Finite-difference full-vectorial beam propagation method development and microlens design for fiber to laser diode coupling

The first part of this work is related to the development of the finite-difference full-vectorial beam propagation method (FD-FV-BPM), which is one of the most popularly used simulation tools for optical waveguides and circuits design. Firstly, the general FD formula of the FD-FV-BPM is reviewed and demonstrated for computing the fundamental modes of an index-guiding photonic crystal fiber. The numerical accuracy and convergence behavior of the FV-FD-BPM for modal index calculation are detailedly investigated. Secondly, an improved FD-FV-BPM is introduced with a dramatic improvement in accuracy compared to the conventional methods. This method is developed based on the generalized Douglas scheme and novel FD formulas for the cross-coupling terms. The much higher accuracy is demonstrated by testing it on a strongly-guiding rib waveguide.; The second part of this work is related to microlens design for fiber to laser diode coupling. Three types of microlens design are developed, i.e., modified wedge-shaped fiber lens design for single-mode fiber to 980nm laser diode coupling, graded-index fiber taper design for single-mode fiber to 1350nm or 1550nm laser diode coupling, and ideal microlens design for flatting the equiphase distribution of a Gaussian laser beam. The first two of the three types of microlens design are demonstrated with a nearly 90% efficiency for fiber to laser diode coupling, while the lens profiles are simple and easy to fabricate. The third type shows a perfect and high-accuracy microlens profile, which is capable of completely flatting the equiphase distribution of a Gaussian laser beam even under long working distance (>500mum). The ideal microlens design enables a nearly 100% efficiency of fiber to laser diode coupling. All the designs are based on the accurate wide-angle BPM simulation.