We have developed a simple and low-cost microlens for optical communication systems involving the coupling of laser diodes or integrated waveguides to single-mode fibers (SMFs), and fiber-to-fiber interconnection. More generally, the applications concern coupling active or passive components to SMFs. The novelty consists in using a graded-index section of core diameter without cladding and taking into account the diffraction effects. This new microlens offers a wider range of mode field diameters (from around 5 to ) and working distances (up to ) than previously demonstrated. This paper investigates the influence of the Fresnel diffraction of a Gaussian beam, during its propagation through the microlens, on the mode field intensity profile, the working distance, and the coupling efficiency of this kind of microlens in front of a SMF. It shows that while truncation causes multiple maxima of the coupling efficiency as a function of displacement, it does not decrease the maximum coupling efficiency.