Conical diffraction and gap solitons in honeycomb photonic lattices.

We study wave dynamics in honeycomb photonic lattices, and demonstrate the unique phenomenon of conical diffraction around the singular diabolical (zero-effective-mass) points connecting the first and second bands. This constitutes the prediction and first experimental observation of conical diffraction arising solely from a periodic potential. It is also the first study on k space singularities in photonic lattices. In addition, we demonstrate "honeycomb gap solitons" residing in the gap between the second and the third bands, reflecting the special properties of these lattices.