Coupling of a laser diode to single mode circular core trapezoidal index fiber via hyperbolic microlens on the fiber tip and construction of empirical relations to determine the optimum back focal length

The fiber tip based hyperbolic microlens coupling efficiency of circular core trapezoidal index single mode fiber and a laser diode is theoretically studied. The corresponding analytical expressions are formulated considering ABCD matrix for hyperbolic microlens following paraxial approximation and also Gaussian field distributions are considered for both the source and the fiber. Here, we study for two different light-emitting wavelengths of practical importance for such fibers. Then, we construct simple empirical formulations to find out the optimum back focal length as function of normalized frequency and aspect ratio of such fibers for optimal excitation of fiber. These handy relations should guide system designer in designing hyperbolic microlens directly on the tip of such fiber carrying the information signal with no need of dependence on rigorous methods to estimate the optimum back focal length.