Laser diode to single-mode triangular-index fiber excitation via upside down hemispherical microlens on the fiber tip: Prescription of ABCD matrix of transmission and estimation of coupling efficiency

We briefly introduce the upside-down taper lens drawn from the end of single-mode circular core triangular-index fiber and analyse it. Based on paraxial approximation, we formulate ABCD transformation matrix of such fiber end. The said prescription involves modelling of refractive index profile in tapered region, ray trace equation and also the ray refraction formula at a spherical surface. The analysis can be employed for design of micro-optic image systems and also for study of coupling optics involving such tapered lensing device. Employing the prescribed ABCD matrix of transmission, we formulate analytical expression for coupling efficiency and employ them to predict the concerned coupling optics. In this context, Gaussian field distributions for both the source and the fiber are assumed. In our present study, we use two practical wavelengths namely 1.3 μm and 1.5 μm. This simple but accurate method will prove beneficial to the designers and packagers working with the field of launch optics.