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For an elliptical beam (which could come from a waveguide or a laser diode) injected with two lenses into a single mode fiber, calculates the distance from the lens to the refracted beam waist in the XZ plane (according to the fact that for the refracted beam, waists in the XZ and YZ planes may be at different locations) as well as the coupling ratio (considering that without misalignments, the fiber optic is located at the aforesaid "waist in the the XZ plane" position and centered on it) as functions of the incident beam waist position and widths, the wavelength, the focal lengths and distance between lenses, the fiber mode radius, the transmission coefficient at the fiber entrance and the eventual misalignments.