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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 aGaussian laser beam is obtained analytically by a design tool based on the combination of Gaussian beam theory and ray optics.