Optimal focusing of gaussian beams

Abstract It is well known that a thin focusing lens, placed at the waist of a Gaussian beam with spot size wo, produces a new beam with a smaller waist spot size, given approximately by w'o ⋍ wof/zR, located approximately at the lens focus (where zR is the beam Rayleigh range and f is the lens focal length). We show that the worst situation, corresponding to the maximum waist spot size, occurs when the lens is placed such that the waist of the original beam is at the lens focus. For this case, the focused beam has its new waist at the other lens focus and its spot size is exactly equal to wof/zR. To optimize (minimize) the focused beam waist spot size the lens should be placed as far away as possible from the original beam waist.