LASER-DIODE TO SINGLE-MODE FIBER EXCITATION VIA HYPERBOLIC LENS ON THE FIBER TIP - FORMULATION OF ABCD MATRIX AND EFFICIENCY COMPUTATION

From ray optics, we present a simple formulation of the ABCD matrix un der paraxial approximation for reflection and refraction of light beam s at a hyperbolic interface separating media of different refractive i ndices. Based on the formulated ABCD matrix for refraction by a hyperb olic interface, we report a simple theoretical investigation of the co upling efficiency of a laser diode to a single-mode fibre via a hyperb olic lens formed on its tip. Our results agree excellently with a rece ntly published experimental result and also with the theoretical findi ngs using quite involved phase distribution models. The analysis justi fies the correctness of the prescription of the said ABCD matrix and a lso the simplicity of efficiency calculation, executable even by a poc ket calculator, The technique will be useful in designing suitable mic rolenses employing laser micromachining technique.