  Edge states of photonic crystals have attracted much attention for the
potential applications such as high transmission waveguide bends, spin
dependent splitters and one-way photonic circuits. Here, we theoretically
discuss and experimentally observe the deterministic edge states in
checkerboard photonic crystals. Due to the self-complementarity of checkerboard
photonic crystals, a common band gap is structurally protected between two
photonic crystals with different unit cells. Deterministic edge states are
found inside the common band gap by exploiting the Zak phase analysis and
surface impedance calculation. These edge states are also confirmed by a
microwave experiment.
