Fig. 3: The gain effect in the vortex beam laser device at different crystallization ratios.

a Spectra of the background gain-dependent cavity quality factor at various \(j\). Increasing \({n}_{b}\) is used to mimic the uniform pumping produced by a gain-increasing process of InGaAsP microring. The \(Q\) factor is ~365 for the ring cavity without gain. The \(Q\) factor increases with the gain coefficiency by orders of magnitude, showing that the loss is compensated by the gain. Moreover, the inset shows a detailed enlarged image of the peak. b Characteristic frequency of the microring laser at various \(j\). The vortex beam laser is at the EP (\({n}^{{\prime} }={n}^{\prime\prime}=\) 0.01) with crystallization ratios of \(j=\) 0, 0.2, 0.4, 0.6, 0.8, and 1. The theoretical value is calculated by Eq. 5, and the simulated value is obtained by COMSOL Multiphysics simulation