Properties of a one-dimensional metallophotonic crystal

We analyze the structure of a periodic arrangement of optically thick metallic gratings that have very narrow slits. This structure permits perfect transmission of light in some frequency range and is analogous to a one-dimensional all-dielectric photonic crystal. Our study shows this structure has many unusual features due to evanescent modes. One of these is that its band diagram has flat bands at long wavelengths. Another feature is that this structure can enhance the fields locally. More significantly, we show that a manipulation of the positions of the slits on adjacent metal films produces lateral displacement along the grating surface for a transmitted beam of finite cross section. This shift is similar to the birefringence in crystal optics.

Figure 1

(Color online) Schematics of the geometry. Shown in each graph is a 3-layer example. (a) The slits are perfectly aligned, $l=0$. (b) The slits are displaced by a distance $l$ relative to previous layers.

Figure 2

(Color online) Band structure of infinite multilayered metal gratings with narrow slits perfectly aligned. The shaded area corresponds to passing bands, and white regions to stop gaps. The thick line indicates the light cone. $a=\frac{1}{7}$, $d=1$, $h=\frac{8}{7}$, and $s=\frac{4}{7}$. $d$, the lattice constant on the film, is the length unit.

Figure 3

The dispersion relation between $K$ and $\omega$ when $l=0$. The Bloch wave vector $K$ is in units of $\Lambda \equiv h+s$, the frequency $\omega$ is in units of $2\pi c∕d$, i.e., $K=\text{Block}\text{wave}\text{vector}\times \Lambda$, $\omega =d∕\lambda$. $a=1∕7$, $d=1$, $h=8∕7$, $s=4∕7$, and $l=0$.

Figure 4

Zeroth-order transmittance curves for normally incident light. $a=\frac{1}{7}$, $d=1$, and $h=\frac{8}{7}$. (a) Single layer. (b), (c), (d) Four layers. (b) $s=\frac{4}{7}$, $l=0$. (c) $s=\frac{2}{7}$, $l=0$. (d) $s=\frac{2}{7}$, $l=0.3$. Capital letters label the transmittance peaks.

Figure 5

Contour plot of the intensity of electric fields for normally incident light for two layers of metal films (shown as gray shaded regions). The electric field amplitude of the incident light is 1. (a) at the resonance frequency $\omega =0.388$ (the first flat band). (b) at the resonance frequency $\omega =0.089$ (the lowest band). The strong field enhancement in the proximity of the entrance and exit of the slits are clearly seen. $a=\frac{1}{7}$, $d=1$, $h=\frac{8}{7}$, and $s=\frac{4}{7}$. The amplitude enhancement factor is $1∕f=d∕a=7$. The arrows indicate the orientations of the electric fields at each location.

Figure 6

Lateral displacement $d_x$ as a function of $k_x$ for four layers of metal films. The capital letter by each curve indicates the corresponding transmittance peak in Fig. 4. The gray curve $E$ has the same parameters as curve $C$ but with 8 layers, instead of 4 layers. Peaks $A$ and $A^{\prime }$, $B$ and $B^{\prime }$, $C$, and $D$ have similar behaviors, respectively.