Abstract
We report here the first theoretical prediction of coupling efficiency of the laser diode to single-mode graded-index fiber coupling via cylindrical microlens on the tip of the fiber in presence of possible transverse and angular mismatches. Moderately efficient cylindrical microlens on the fiber is easily fabricable and graded-index fiber has less sensitivity to macro as well as micro bending. Thus this coupling device emerges as a potential candidate in the field of coupling optics. The analysis takes into consideration the allowable aperture provided by cylindrical microlens. Further, we shall consider here the coupling in the vertical plane only since the coupling in the horizontal plane has poor performance. Using the relevant ABCD matrix of refraction for a cylindrical lens in the vertical plane, we prescribe analytical expressions of the coupling efficiencies in presence of said kinds of misalignments. In our analysis, we use Gaussian field distribution for both the laser and fiber fields. We carry on our investigation for two commonly used wavelengths namely 1.3 and 1.5 µm. As an example of graded-index fiber, we use some typical step, parabolic, and triangular index fibers in our study. The execution of the prescribed formulations involves little computation. Thus the evaluation of the concerned coupling efficiencies is very much user friendly. The present analysis surfaces the tolerance factors of the coupling devices. Accordingly, the results will prove beneficial to designers and packagers in respect of the design of such coupler involving cylindrical microlens in the field of optimum launch optics.
