Broadband Slow Light Metamaterial Based on a Double-Continuum Fano Resonance

We propose a concept of a low-symmetry three-dimensional metamaterial exhibiting a double-continuum Fano (DCF) optical resonance. Such metamaterial is described as a birefringent medium supporting a discrete dark electromagnetic state weakly coupled to the continua of two nondegenerate bright bands of orthogonal polarizations. It is demonstrated that light propagation through such DCF metamaterial can be slowed down over a broad frequency range when the medium parameters (e.g., frequency of the dark mode) are adiabatically changed along the optical path. Using a specific metamaterial implementation, we demonstrate that the DCF approach to slow light is superior to that of the electromagnetically induced transparency because it enables spectrally uniform group velocity and transmission coefficient.

Figure 1

(a) Band structure of DCF metamaterial as predicted by the analytical model of coupled oscillators [see Eqs. (1, 2)]. Different line styles correspond to the reduction of the spatial symmetry of a metamaterial: from two mirror-symmetry planes (solid line) to none (dashed line). (b) Broadband SL: the medium is comprised of multiple layers of DCF metamaterials with spatially varying resonance frequency ${\Omega }_Q$ in the ${\omega }_0-\Delta \omega <{\Omega }_Q<{\omega }_0+\Delta \omega$ range. The incoming light undergoes polarization transformation and is slowed down.

Figure 2

PBS for SL metamaterials based on the DCF resonance (a) and on the EIT (b). The insets show the geometry and dimensions of the unit cell and the three supported resonances: (i) horizontal dipole, (ii) vertical dipole, and (iii) the quadrupole. Solid lines: PBS computed for a symmetric unit cell ($s_x=0$ and $s_y=0$). (a) Propagation bands for DCF-based metamaterial (dashed lines): $s_x=700\mathrm{nm}$, $s_y=2\mu \mathrm{m}$, $L_1=2\mu \mathrm{m}$. The avoided crossings marked (1, 2) are caused by $s_y\ne 0$ and $s_x\ne 0$, respectively. (b) Propagation bands for the EIT-based metamaterials (dashed lines) with partial symmetry breaking ($s_x=0\mathrm{nm}$, $s_y=500\mathrm{nm}$, $L_1=3.8\mu \mathrm{m}$): emergence of SL for the spectrally narrow middle band. For (a) and (b): $t=400\mathrm{nm}$, $h=400\mathrm{nm}$, $L_2=4\mu \mathrm{m}$, $w=800\mathrm{nm}$, $g=2.2\mu \mathrm{m}$. The metamaterial’s periodicities are $6\mu \mathrm{m}\times 7\mu \mathrm{m}\times 7\mu \mathrm{m}$, and the electromagnetic waves are assumed to propagate in the $z$ direction.

Figure 3

Field enhancements of four different frequency components propagating in an adiabatically varying DCF-based metamaterial. Inset: single-layer unit cell. Spectral position of the SL is adiabatically varied: $L_2[\mu \mathrm{m}]=3.75+z/700$. Field intensity is calculated at the red circle shown in the inset. Other parameters: $s_y=L_2/4$, $w=t=0.8\mu \mathrm{m}$, $g=2.7\mu \mathrm{m}$, and $\mathrm{\text{gap}}=1.7\mu \mathrm{m}$.

Figure 4

Transmission (solid green lines), absorption (dashed red lines), and group velocity (solid blue lines) of (a) adiabatic DCF-based and (b) EIT-based metamaterials. $x$-polarized incident light is assumed. Parameters of the DCF-based metamaterial: the same as in Fig. 3. The EIT-based metamaterial is made of 20 identical layers shown in Fig. 2, with the parameters $L_2=4\mu \mathrm{m}$, $L_1=3.8\mu \mathrm{m}$, $w=t=0.8\mu \mathrm{m}$, $g=2.7\mu \mathrm{m}$, $h=0.9\mu \mathrm{m}$, $s_y=0.6\mu \mathrm{m}$, and periodicity $L_x=L_y=L_z=7\mu \mathrm{m}$.