Gaussian beams is a beautiful phenomenon in optics. As they propagate through space they retain their Gaussian shape, and only get broader or narrower. They are symmetric along the optical axis. No matter how many lenses you use to focus and defocus your laser beam, it will remain Gaussian. And it's shape is described by a few simple formulas , which define their thinnest section (w 0 , 'waist'), radius of wavefront (R), and divergence angle (Theta). Some immediate applications include fiber coupling, confocal microscopy, and light-sheet microscopy. The formulas describing Gaussian beams were derived in the 1960-s, soon after the invention of lasers, by solving the wave equation for electromagnetic waves, and were analysed exhaustively in paraxial approximation (Kogelnik and Li, 1966). Paraxial approximation means that angle of beam divergence angle is small (theta ~ tan(theta)). However, modern microscopy pushes limits to high-NA objectives and laser beam...
I have no commercial interest in any private company mentioned here, all opinions are my personal.