Super-resolution for a point source better thanλ/500 using positive refraction

Leonhardt (2009 New J. Phys. 11 093040) demonstrated that the two-dimensional (2D) Maxwell fish eye (MFE) lens can focus perfectly 2D Helmholtz waves of arbitrary frequency; that is, it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a 'perfect point drain' located at the corresponding image point. Moreover, a prototype with λ /5 super-resolution property for one microwave frequency has been manufactured and tested (Ma et al 2010 arXiv:1007.2530v1; Ma et al 2010 New J. Phys . 13 033016). However, neither software simulations nor experimental measurements for a broad band of frequencies have yet been reported. Here, we present steady-state simulations with a non-perfect drain for a device equivalent to the MFE, called the spherical geodesic waveguide (SGW), which predicts up to λ /500 super-resolution close to discrete frequencies. Out of these frequencies, the SGW does not show super-resolution in the analysis carried out.