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.

Perfect imaging of point sources with positive refraction

The capability of a device called the Spherical Geodesic Waveguide (SGW) to produce images with details below the classic Abbe diffraction limit (super-resolution) is analyzed here. The SGW is an optical system equivalent (by means of Transformation Optics) to the Maxwell Fish Eye (MFE) refractive index distribution. Recently, it has been claimed that the necessary condition to get super-resolution in the MFE and the SGW is the use of a Perfect Point Drain (PPD). The PPD is a punctual receptor placed in the focal point that absorbs the incident wave, without reflection or scattering. A microwave circuit comprising three elements, the SGW, the source and the drain (two coaxial lines loaded with specific impedances) is designed and simulated in COMSOL. The super-resolution properties have been analyzed for different position of the source and drain and for two different load impedances: the PPD and the characteristic line impedance. The results show that in both cases super-resolution occurs only for discrete number of frequencies. Out of these frequencies, the SGW does not show SR in the analysis carried out.

Experimental evidence of super-resolution better than lambda/105 with positive refraction

Super-resolution (SR) systems surpassing the Abbe diffraction limit have been theoretically and experimentally demonstrated using a number of different approaches and technologies: using materials with a negative refractive index, utilizing optical super-oscillation, using a resonant metalens, etc. However, recently it has been proved theoretically that in the Maxwell fish-eye lens (MFE), a device made of positive refractive index materials, the same phenomenon takes place. Moreover, using a simpler device equivalent to the MFE called the spherical geodesic waveguide (SGW), an SR of up to λ/3000 was simulated in COMSOL. Until now, only one piece of experimental evidence of SR with positive refraction has been reported (up to λ/5) for an MFE prototype working at microwave frequencies. Here, experimental results are presented for an SGW prototype showing an SR of up to λ/105. The SGW prototype consists of two concentric metallic spheres with an air space in between and two coaxial ports acting as an emitter and a receiver. The prototype has been analyzed in the range 1 GHz to 1.3 GHz.

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