Design of optical coupling systems between two-dimensional quasi-stadium laser diodes and single-mode optical fibers

Optical coupling systems between a two-dimensional quasi-stadium laser diode and single-mode optical fibers using gradient-index rod lenses are designed for both stable and unstable laser resonators for the first time. A novel numerical approach using a combination of the extended Fox-Li calculation method and Gaussian beam transformations is proposed. In the case of a stable laser resonator, two kinds of beam propagation modes appear, namely the axis mode, in which an optical beam propagates along the cavity axis, and the ring mode, in which optical beams propagate along the diamond-shaped trajectory. The coupling efficiencies are found to be 54% for the axis mode and 52% for the ring mode. In contrast, an unstable laser resonator exhibits complicated modes, in which several highly directional beams are emitted from the end mirrors. The total coupling efficiency for these output beams is calculated to be 9.6%. The 3-dB tolerances for the lens pitch and alignment angles of the gradient-index rod lenses are also discussed.