Parametric patterns in optical fiber ring nonlinear resonators

We propose that parametrically excited patterns, also known as Faraday patterns, can be observed in nonlinear fiber resonators, where the coefficient of Kerr nonlinearity is periodically varying along the fiber in the resonators. We study the parametric instability analytically on the basis of the Floquet theory and also numerically by direct integration of the system. Instead of a classical Faraday wave excitation scenario, where modulation in time causes the formation of patterns in space, here we propose an inverted scenario, where the modulation in space excites the patterns in time.