Near-field probes using double and single negative media

Evanescent probe imaging is a powerful characterization technique with subwavelength resolution. In this paper, we present a theoretical and numerical study of the effect of using double negative (DNG) and single negative (SNG) metamaterials in evanescent probe imaging. A sensitivity definition is introduced for evanescent probes and it is shown using quantitative measures that the sensitivity can be increased using DNG material for a target in vacuum and for a buried target. A minimum DNG thickness is required to achieve an improvement in the sensitivity. For a buried target, there is a fundamental limitation on the maximum achievable sensitivity, in addition to a limitation due to the loss of DNG materials. SNG metamaterials have similar improvements over the sensitivity as the DNG materials but there are additional limitations due to the different transmission characteristics of SNG media. To validate the theoretical findings, numerical simulations are presented.

Figure 1

(a) A generic probe is depicted by a cavity with a thin wire or tip coming out of it. (b) The probe is modeled as a transmission line with a certain terminal impedance. (c) A probe encountering a target is analogous to changing the terminal impedance of the transmission line, thus leading to a shift in S11.

Figure 2

The three components representing a generic probe: The resonator, the interface with the material to be interrogated (the interface is represented here as a short transmission line), and the probe medium, which is a volume containing all the electric and magnetic energies excited by the resonator in the presence of the target medium.

Figure 3

(Color online) The probe and target interaction is modeled by a plane wave in a multilayered structure. The incident field is assumed to be excited at $Z_1$, which represents the probe location. The last region is assumed to be an infinite half space.

Figure 4

(Color online) A DNG slab is inserted between the target medium and the field excitation.

Figure 5

(Color online) Sensitivity as a function of lens-to-target distance, for DNG thicknesses of $t$, $2t$, $3t$, and $4t$ $(t={\lambda }_0∕75)$. As the DNG thickness is increased, the sensitivity increases. The nonmagnetic target is $t$ thick with ${ϵ}_r$ of 6.

Figure 6

(Color online) The $\mathbf{H}$ field and $\mathbf{E}$ field energy differences normalized by the difference without any target, $\frac{{(U_m-U_e)}_{\text{with}\text{target}}}{{(U_m-U_e)}_{\text{without}\text{target}}}$, plotted as a function of the lens-to-target distance $t$. When there is no DNG layer the target reduces the difference. On the other hand, when there is a DNG layer the target increases the difference.

Figure 7

(Color online) The sensitivity as a function of normalized $k_x$. The inset shows that sensitivities of the fields with higher $k_x$ values experience better enhancements. Sensitivity improvement achieved by a DNG lens is defined as the sensitivity normalized by the sensitivity of the corresponding case without the DNG lens. The lens-to-target distance is $3t$ for all cases.

Figure 8

(Color online) Sensitivity vs target depth for a buried target. The target medium has a relative permittivity of 2 and the target has a permittivity of 6 with a thickness of $t$. The sensitivity is plotted for five different lens thicknesses.

Figure 9

(Color online) The sensitivity behavior for a lossy DNG case. Sensitivity is plotted as a function of the lens-to-target distance for DNG thicknesses of $10t$, $15t$, $16t$, $17t$, and $21t$. The target medium and the target have a relative permittivity of 2 and 6, respectively, and the target thickness is $t$. The DNG lens has an imaginary part of complex permittivity (loss tangent) equal to 0.2.

Figure 10

(Color online) The transmission coefficient as a function of normalized $k_x$ is plotted for SNG and DNG lenses. Both lenses have a thickness of $t$. The SNG lens exhibits a singularity at $k_x=121.3k_0$. The inset shows that before the singularity the SNG lens follows an amplification characteristic very similar to the DNG lens.

Figure 11

(Color online) Sensitivity vs target distance for a target medium and target having relative permittivity of 2 and 6, respectively, and a target thickness of $t$. The $5t$ SNG slab results in a sensitivity improvement similar to the DNG slabs. The $9.22t$ slab has a singularity when the target is at $1.5t$. The $20t$ slab reduces the sensitivity.

Figure 12

(Color online) The effect of the target on the $\mathbf{E}$ field distribution without (a) and with (b) a DNG layer. The upper panels show the field distributions when the lens-to-target distance is $4{\lambda }_0∕5$. The lower panels show the field distributions when the lens-to-target distance is ${\lambda }_0∕25$. The rectangular waveguide has a side length of ${\lambda }_0∕5$. The target thickness is ${\lambda }_0∕37.5$ and the lens thickness is ${\lambda }_0∕5$.

Figure 13

(Color online) Schematic showing a side view of the waveguide probe positioned on top of the aluminum plate having a crack. The SNG layer is positioned immediately at the opening of the waveguide.

Figure 14

(Color online) The phase shift due to a target along the centerline of the waveguide as a function of the SNG layer thickness.

Figure 15

(Color online) The image of the $1\mathrm{mm}$ crack generated by scanning the waveguide in the $xy$ plane: (a) with an $0.85\mathrm{mm}$ SNG layer having $-0.2$ loss tangent and (b) without an SNG layer.

Figure 16

(Color online) The 1D images with (a) $0\mathrm{mm}$, (b) $0.5\mathrm{mm}$, (c) $0.85\mathrm{mm}$, and (d) $1.4\mathrm{mm}$ SNG layers. All images are scaled with the same color map; black corresponds to $-0.5°$ and white corresponds to 3.2°.