Gain circulation in multimode lasers

Self-organized collective behavior in globally coupled multimode lasers is investigated by introducing a new physical quantity, gain cirulation, that characterizes the gain transfer among lasing modes. Numerical simulations indicate that the self-organization is established such that the gain circultions in all the closed interaction paths involving arbitrary multiple lasing modes become neglibibly small as compared with direct mode-to-mode gain circulations. This implies that the nonreciprocal local (i.e., mode-to-mode) gain transfers are self-organized so as to ensure reciprocal average gain flow among modes approximately and that temporal evolutions of individual mode intensities are determined accordingly.