  A three-wave Budden model with two resonance layers is constructed that
allows recirculation of energy fluxes along a quadrangle in ray phase space.
The transmission, reflection, and conversion coefficients for this extended
Budden problem are calculated by ray phase-space methods and the
modular-eikonal approach. Analytical and numerical results show that all
coefficients exhibit interference effects that depend on an interference phase
calculated from the coupling constants and the area enclosed by the quadrangle.
