Employing the prescribed ABCD matrix for refraction of paraxial rays by hemispherical lens, we derive analytical expression of efficiency of coupling of a laser diode to single-mode circular core dispersion-shifted as well as dispersion-flattened fiber via hemispherical microlens on the fiber tip. For the sake of simplicity, we assume Gaussian field distribution for both the source and the fiber. In our analysis, we also take care of limited aperture allowed by the hemispherical lens. The lens refracted spot size of the source, which is taken to be Gaussian, is matched with Petermann II spot size of the fiber for maximum coupling efficiency, since deviation from Gaussian nature of field for such fiber as per the recent design has to be taken care of. We carry out our study for two different wavelengths namely 1.3 μm and 1.5 μm. Our formalism is simple but accurate and executable easily requiring little computations. The results obtained by such user friendly method should benefit the designer of such coupling device in the field of optimum launch optics.
©2014 by Walter de Gruyter Berlin/Boston