The effect of misalignment on the coupling optics involving laser diode and single-mode triangular index fiber with an upside down tapered hyperbolic microlens on its tip

This article contains theoretical investigation of the performance of the coupler comprising laser diode and mono-mode circular core triangular index fiber (TIF), which contains on its tip an upside down tapered hyperbolic microlens (UDTHM). Here, we take care of probable angular and transverse mismatches. In our derivation, we use the refractive index distribution in the tapering area, the ray equation, and the relation involving refraction by hyperbolic microlens. We report analytical formulation of coupling efficiencies in the presence of specified types of misalignments using a relevant ABCD refraction matrix for a UDTHM in the vertical plane. In the fields of lasers and fibers, we use Gaussian field distribution in our analysis. Our research is based on two widely employed wavelengths, 1.3 µm and 1.5 µm. In this study, we used three TIF with V numbers of 4.380, 3.511, and 1.924, respectively. Little computation is required to execute the prescribed formulations. This study surfaces the sensitivity of the coupler in presence of the aforementioned types of offsets. The found results will prove valuable to manufacturers working in the domain of UDTHM.