Analysis of a single-mode fiber with taper lens end

The upside-down taper lens optical fiber end is a new type of fiber end that may be useful for micro-optic image systems. We give the index distribution of this kind of fiber end, and the ray refraction formula at a spherical surface and the ray trace equation are used to analyze the ray transformation properties. Under the paraxial approximation, the optical transformation matrix of the upside-down taper lens fiber end is given.