Optimize design of the parabolic gradient-index coupling lens for a laser diode to single-mode fiber

In this paper,we theoretically study the optimize design of the parabolic gradient-index lens used as laser diode to single mode fiber coupling lens. In order to enhance the coupling efficiency between the LD and the SMF, we have calculated the aberration (longitudinal spherical aberration (LSA), offense against sine condition(OSC))and optimized the parameter of the parabolic gradient-index coupling lens by solving the ray equation with the standard Runge-Kutta method. From analysis of the parabolic GRIN coupling lens, it turns out as follow: i) axis GRIN constant L can affect the aberration, ii)the plane-convex parabolic GRIN coupling lens with small end towards LD is the best design, iii) we obtain groups of optimized biplane,plane-convex parabolic GRIN coupling lens.