Based on the prescribed ABCD matrix for the transmission of paraxial rays, we analyze theoretically laser diode to single mode graded index fiber excitation via an upside-down tapered parabolic microlens on the fiber tip. In this context, we use some typical step, parabolic and triangular index fibers. The ABCD transformation matrices for upside down tapered parabolic microlens on the tips of step-index, triangular-index and parabolic-index fibers are employed in our analysis. In this formalism, we employ Gaussian field distributions for both the source and the fiber. In our study, we use here two different laser diodes emitting wavelengths 1.3 μm and 1.5 μm respectively. The execution of the prescribed formalism requires little computation. Such formalism is expected to generate tremendous interest for study of coupling optics related to such kind of coupler. © 2019