Substituting scheme for nonlinear couplers:: A group approach -: art. no. 033808

We consider a substituting scheme for nonlinear optical couplers operating by means of degenerate parametric down-conversion with strong coherent pumping. The proposed scheme, which provides the same unitary input-output transformation as the original coupler, consists of simple linear and nonlinear optical devices: beam splitter and optical parametric amplifiers. Using a group-theoretical approach, we find analytical formulas for parameters of these optical elements. The scheme allows us to get a better insight into the coupler behavior, because the complex dynamics of the coupler is transformed into a sequence of simpler evolutions governed by the beam splitter and parametric amplifiers, whose properties are well known and understood. We demonstrate that various dynamical regimes of the coupler are clearly reflected by the substituting device.