We predict a novel type of cavity solitons, Bloch cavity solitons, existing in nonlinear resonators with
the refractive index modulated in both longitudinal and transverse directions and for both focusing (at
normal diffraction) and defocusing (at anomalous diffraction) nonlinearities. We develop a modified
mean-field theory and analyze the properties of these novel cavity solitons demonstrating, in particular,
their substantial narrowing in the zero-diffraction regime
