Reduced models and design principles for half-harmonic generation in   synchronously-pumped optical parametric oscillators
  We develop reduced models that describe half-harmonic generation in a synchronously-pumped optical parametric oscillator above threshold, where nonlinearity, dispersion, and group-velocity mismatch are all relevant. These models are based on (1) an eigenmode expansion for low pump powers, (2) a simulton-like sech-pulse ansatz for intermediate powers, and (3) dispersionless box-shaped pulses for high powers. Analytic formulas for pulse compression, degenerate vs. nondegenerate operation, and stability are derived and compared to numerical and experimental results. 
Ryan Hamerly, Alireza Marandi, Marc Jankowski, Martin M. Fejer,   Yoshihisa Yamamoto, and Hideo Mabuchi
physics.optics nlin.PS