Ikeda instability and transverse effects in nonlinear ring resonators

By analogy to the modal theory of optical bistability we develop a simple model for the study of Ikeda instability in the Kerr-type nonlinear ring cavity. Our approach leads, in the plane-wave approximation, to a complete analytical description of the period-two attractor of the system. The simplicity of our developments allows us to include the transverse dimension of the cavity in the model. An analytical study of the role of diffraction in the onset of period-doubling instabilities is proposed. A parallel is drawn between period doubling and optical bistability in nonlinear resonators with special emphasis on the physical process of transverse modulational instability.