Photonic zero-energy modes in a metal-based Lieb lattice

Abstract

We design a photonic tight-binding system using the dispersive background, and observe the noncompact photonic zero-energy modes for both monopole and dipolar states in a finite Lieb lattice with flat truncations. In such a photonic Lieb system, the compact localization of s, p, and d flat bands is also checked. We show that this photonic zero-energy mode is provided by one dispersive band for singular touching, which has the same frequency with the flat band states. Specially, the zero-energy mode can be completely excited by merely one point source at the flat band frequency, covering all the minority sites and forming a noncompact state. This work may provide a deep understanding about the photonic zero-energy mode for higher order states in the Lieb or other flat band models.