Lasers and Focusing Lenses

all laser beams are zernike hermite polynomial functions(mostly),
however the basic TEM00 mode is guassian, these beams, have a beam waist, where the are the thinnest, or where the spot size is least, correspondingly they have what is called a railegh range, within which the beam does not diverge appreciably, if you force it to converge by a lens, you reduce the rayleigh length, further to burn the paper, you need high energy focussed, but you are also limited by your laser energy, you need to keep it long at the beam waist to actually burn it, if you are working with an ordinary low power laser