title: Multicomponent cnoidal waves in cascade quasisynchronous frequency conversion.
abstract: It is shown that cascade quasisynchronous frequency conversion due to quadratic nonlinearity can be described in terms of an effective cubic nonlinearity. This enables one to reduce a four-mode interaction problem to solving a system of two coupled nonlinear Schrödinger equations for the amplitudes of the waves participating in both nonlinear processes. Exact analytic solutions of the corresponding system are found in the form of multicomponent cnoidal waves with components expressed through a sum and a difference of two similar fundamental solutions of the Lamé equation with shifted arguments. It is shown that solutions obtained in such a way enable one to optimize the conversion efficiency because of full coverage of the range of possible boundary conditions.
authors.affiliation: M.V. Lomonosov Moscow State University, Vorob'evy Gory, Moscow 119992, Russia.
authors.forename: V M
authors.initials: VM
authors.lastname: Petnikova
authors.forename: V V
authors.initials: VV
authors.lastname: Shuvalov