The exploration of photonic systems embracing the concept of parity-time ($\mathcal{PT}$) symmetry has become highly active in recent years. Studies on this topic potentially have significant technological implications, enabling unidirectional transmission in optical systems with unusual states of light. Here, we investigate the existence of a flat band in a two-dimensional photonic crystal and the consequences in the context of $\mathcal{PT}$ symmetry. The flat band is ascribed to a pair of two dipolar states and a monopolar state, which is verified by the proposed coupled mode equations. This flat band is protected by the interactions of these three states; therefore it has tremendous potential to investigate the localized stationary eigenstates, and gives rise to intriguing modulations under the perturbation of gain and loss. Especially, gain-loss configurations predominantly act on the coupling behavior of originally orthogonal states, including thresholdless $\mathcal{PT}$ transition, absence, and emergence of $\mathcal{PT}$ transition. The gain-loss configurations, together with the flat band, determine the peculiar band structures and the resultant interesting transmission phenomena. By means of coupled mode equations, we disclose the dynamics upon the perturbation of the gain and loss and the wave vector, and show various transmission modulations including unidirectional behavior.

• Received 28 May 2018

DOI:https://doi.org/10.1103/PhysRevA.98.043844