Abstract
From ray optics, we present a simple formulation of the ABCD matrix under paraxial approximation for reflection and refraction of light beams at a hyperbolic interface separating media of different refractive indices. Based on the formulated ABCD matrix for refraction by a hyperbolic interface, we report a simple theoretical investigation of the coupling efficiency of a laser diode to a single-mode fibre via a hyperbolic lens formed on its tip. Our results agree excellently with a recently published experimental result and also with the theoretical findings using quite involved phase distribution models. The analysis justifies the correctness of the prescription of the said ABCD matrix and also the simplicity of efficiency calculation, executable even by a pocket calculator. The technique will be useful in designing suitable microlenses employing laser micromachining technique.
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