This book describes two categories of work, i.e., the finite-difference full-vectorial beam propagation method (FD-FV-BPM) development and microlens design for single-mode fiber (SMF) to laser diode (LD) coupling. Chapter 2 gives a review of the general formula to solve the FV-BPM equation of electric formula by using the FD method. The FD-FV-BPM based eigenmode solver is then successfully employed to investigate the effective index of the fundamental modes in an air-filled silica index-guiding photonic crystal fiber. Chapter 3 presents an improved FD-FV-BPM for arbitrary optical waveguides simulation with a dramatic improvement in accuracy. In Chapter 4, an improved wedge-shaped fiber design is presented for coupling 980nm pump LDs to SMFs. In Chapter 5, a tapered and hemispherically-ended graded-index fiber (GIF) structure is demonstrated for the coupling between SMFs and 1330nm or 1550nm LDs. In Chapter 6, an ideal microlens profile for flatting the equiphase distribution of a Gaussian laser beam is obtained analytically by a design tool based on the combination of Gaussian beam theory and ray optics.