Superlens

The superlens experiment was carried out using a linear polarized z propagating Gaussian beam (488 nm, 46 μW power) focused to its minimum 20 μm FWHM waist in a plane 5 mm before the crystal input facet (‘object’ plane, Fig. 4A). In other aspects, the system is the same as that reported in Fig. 2, the sample being of the same composition but now with no deposited mask. The beam size at the input facet is a slightly diffracted Gaussian beam with a 50 μm FWHM (Fig. 4B) that, without a topological transition (T > T_C), diffracts to an 80 μm FWHM in a plane 5 mm from the output facet (’image’ plane). Results are reported for t = 100 s, while the sample is rapidly cooled from T(0) = T_C + 64 K to T(∞) = T_C − 3 K (in this specific case, T˙≃0.5∘C/s). As expected for the resulting superlens effect, the beam expands as it reaches the output facet (Fig. 4C), after the internal focus point, and refocuses on exiting the crystal (Fig. 4D–F) to then re-expand after the image focus (Fig. 4G). The position of the focus, that in the reported case is 5 mm from the output facet, is dependent on the cooling rate T˙ and exposure t, and was observed in the range of 2–5 mm from the output facet changing T˙ in the range 0.3−0.8 °C/s. It is useful to discuss the details in terms of the transverse spatial spectrum of the superlensing in Fig. 4 compared to the experiments in Figs. 2 and ​and3.3. Experiments in Figs. 2 and ​and33 involve a transverse spectrum with Airy rings and a characteristic ∣k_⊥∣ ~ 5 × 10⁵ m⁻¹ able to populate, for the values of α inspected, regions of the hyperbolic branches. In turn, in the conditions of Fig. 4, the spectrum is a localized Gaussian (∣k_⊥∣ ~ 5 × 10⁴ m⁻¹), and the propagation is dominated by the central parabolic region of the dispersion hyperbola.