Disorder-Induced Topological State Transition in Photonic Metamaterials

The topological state transition has been widely studied based on the quantized topological band invariant such as the Chern number for the system without intense randomness that may break the band structures. We numerically demonstrate the disorder-induced state transition in the photonic topological systems for the first time. Instead of applying the ill-defined topological band invariant in a disordered system, we utilize an empirical parameter to unambiguously illustrate the state transition of the topological metamaterials. Before the state transition, we observe a robust surface state with well-confined electromagnetic waves propagating unidirectionally, immune to the disorder from permittivity fluctuation up to 60% of the original value. During the transition, a hybrid state composed of a quasiunidirectional surface mode and intensively localized hot spots is established, a result of the competition between the topological protection and Anderson localization.

Figure 1

(a) Equal frequency surfaces of a chiral hyperbolic metamaterial. (b) Cross section of the equal frequency surfaces at $k_y=0$. The blue solid line corresponds to the surface states. (c) The spatial distribution of ${\epsilon }_i^d$ in the $x\text{−}y$ plane for ${\sigma }_i=0$, 1, 2, 4, separately.

Figure 2

(a)–(e) Normalized $E_z$ in the disorder-perturbed metamaterial for different values of $\sigma$. (f)–(j) The corresponding intensities of the field $I=|\mathbf{E}{|}^2$ for different values of $\sigma$.

Figure 3

The topological state transition induced by the disorder in the permittivity at $k_z=1.5k_0$.

Figure 4

The hybrid states for (a) localization $A$ and (b) localization $B$. The magenta arrows are the normalized Poynting vectors. The white scale bar corresponds to the wavelength in vacuum.

Figure 5

Disorder-induced topological state transition for different $k_z$.