm \(\lambda=\) nm \(M^2=\)
\(f=\) mm \(w_\mathrm{L}=\) mm \(w=\) mm

Relevant Relations

\(w(z) = w_0 \sqrt{1+\left(\frac{z \lambda M^2}{\pi w_0^2}\right)^2} = \frac{\lambda f M^2}{\pi w_\mathrm{L}} \sqrt{1 + \left(\frac{z \pi w_\mathrm{L}^2}{\lambda f^2 M^2} \right)^2} \)

Gaussian Pulse Peak Intensity

\(E=\) µJ \(w=\) mm \(\tau_\mathrm{p}=\) fs
\(I_0=\) W/m2 \( = \) W/cm2

Relevant Relation

\(I_0 = \frac{2E}{\pi w^2} \sqrt{\frac{\mathrm{ln} 16}{\pi \tau_\mathrm{p}^2}} \)