Relation between the delay time and the tipping angle for superradiance
Xi‐an Mao, Jin-Hong Chen · Physical Review A · 1999
In optical superradiance studies, data were reported supporting a relation between the delay time $({\ensuremath{\tau}}_{D})$ and the tipping angle $({\ensuremath{\delta}}_{0}),$ ${\ensuremath{\tau}}_{D}=({\ensuremath{\tau}}_{R}/4)[\mathrm{ln}({\ensuremath{\delta}}_{0}/2\ensuremath{\pi}){]}^{2},$ where ${\ensuremath{\tau}}_{R}$ is the radiation damping time constant. We found that the same data also satisfy another relation, ${\ensuremath{\tau}}_{D}={\ensuremath{\tau}}_{R}\mathrm{ln}[\mathrm{cot}({\ensuremath{\delta}}_{0}/2)].$ The derivation of the two relations is reexamined. It is found that the former relation does not have sound theoretical background, and could lead to considerable errors when it is used to interpret experimental results.