Electromagnetically-induced-transparency–like phenomenon with resonant meta-atoms in a cavity

We experimentally investigate a cavity in which two resonant meta-atoms are embedded. Its corresponding response spectrum to an incident microwave shows an electromagnetically-induced-transparency–like (EIT-like) phenomenon when the meta-atoms are arranged in the sequence node-antinode but not in the sequence antinode-node. We carry out in situ measurements of the cavity field to bring physical insight into this asymmetric response, and use the transfer matrix method joined with coupled-mode theory to give a quantitative analysis. Finally, we demonstrate the unidirectional EIT-like behavior in a two-port design. Our results may benefit novel nonreciprocal devices in the future by exploring the nonlinearity of the meta-atoms with this asymmetric arrangement.

Figure 1

(a) A sketch of one sample. The cavity and the meta-atoms are etched on the surface and fed by a $50\mathrm{\Omega }\mathrm{port}$. $R$ refers to a $50\mathrm{\Omega }$ resistor mounted into the connection. (b) Detailed configurations of the dark (bright) meta-atom with $w=0.2\mathrm{mm},g=0.2\mathrm{mm},a=5\mathrm{mm},b=10.25\mathrm{mm}$, and $s_1=0.8\mathrm{mm}$ $\left(s_2=0.1\mathrm{mm}\right)$. (c) The homemade instrument for the field measurements. (d) Detailed configurations of the $H$-field probe—a small loop with $c=4.5\mathrm{mm},h=3\mathrm{mm},f=0.4\mathrm{mm}$, and $d=0.5\mathrm{mm}$.

Figure 2

Reflection and field distribution for each sample (a)—(g). Left column: measured (black solid lines with symbol), simulated (blue dashed lines), and calculated (red solid lines) reflection spectra. Middle column: simulated magnetic field distributions in the plane $0.4$ mm above the upper surface of the samples at EIT frequencies. Right column: normalized results for the measured (black dots), simulated (blue dashed lines), and calculated (red solid lines) $H$-field distributions along the cavity at EIT frequencies. The corresponding structures are (a) the bare cavity, (b) the cavity with one meta-atom placed at node III, (c) the cavity with one meta-atom placed at antinode II, (d) the cavity with one meta-atom placed at antinode IV, (e) the cavity with two meta-atoms placed at III and IV, (f) the cavity with two meta-atoms placed at I and IV, and (g) the cavity with two meta-atoms placed at II and III.

Figure 3

The model of the structure for calculation has one port, a resistor $\left(R\right)$, and a cavity with meta-atoms (circles) in proper order. ${\mathrm{s}}_j^{\pm }$ refer to the forward (backward) wave in each part. ${\gamma }_1$ and ${\gamma }_2$ denote the scattering losses of the meta-atoms, while ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ give the dissipative losses. $M_{j\to j+1}$ and $D_j$ refer to the transmission matrices and propagation matrices of the corresponding parts, respectively.

Figure 4

Measured (black solid line with symbol), analytical (green solid line with symbol), and TMM calculated (red solid line) reflection spectra of the EIT and non-EIT structures.

Figure 5

(a) Photograph of the sample: a two-port cavity with two meta-atoms. The middle one is a bright meta-atom, while the left one is a dark meta-atom. (b) Simulated (line without symbol) and measured (line with symbol) reflection spectra for different incident directions (forward, F; backward, B). The inset shows the contrast ratio between the reflectance in forward and backward operation around the EIT frequency. (c) The $H$-field distributions when the wave enters in the forward and backward directions.