Microwave response of hole and patch arrays

The electromagnetic response of two-dimensional square arrays of perfectly conducting square patches, and their complementary structures, is modeled utilizing a modal matching technique and employing Babinet’s principle. This method allows for the introduction of progressively higher diffracted orders and waveguide modes to be included in the calculation, hence aiding understanding of the underlying causal mechanism for the observed response. At frequencies close to, but below, the onset of diffraction, a near-complete reflection condition is predicted, even for low filling fractions: conversely, for high filling fractions a near-complete transmission condition results. These resonance phenomena are associated with evanescent diffraction, which is sufficiently strong to reverse the step change in transmission upon establishment of electrical continuity; i.e., the connected structure demonstrates increased transmission with increasing filling fraction.

Figure 1

Schematic showing: (a) investigated system; structure A and its complementary system ${\text{A}}^{\ast }$; (b) defined regions (I–III) of the system used by the modal matching method.

Figure 2

(Color online) (a) Comparison between modal matching model with third family of evanescent orders in the calculation, compared to a full solution FEM model for structure ${\text{A}}^{\ast }$ with $a=3\text{mm}$ and $d=10\text{mm}$. (b) Comparison between modal matching model data after application of Babinet’s principle with a full solution FEM model for structure A with $a=3\text{mm}$ and $d=10\text{mm}$.

Figure 3

(a) Schematic of dipole array description showing the regions of enhanced $\mathit{E}$ field for structure A; (b) $\mathit{E}$ field plots using a commercial FEM program (Ref. 27) 8 mm below the structure showing the $\mathit{E}$ field enhancement for structure A with the incident $\mathit{E}$ field polarized along the $y$ axis illustrating the domination of scattering from the $\left(0,k_g\right)$ grating.

Figure 4

(a) Schematic of surface current description showing the regions of enhanced $\mathit{H}$ field for structure ${\text{A}}^{\ast }$ (b) $\mathit{H}$ field plots using a commercial FEM program (Ref. 27) 8 mm below the structure showing the $\mathit{H}$ field enhancement for structure ${\text{A}}^{\ast }$ with the incident $\mathit{E}$ field polarized along the $x$ axis illustrating the domination of scattering from the $\left(m,0\right)$ grating.

Figure 5

Dispersion plots using the modal matching model for the transmission for TM and TE polarizations for structures A and ${\text{A}}^{\ast }$ with $a=6\text{mm}$ and $d=10\text{mm}$. The complementary nature of the responses between the two arrays is clearly evident.

Figure 6

(Color online) (a) Schematic of the modified structure B and its complementary system ${\text{B}}^{\ast }$ and (b) transmission through structure ${\text{B}}^{\ast }$ at normal incidence as a function of metal filling fraction for 13 and 35 GHz.