Super-resolution for a point source using positive refraction

Leonhardt demonstrated (2009) that the 2D Maxwell Fish Eye lens (MFE) can focus perfectly 2D Helmholtz waves of arbitrary frequency, i.e., it can transport perfectly an outward (monopole) 2D Helmholtz wave field, generated by a point source, towards a receptor called "perfect drain" (PD) located at the corresponding MFE image point. The PD has the property of absorbing the complete radiation without radiation or scattering and it has been claimed as necessary to obtain super-resolution (SR) in the MFE. However, a prototype using a "drain" different from the PD has shown λ/5 resolution for microwave frequencies (Ma et al, 2010). Recently, the SR properties of a device equivalent to the MFE, called the Spherical Geodesic Waveguide (SGW) (Miñano et al, 2012) have been analyzed. The reported results show resolution up to λ /3000, for the SGW loaded with the perfect drain, and up to λ /500 f for the SGW without perfect drain. The perfect drain was realized as a coaxial probe loaded with properly calculated impedance. The SGW provides SR only in a narrow band of frequencies close to the resonance Schumann frequencies. Here we analyze the SGW loaded with a small "perfect drain region" (González et al, 2011). This drain is designed as a region made of a material with complex permittivity. The comparative results show that there is no significant difference in the SR properties for both perfect drain designs.

Super-resolution properties of the Spherical Geodesic Waveguides using the perfect drain

Perfect drain for the Maxwell Fish Eye (MFE) is a nonmagnetic dissipative region placed in the focal point to absorb all the incident radiation without reflection or scattering. The perfect drain was recently designed as a material with complex permittivity ? that depends on frequency. However, this material is only a theoretical material, so it can not be used in practical devices. Recently, the perfect drain has been claimed as necessary to achieve super-resolution [Leonhard 2009, New J. Phys. 11 093040], which has increased the interest for practical perfect drains suitable for manufacturing. Here, we analyze the superresolution properties of a device equivalent to the MFE, known as Spherical Geodesic Waveguide (SGW), loaded with the perfect drain. In the SGW the source and drain are implemented with coaxial probes. The perfect drain is realized using a circuit (made of a resistance and a capacitor) connected to the drain coaxial probes. Superresolution analysis for this device is done in Comsol Multiphysics. The results of simulations predict the superresolution up to ? /3000 and optimum power transmission from the source to the drain.