AN EXACTLY SOLVABLE MODEL FOR NONLINEAR RESONANT SCATTERING

The interaction of radiation with an open resonator is known to result in highly sensitive frequency dependence of the response field. This resonant behavior in the lin-ear setting has been analyzed theoretically in a variety of continuous and discrete systems (e.g., [1], [2], [3]). When nonlinearity is introduced into the structure, bista-bility emerges [4]. This means that the system admits multiple responses to the same exterior source field, at a fixed frequency and intensity. The purpose of this work is to provide an exactly solvable model in which bistability can be demonstrated analytically. Specifically, we study the effects of introducing nonlinearity into a system that, in the linear setting, exhibits resonance due to the pertur-bation of a system with an embedded eigenvalue. The Mode