The output linewidth and the electrical-to-optical power conversion efficiency of a grating-feedback external-cavity diode laser are directly related to the coupled optical power which is fed back into the laser cavity by the diffraction grating. This coupled power not only relies on the first-order grating reflectivity but also on the back-coupling efficiency which ultimately determines how much feedback optical power can couple into the diode laser cavity. It is qualitatively shown that the change in the collimating lens position could contribute significantly to the output linewidth in experiment. In this paper, the influence of the misaligned collimating lens on the back-coupling efficiency is numerically simulated and analyzed based on the beam coupling theory and ray transfer matrix theory. The results indicate that the distance from the lens to grating has little effect on the back-coupling efficiency, and the back-coupling efficiency reaches the maximum value when the diode laser front-facet is separated from the lens by the lens focal length. Meanwhile, it is found the back-coupling efficiency remains almost unchanged while the lens is tilted with respect to the axis perpendicular to opitcal aixs at small angle. Beside, the relationship between the coupling efficiency and the lens lateral displacement is also analysized and discussed.
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