Nonlinear frequency conversion in coupled ring cavities

The steady-state distribution of circulating power in coupled, unidirectional ring resonators containing a diode-pumped laser crystal and nonlinear optical elements is computed. The full set of transcendental nonlinear equations describing the interactions between the circulating power and the optical elements is solved by a numerical root find function of a commercial mathematics software. The method allows computation of the output of sequential nonlinear processes such as laser gain, second harmonic generation and optical parametric amplification as a function of the input diode pump power. It is also possible to optimize the nonlinear interaction by selecting the optimum interaction cross-section or crystal length. The circulating power may thereby be re-distributed to obtain the lowest possible passive loss.