Subwavelength terahertz imaging via virtual superlensing in the radiating near field

Abstract

Imaging with resolutions much below the wavelength λ - now common in the visible spectrum - remains challenging at lower frequencies, where exponentially decaying evanescent waves are generally measured using a tip or antenna close to an object. Such approaches are often problematic because probes can perturb the near-field itself. Here we show that information encoded in evanescent waves can be probed further than previously thought, by reconstructing truthful images of the near-field through selective amplification of evanescent waves, akin to a virtual superlens that images the near field without perturbing it. We quantify trade-offs between noise and measurement distance, experimentally demonstrating reconstruction of complex images with subwavelength features down to a resolution of λ/7 and amplitude signal-to-noise ratios < 25dB between 0.18-1.5 THz. Our procedure can be implemented with any near-field probe, greatly relaxes experimental requirements for subwavelength imaging at sub-optical frequencies and opens the door to non-invasive near-field scanning.

Fig. 1. Concept schematic of virtual superlens.

i Sub-wavelength spatial features are carried by evanescent waves which exponentially decay over a L (red). ii The resulting lower-resolution image is detected by a near-field probe. The collected evanescent fields are then numerically amplified over L (green), leading to iii the original image, analogously to a superlens (blue). Wavelength-scale information is carried by propagating waves (dashed).

Fig. 2. Numerical example of virtual SL.

a An x-polarized field is incident on sub-wavelength apertures (d = λ/5, blue), which cannot be discerned at z = λ/2 (red). b Associated spatial Fourier transform. Black/purple regions are propagating/evanescent. c Images after virtual lens ($k_{\max }=k_0$, green), after SL using the full spectrum (black), and using the low-passed (LP) filtered spectrum ($k_{\max }=2.5k_0$, blue). d Associated spatial Fourier transforms.

Fig. 3. Numerical example illustrating the effect of the SNR.

a Left: raw simulation of the amplitude E_x(x) as a function of z/λ for the double aperture case of Fig. 2, before any superlens procedure. Right shows the target amplitude at the source. b Dashed blue line shows an example $\mid {\tilde{E}}_x\mid$ at a distance z/λ = 0.5, as per Fig. 2b. The red line shows the same field after adding random amplitude and phase resulting in a flat SNR of 30 dB. c Calculated normalized amplified spatial Fourier transform for the flat SNR = 30 dB, as a function of its normalized propagation length z/λ. Color scale has been saturated to 1 for clarity. Solid curves show Eq. (5) choosing different values of Δ_SNR as labeled. Note that the case Δ_SNR = SNR = 30 dB corresponds to the boundary between where high spatial frequencies have a comparable magnitude to propagating waves. d Resulting $E_x^{SL}\left(x\right)$ after applying the superlens procedure, using a low-pass filter function bounded by k_x/k₀ as per Eq. (5) for different values of Δ_SNR as labeled. If Δ_SNR > SNR, the aperture images are plagued by noise; if Δ_SNR ≤ SNR, the maximum distance at which the retrieval procedure produces the image is gradually reduced.

Fig. 4. Superlens experiment, imaging two apertures.

Measured ∣E_x∣² and $\mid {\tilde{E}}_x\mid$ for two apertures of diameter/separation d = 200 μm, at a 1.5 THz and b 0.38 THz, with SNR as labeled. Dashed white circles show ∣k∣ = k₀. c Corresponding intensity profile in x as a function of frequency averaged over y = 0 ± 100 μm. d $\mid E_x^{\mathrm{SL}}{\mid }^2$ after the superlens at 1.5 THz and e 0.38 THz. f Corresponding intensity profile in x as a function of frequency averaged over y = 0 ± 100 μm. Vertical artefacts in c, f are absorption lines due to air humidity.

Fig. 5. Superlens experiment, imaging the letters “THZ”.

a Measured ∣E_x∣² at different frequencies labeled left, with associated d and L in terms of λ. b Corresponding ∣E_x∣² after image reconstruction with $k_{\max }=k_0$ (lens) and c when $k_{\max }>k_0$ ($\mid E_x^{\mathrm{SL}}{\mid }^2$, superlens). d $\mid E_y^{\mathrm{SL}}{\mid }^2$ after the superlens with $k_{\max }>k_0$. e Reconstructed images using measured x − and y − polarized fields in (c, d). The ratio $k_{\max }/k_0$ for each row is shown on the right. Each window area is 4 mm × 2 mm. The smallest feature size is d = 150 μm and the detector distance is L = 440 μm.