Just to make sure we understand the approximation, the existence of a focal point requires not only an ideal thin lens approximation, but also requires us to assume there are no wave phenomena (as we usually assume for these purposes). To go beyond that we could use the gaussian beam approximation, where a beam is categorized not only by the location of its focal point and its direction, but also its wavelength and beam waist (the approximate nonzero size at the focal point). See more at https://en.wikipedia.org/wiki/Gaussian_beam#Beam_waist

Just to make sure we understand the approximation, the existence of a focal point requires not only an ideal thin lens approximation, but also requires us to assume there are no wave phenomena (as we usually assume for these purposes). To go beyond that we could use the gaussian beam approximation, where a beam is categorized not only by the location of its focal point and its direction, but also its wavelength and beam waist (the approximate nonzero size at the focal point). See more at https://en.wikipedia.org/wiki/Gaussian_beam#Beam_waist