Waveguide characteristics of beam-expanders integrated with laser diodes were numerically analyzed by the beam propagation method (BPM) or the finite-difference time-domain (FD-TD) method. It was demonstrated that the vertically and horizontally hybrid tapered structure or an optimized refractive index in the cladding layer improve the trade-off relationship between fiber coupling efficiency and lasing characteristics. It was also demonstrated that exponentially tapering stripe width can reduce device length without sacrificing device properties.