I am doing a Gaussian Beam Optics Experiment - where I observe how lasers have a gaussian intensity profile. I've measured the beam radius at several points from the Laser in the far-field (ie. position 'z' >> Rayleigh Range). I want to know why is there a beam waist inside the laser. How do I calculate the beam waist from the measurements I have. And what is the significance of the Rayleigh Range? Any other important points would help.