Astigmatism and spontaneous emission factor of laser diodes with parabolic gain

An explicit relation between the astigmatism and the spontaneous emission factor of gain guiding lasers has been derived with the assumption that the gain profile can be approximated to be a parabola or that the lowest order mode in the cavity is approximately Gaussian. The maximum value of the spontaneous emission factor is shown to be √2 if index guiding is dominant. Beyond K=√2, where gain guiding is dominant in this region, the astigmatism decreases with the spontaneous emission factor. It is also shown that the spontaneous emission factor of the gain guiding lasers does not much exceed ten and this conclusion has been confirmed experimentally for those whose stripe widths are larger than 4 μm.