Dielectric sensing in $ϵ$-near-zero narrow waveguide channels

We exploit here the dramatic field enhancement caused by energy squeezing and tunneling (i.e., “supercoupling”) in metamaterial-inspired ultranarrow waveguide channels with near-zero effective permittivity in order to sense small permittivity variations in a tiny object. The supercoupling effect is accurately modeled analytically and closed-form expressions are derived to describe the presence of defects or permittivity perturbations along the channel. Applications for tailoring its pass-band frequency and for high-$Q$ sensing are proposed at microwave frequencies.

Figure 1

(Color online) Geometry of the structure proposed as a permittivity sensor. The two input and output rectangular waveguides are connected via an ultranarrow channel (shown in blue). In the middle, an object (i.e., a cavity region) with permittivity ${ϵ}_{\text{cav}}$ different from that of the channel is inserted. The structure is all surrounded by conducting walls.

Figure 2

(Color online) Transmission coefficient for the U channel of Fig. 1 with $L=127\text{mm}$, $b=2a=101.6\text{mm}$, $ϵ=2{ϵ}_0$, and ${ϵ}_{\text{ch}}={ϵ}_0$: (a) $a_{\text{ch}}=a/64$, $L_{\text{cav}}=L/10$; (b) $a_{\text{ch}}=a/16$, $L_{\text{cav}}=L/10$; and (c) $a_{\text{ch}}=a/64$, $L_{\text{cav}}=L/5$. Solid lines: full-wave simulations (Ref. 12); dashed lines: TL model.

Figure 3

(Color online) Variation of (a) the ENZ-related tunneling frequency and (b) the ENZ-related transmission coefficient at the channel’s cutoff frequency $f=1.48\text{GHz}$ vs normalized ${ϵ}_{\text{cav}}$ for the geometries of Fig. 2.

Figure 4

(Color online) Normalized (a) electric-field $E_y$ and (b) magnetic-field $H_x$ distributions [real (solid) and imaginary (dashed) part] on the bottom plate of the waveguide at the tunneling frequencies $f=1.327\text{GHz}$ and $f=1.206\text{GHz}$, respectively, for the geometries of Figs. 2a, 2c with ${ϵ}_{\text{cav}}=3{ϵ}_0$. The channel region is highlighted in the plots.