Equations for beam waist measurement of high peak power lasers

We have derived a set of equations for beam waist at lens focus as a function of variable spot size and demonstrated their physical validity. The derived equations are useful for the estimation of the beam waist size of high peak power lasers focused with high numerical aperture lenses and for spot size measurement of long-range collimated Gaussian beams for several meters. We have described an indirect method to estimate the high peak power focused laser beam waist. The same treatment is extended to the Gaussian vortex beam for estimating its parameters at the beam waist. These results can be useful in the focused Gaussian beam and Gaussian vortex beam applications.