An approximate analytical model is developed for calculating the out-of-plane coupling efficiency between an elliptical Gaussian beam from a laser diode and an angled single-mode fiber. The simulation results obtained from the model indicate that when a laser diode has no tilt the coupling efficiency varies with relative rotation angle at a period of \pi rather than remains constant, and the period changes from \pi toward 2\pi as the tilt angle of laser diode increases. A proof-of-principle experiment is performed to demonstrate the validity of the model as the elliptical factor becomes large. Potential applications by employing the model are discussed.
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