  We investigate linear and nonlinear evolution dynamics of light beams
propagating along a dislocated edge-centered square lattice. The band structure
and Brillouin zones of this novel lattice are analyzed analytically and
numerically. Asymmetric Dirac cones as well as the corresponding Bloch modes of
the lattice are obtained. By adopting the tight-binding approximation, we give
an explanation of the asymmetry of Dirac cones. By utilizing the appropriate
Bloch modes, linear and nonlinear asymmetric conical diffraction is
demonstrated. We find that both the focusing and defocusing nonlinearities can
enhance the asymmetry of the conical diffraction.
