Laser diode to single-mode triangular index fiber coupling via upside down tapered hyperbolic microlens on the fiber tip: Prediction of coupling efficiency by ABCD matrix formalism

Abstract

We prescribe ABCD matrix of transmission relating to the upside down tapered hyperbolic micro lens drawn from the end of single-mode circular core triangular index fiber. The said prescription takes care of the refractive index profile in the tapered region, the ray trace equation and also the refraction formula at a hyperbolic interface. The analysis will also be helpful for the design of micro-optic image systems. Using the prescribed ABCD matrix of transmission, we formulate analytical expression for the coupling efficiency and employ it for prediction of the coupling optics. Here, we assume Gaussian distributions of the fields for both the source and the fiber. The execution of our formulation involves little computation and as such it is user friendly. We investigate the launch optics for two commonly used wavelengths such as 1.3 μm and 1.5 μm. This simple but accurate formalism will immensely benefit the designers and packagers concerned with launch optics.