Shockley and Tamm surface states in photonic crystals

Existence of the Shockley surface states in photonic crystals is demonstrated for the first time. We show that in photonic crystals, the surface states of defect chain with unit cell containing one defect are the Tamm rather than Shockley states as commonly assumed. The Shockley states can appear only in the defect chain with unit cell containing more than one defect. We first analyze the surface states using the tight-binding theory. Theoretical predictions are confirmed by the numerical simulations.