Phase transitions in formation of spatially coherent laser beams

The results are reported of an investigation of the changes in the spatial coherence (correlation) radius $r_c$ and radiation intensity $I$ on approach to the laser threshold. It is shown that their behavior obeys the laws $r_c\propto(\delta-\delta_{\text{th}})^{-\alpha}$ and $I\propto(\delta-\delta_{\text{th}})^{-\beta}$ where $\delta_{\text{th}}$ is the threshold value of the losses at which stimulated emission begins; $\alpha$ and $\beta$ are the critical exponents. It is reported that measurements carried out on an He–Ne laser give $\alpha=0.49\pm0.05$ and $\beta =0.9\pm0.2$. These values of $\alpha$ and $\beta$ are in agreement with the theory of formation of spatially coherent beams in lasers based on the wave approach ($\alpha=0.5$, $\beta=1.0$). The agreement of the experimental results with the Landau theory of phase transitions of the second kind is discussed.