We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as was studied recently in experiments for optically-induced photonic lattices [H. Trompeter et al., Phys. Rev. Lett. textbf{96}, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in a generic case of the Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, the higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.
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