Metamaterial broadband angular selectivity

We demonstrate how broadband angular selectivity can be achieved with stacks of one-dimensionally periodic photonic crystals, each consisting of alternating isotropic layers and effective anisotropic layers, where each effective anisotropic layer is constructed from a multilayered metamaterial. We show that by simply changing the structure of the metamaterials, the selective angle can be tuned to a broad range of angles; and, by increasing the number of stacks, the angular transmission window can be made as narrow as desired. As a proof of principle, we realize the idea experimentally in the microwave regime. The angular selectivity and tunability we report here can have various applications such as in directional control of electromagnetic emitters and detectors.

Figure 1

Effective index for $p$-polarized light in an isotropic $\left(A\right)$ -anisotropic $\left(B\right)$ multilayer system. Left panel: all the layers have the same index. Right panel: the change in incident angle leads to a change in the index of the anisotropic $\left(B\right)$ material layers.

Figure 2

Metamaterial behavior. (a) Schematic illustration of a stack of isotropic-anisotropic photonic crystals. Layer $A$ is an isotropic medium; layer $B$ is an effective anisotropic medium consisting of two different isotropic media with dielectric constants ${\epsilon }_1$ and ${\epsilon }_2$. (b) $p$-polarized transmission spectrum for a 30-bilayer structure with $\{{\epsilon }_{\mathrm{iso}},{\epsilon }_1,{\epsilon }_2\}=\{2.25,10,1\}$, and $r=6.5$. The unit of $y$ axis—$a_1$ is the periodicity of the structure. (c) $p$-polarized transmission spectrum of three stacks of 30-bilayer structures described in part (b). The periodicities of these stacks form a geometric series $a_i=a_1{q}^{i-1}$ with $q=1.26$, where $a_i$ is the periodicity of the $i\text{th}$ stack. (d) $p$-polarized transmission spectrum of 30 stacks of 30-bilayer structures described in part (b). The periodicities of these stacks form a geometric series $a_i=a_1{q}^{i-1}$ with $q=1.0234$, where $a_i$ is the periodicity of the $i\text{th}$ stack.

Figure 3

Photonic band diagram of one-dimensional isotropic-anisotropic quarter-wave stacks. Modes that are allowed to propagate (so-called extended modes) exist in the shaded regions; no modes are allowed to propagate in the white regions (known as band gaps). The Brewster angles (defined in isotropic layers) are marked with a dashed line in each case.

Figure 4

Angular selectivity at oblique angles. Same materials and structure as illustrated in Fig. 2, $n=m=30$, and $q=1.0373$ but with different $r$. In (a), (b), and (c) we used ${\epsilon }_1=10,{\epsilon }_2=1$, and ${\epsilon }_{\mathrm{iso}}=2.25$. (a) $r=9$ and ${\theta }_B={24}^{\circ }$. (b) $r=11$ and ${\theta }_B={38}^{\circ }$. (c) $r=30$ and ${\theta }_B={50}^{\circ }$. (d) Dependence of the Brewster angle (coupled in from air) on $r$ for various values of ${\epsilon }_1$ and ${\epsilon }_2$. Solid and dashed lines correspond, respectively, to ${\epsilon }_2$ for air and ${\epsilon }_2$ for PDMS.

Figure 5

Experimental verification. (a) A schematic illustration of the experimental setup. (b) Photo of the fabricated sample. (c), (d) Comparison between $p$-polarized transmission spectrum of transfer matrix method and the experimental measurements.