The contour structures (first column) of 2D moiré optical lattices and the associated band-gap spectra (second column), photonic density of states (third column), the linear Bloch-wave within one unit cell. Contour geometries of periodic (a1, b1, c1) and aperiodic (d1) moiré optical lattices under different twisted angle: (a1) θ=atan(3/4), (b1) θ=atan(5/12), (c1) θ=atan(8/15), and (d1) θ=π=4. The associated band-gap spectra in the reciprocal lattice momentum space (a2, b2, c2, d2) and the photonic density of states (a3, b3, c3, d3). The first four linear Bloch waves (within a primitive lattice cell) of the moiré optical lattice under θ=atan(8/15). Yellow arrows in (a1, b1, c1) denote the primitive lattice vectors.