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By employing Gaussian field distributions for both the source and the fiber and also the recently derived ABCD matrix for parabolic microlens, we investigate theoretically the coupling optics involving laser diode emitting practically interesting wavelengths of 1.3 mim and 1.5 mim and three elliptic core step index single-mode fiber via parabolic 3 microlens on the fiber tip in presence of possible transverse and angular misalignments. Elliptic core single-mode fiber has already emerged as a potential candidate in polarisation conserving fiber optic sensor, coherent fiber optical communication etc.. Our formalism is very simple in comparison to the other existing methods involving cumbersome numerical integrations. The results are extremely useful for assessing deeply the sensitivity of such coupler with reference to above kind of misalignments. Such analysis which as per our knowledge is the first theoretical investigation, will be extremely important for the design of optimum launch optics involving elliptic core single-mode fiber.