Frequency tunable terahertz metamaterials using broadside coupled split-ring resonators

We present frequency tunable metamaterial designs at terahertz (THz) frequencies using broadside coupled split-ring resonator (BC-SRR) arrays. Frequency tuning, arising from changes in near-field coupling, is obtained by in-plane displacement of the two SRR layers. For electrical excitation, the resonance frequency continuously redshifts as a function of displacement. The maximum frequency shift occurs for vertical displacement of half a unit cell, resulting in a shift of 663 GHz (51% of $f_0$). We discuss the difference in the BC-SRR response for electrical excitation in comparison to magnetic excitation in terms of hybridization arising from inductive and capacitive coupling.

Figure 1

The BC-SRR orientations and dimensions. The BC-SRR under (a) electrical and (b) magnetic excitation. (c) Vertically and (d) horizontally shifting between two layers. (e) Dimensions for a single SRR layer, which forms a BC-SRR structure in (f). $P=60$ μm, $l=40$ μm, $w=11$ μm, $g=5$ μm, substrate thickness ($t_{\mathrm{sub}}=5$ μm), and superstrate thickness ($t_{\mathrm{super}}$ $=$ 5 μm).

Figure 2

Hybridization in broadside coupled SRRs. Top panel: For single SRRs within a unit cell, the magnetically and electrically excited modes are degenerate. The broadside configuration leads to hybridization removing the degeneracy, leading to an increase (decrease) in the resonance frequency for electric (magnetic) excitation. Lower panel: Full-wave calculations of the transmission for demonstrating splitting of the resonances for BC-SRRs. The dimensions used for the simulation are listed in Fig. 1.

Figure 3

Schematic views of the surface charge distributions and their corresponding surface current distributions for (a) magnetically and (b) electrically excited BC-SRR structures. The top and bottom layers are shown displaced for clarity.

Figure 4

(a) Optical microscope pictures of BC-SRR structures shifted along the vertical direction for 0 (no shift), 15, and 25 μm. (b) Simulation and (c) experimental results for transmission characteristics of BC-SRR structures shifted along the vertical direction for 0, 5, 10, 15, 20, 25, and 30 μm.

Figure 5

Broadband transmission of shifted BC-SRR arrays for electrical excitation. The transmission curves were simulations in steps of 0.5 μm from 0 to 30 μm. In addition, the overlaid crosses represent the −10 dB points from experiment. In contrast to Fig. 5 of Ref. 24, we excite only a single mode in these arrays. The second mode, if present, would mirror the behavior about the line ω/ω${}_0$ $=$ 1 [i.e., it would start near (ω/ω${}_0$ $=$ 0.6, shift/period$=$ 0) and curve up and toward the right (ω/ω${}_0$ $=$ 1.3, shift/period $=$ 0.5)]. The figure is plotted in dB for clarity.