Three-dimensional crystals and localized structures in diffractive and dispersive nonlinear ring cavities

When diffraction operates together with chromatic dispersion, the type II second-harmonic generation exhibits a three-dimensional (3D) modulational instability leading to the formation of 3D periodic solutions travelling at the group velocity of light within the cavity. Numerical analysis reveals the occurrence of 3D localized structures in the form of isolated light drops or cylinders. They are specific to the parameter range where 3D stable periodic patterns coexist with the single homogeneous steady state.