Photonic band gap of a graphene-embedded quarter-wave stack

Here, we present a mechanism for tailoring the photonic band structure of a quarter-wave stack without changing its physical periods by embedding conductive sheets. Graphene is utilized and studied as a realistic, two-dimensional conductive sheet. In a graphene-embedded quarter-wave stack, the synergic actions of Bragg scattering and graphene conductance contributions open photonic gaps at the center of the reduced Brillouin zone that are nonexistent in conventional quarter-wave stacks. Such photonic gaps show giant, loss-independent density of optical states at the fixed lower-gap edges, of even-multiple characteristic frequency of the quarter-wave stack. The conductive sheet-induced photonic gaps provide a platform for the enhancement of light-matter interactions.

Figure 1

Schematic of the graphene-embedded photonic crystal in investigation: high-index ($\sqrt{{\epsilon }_h}$), low-index ($\sqrt{{\epsilon }_l}$) dielectric layers with thicknesses $d_h$ and $d_l$ are separated by graphene sheets (black lines); all are lying on the $xy$ plane, and light propagates along the $z$ direction.

Figure 2

Comparison of the complex band structures of (a) a conventional quarter-wave stack, and of (b) a graphene-embedded quarter-wave stack. (c) The density-of-optical states (DOS) of the graphene-embedded quarter-wave stack corresponding to Fig. 2b.

Figure 3

Spectra of the trace of the transfer matrices for a conventional quarter-wave stack and a graphene-embedded quarter-wave stack.

Figure 4

Density-of-optical states (DOS) spectra of graphene-embedded quarter-wave stacks by changing the collision frequency (in units of ${\gamma }_0$, ${\gamma }_0=2$ THz) with other quantities of the graphene sheets as stated above.

Figure 5

Electric fields (amplitude) of eigenmodes at the lower-gap edges of the first (5.0 THz, upper panel) and the second (10.0 THz, lower panel) graphene-induced gaps of the graphene-embedded quarter-wave stack are plotted for the unit cell (blue dashed box in Fig. 1).