Three‐Dimensional Super Lens Composed of Fractal Left‐Handed Materials

Abstract

The lens which can focus electromagnetic (EM) waves below the wavelength represents one of the most fundamental building blocks in the optical microscopy. However, the spatial resolution of conventional lenses is commonly confi ned to half of the illuminating wavelength due to the diffraction limits. A survey of state of the art indicates that an explosion of activities and efforts, both theoretical and experimental, have been devoted to overcome these limits, namely designing super lenses with better resolution. To date, several techniques are available, e.g., lenses fabricated by using left-handed (LH) bulk materials with negative refractive index (NRI), [1][2][3][4][5][6][7][8] LH transmission-line (TL) materials, [9][10][11][12][13][14][15][16][17][18][19][20] photonic crystals, [ 21 ] gradient-index materials, [22][23][24] chiral medium, [ 25,26 ] biocompatible material, [ 27 ] complementary V-shaped antennas, [ 28 ] near-fi eld plate, [ 29 ] acoustic metamaterial, [ 30 ] perovskites, [ 31 ] silver fi lm or layer, [32][33][34] dielectric elastomers [ 35 ] and even based on compensation mechanism. [ 36 ] Moreover, the progress of super lenses has been extended significantly from the original gigahertz (GHz) region to terahertz and even optical frequencies [32][33][34]37 ] via the excitation of surface plasmons.Among them, the LH material (LHM) lens, also termed as Veselago-Pendry lens, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] has intrigued an enormous and long-holding interest in science and engineering communities since Veselago and Pendry predicted in their seminal work [ 1,2 ] that lens made of LHM slab is able to overcome the conventional diffraction limits. This is especially true for the representative LH-TL lenses due to their low loss and small volume, because the lossy and thick LHM drastically deteriorates the evanescent-wave enhancement which contributes much to the sub-diffraction imaging. The physical mechanism for super resolution is that the LHM lens is not only capable of focusing the propagating waves emanating from the sources but also of amplifying the evanescent waves which restore useful information of sources and decay exponentially in vacuum. [ 10 ] However, the subwavelength imaging is achieved only when some strict requirements are fulfi lled. First, specifi c material parameters are required with the permeability μ eff = − μ 0 and permittivity ε eff = − ε 0 at the focusing frequency in order to make the matched impedance Z = Z 0 and refractive index n eff = −1, where Z 0 is the intrinsic impedance of the free space and μ 0 and ε 0 are the permeability and permittivity in free space. Second, electrically small dimensions of basic elements are required. Third, appropriate position for the focal spot and suffi ciently large transverse dimensions are required in addition to the aforementioned low loss and thin thickness.Although the LH-TL lenses are able to provide a decent resolution, most of them are restricted to the planar TLs which are constructed by peri...

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