Spatially Shifted Beam Approach to Subwavelength Focusing

Although negative-refractive-index metamaterials have successfully achieved subwavelength focusing, image resolution is limited by the presence of losses. In this Letter, a metal transmission screen with subwavelength spaced slots is proposed that focuses the near-field beyond the diffraction limit and, furthermore, is easily scaled from microwave frequencies to the optical regime. An analytical model based on the superposition of shifted-beam patterns is developed that agrees very well with full-wave simulations and is corroborated by experimental results at microwave frequencies.

Figure 1

A qualitative illustration of how an array of dipole slots produces shifted beams in the near-field but identical magnitude distributions in the far field.

Figure 2

Subwavelength focusing from the superposition of shifted beams in the near-field. The transverse electric field at $y=0.15\lambda$ is plotted at several conceptual stages. (a) Shifted beams from slots at $x=-0.1\lambda$ (red), $x=0$ (blue), and $x=0.1\lambda$ (green). (b) The shifted beams multiplied by their weighting factors. (c) The weighted shifted beams superposed to produce a subwavelength focused beam (solid line) and the beam from a single slot (dashed line).

Figure 3

Simulated focused beams for slot arrays with 3 and 9 elements optimized for a focal plane at $y=0.25\lambda$. The thin red line was calculated analytically from Eq. (3) while the thick blue line was extracted from a full-wave simulation. The dotted line indicates the beam formed from a single slot. (a) Three-element array with weights $w_0=1$ and $w_{\pm 1}=0.497\angle 172°$. (b) Nine-element array with weights $w_0=1$, $w_{\pm 1}=0.764\angle 179°$, $w_{\pm 2}=0.373\angle -2°$, $w_{\pm 3}=0.136\angle 175°$, and $w_{\pm 4}=0.032\angle -6°$.

Figure 4

Simulated electric field magnitudes over the $xy$ plane for a single-slot (a) and a triple-slot (b) array under plane-wave excitation at 10 GHz. The fields are normalized along the $x$ direction with respect to the field value at $x=0$ to highlight the profile of the beam. The thin black contour trace indicates the FWHM beam width.

Figure 5

(a) Experimental measurements of the transverse electric field magnitude (solid lines) for single-slot and triple-slot arrays at 10 GHz compared with full-wave simulations (dotted). The slight asymmetry in the measured field profile resulted from the asymmetrical coupling between the slots and the probe antenna (see inset). (b) Measured field magnitudes at three frequencies for the single-slot (dotted) and triple-slot (solid) screens.