A tapered graded-index lens: analysis of transmission properties and applications in fiber-optic communication systems

Propagation properties of a linearly tapered parabolic-index dielectric cylinder are studied using a ray-optics approach. Analytical solutions for trajectories of skew rays with arbitrary initial conditions are obtained for tapers with small slope and small index variations over transverse dimensions. Conditions for an arbitrary ray to remain bound to the core of the taper are derived. Applications of these tapered lenses for coupling of light sources to fibers, for beam expanding/refocusing in microoptics devices, and for splicing two fibers of different core sizes are addressed, Power coupling efficiency for illumination from both Lambertian and narrow-beam light sources are calculated. Improvement in coupling efficiency, when taper is are used to couple power from directed-beam sources to optical fibers, is demonstrated. Radiation losses when a taper is used as a transition element between two fibers of different core radii are evaluated. Plots of skew-ray paths, illustrating the gradual concentration of power as light travels toward the smaller end of the taper, are also presented.