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A tetragonal photonic crystal composed of high-index pillars can exhibit afrequency-isolated accidental degeneracy at a high-symmetry point in the firstBrillouin zone. A photonic band gap can be formed there by introducing ageometrical anisotropy in the pillars. In this gap, gapless surface/domain-wallstates emerge under a certain condition. We analyze their physical property interms of an effective hamiltonian, and a good agreement between the effectivetheory and numerical calculation is obtained.

Gapless surface states originated from accidentally degenerate quadratic band touching in a three-dimensional tetragonal photonic crystal