Focal properties of an aberration-free fiber micro-lens

The focusing properties of an aberration-free fiber micro-lenses are studied. The simulation results show that the focal spot size (radius of the waist) is no changed with micro-lenses clad radius for a given focal length when the micro-lenses clad radius is larger than twice the fiber core radius, and the empirical formulas are given for computing focal shift and spot size respectively, it provide convenient means to make sure the location and size of the waist of the beam emerging from the fiber micro-lenses. The proposed formulas cover the range of parameter range of beam Fresnel number Nw<;2 and Nr>;4Nw.