Aberration Theories And Subwavelength Imaging Experiments For Negative-Index Lenses

In recent years, negative-refractive-index metamaterials (NIMs) have received much attention by the international academic world due to their unique properties and alluring applications, which is becoming one of the front and hot focuses both for electromagnetic and optical research. When the light ray refracts at the interface between a traditional positive-refractive-index material (PIM) and a novel NIM, negative refraction occurs where the refracted ray and the incident ray lie on the same side of the normal line, which means that the emergence of NIMs changes the traditional propagating laws and the basic imaging properties of lenses. Based on the use of such materials, we can design new lenses and imaging systems with lower aberrations as compared to their traditional counterparts. When the electromagnetic wave propagates in a negative refractive index material, the directions of the energy flow and phase velocity are anti-paralleled. Thus the evanescence wave can be amplified in a planar negative-refractive-index slab, which can beat the normal diffraction limit associated with positive refractive index optics and produce a focus with sub-wavelength resolution for a near object.The works presented in this thesis mainly focus on the intensive researches about the light-wave propagating properties at the interface between a PIM and a NIM, the imaging and aberration properties of a flat NIM lens and lens systems, the imaging and aberration properties of a curved NIM lens and lens systems and the sub-wavelength imaging experiment of a flat LC-loaded microstrip transmission-line lens, which are listed in detail as follows:1. The Fermat's principle, Fresnel's coefficients, Goos-Hanchen effect and Brewster angle at an interface between a PIM and a NIM were studied respectively. When the NIMs are introduced, the two traditional descriptions of Fermat's principle are not consistent with each other and the least time principle do not hold true anymore. It is also shown that the optical length of the real path through two points locating on the opposite sides of the interface between a PIM and a NIM undergoes a maximum value as compared its nearby paths. The intrinsic impedances of materials should be used, rather than refractive indiceswhich is associated with positive- refractive-index optics, for the studying of the refracting and reflecting properties about a PIM-NIM interface, due to a NIM is not only a dielectric but also a magnetic material, whose permeability no longer can be regarded as nearly equal to the vacuum's. For the same reason, the Goos-Hanchen shift is negative for both the TE and TM polarization incident waves as the result of the negative pennittivity and negative permeability nature of NIMs served as the rarer medium when total reflection occurring at a PIM-NIM interface. However, as for the dissipative loss medium with only one of permittivity and permeability being negative, the TM or TE polarization incident wave has a negative Goos-Hanchen shift accordingly. It is also found that under certain conditions, Brewster angle exists not only for TM wave but TE wave at a PIM-NIM interface while at a conventional PIM-PIM interface only for the TM wave case. 2. The imaging and aberration properties of NIM flat lens systems are systematically studied. The utilization of NIMs makes the singlet or multi-layer flat lenses having a positive working space possible, which means they can serve as independent imaging systems. As all the refracting interfaces comprising a flat-lens system are planar, the magnification is positive unit and the imaging is free from Petzval field curvature. For the same reason, it also easy for us to determine the stop aperture of the imaging system and calculate its accurate position. The working distance of a well-performing flat lens is about in the same scale as its thickness, so it can only form a near object into a real image and accordingly the scene depth is very short. It is shown that for a singlet lens, only the flat lens with a refractive index, -1, is possibly free from all the monochromatic aberrations and the others always possess certain spherical or oblique aberrations determined by then-thicknesses and refractive indices. However, according to the practical requirement of imaging quality in application, materials with refractive indices near -1 is not always necessary as we can design a multi-layer flat lens with different refractive indices apart from -1 but still retaining a well imaging performance where its aberrations can be counteracted inherently due to the opposite sign of aberration coefficients of each layers. It was found that with the increment of layer number, the spherical and oblique aberrations can be corrected up to higher orders though the corresponding ranges of the refractive indices and working distances become narrower.3. A general analysis of the imaging and aberration properties of the long-distance -imaging NIM lenses with curved surfaces is presented according to the primary aberration theory and it is pointed out that the MM lenses are inherently superior than the conventional PIM lenses when the imaging performance and aberrations are considered. The aberration properties of single curved interface between air and NIM was analyzed showing that its surface shape are more abundant when it is free from spherical aberration and it could be applied to a real imaging systems for the case where the primary spherical aberration, comma and astigmatism are corrected. Based on the Seidel sums formulae of thin lens, four types of NIM thin lenses free from partial primary aberrations are designed with specific parameters and given redundant aberration coefficients. Singlet aspherical thin NIM lenses without spherical aberrations are also discussed and their design methods are provided. As a singlet curved lens is impossible to correct all the five primary aberrations regardless it is made of PIMs or NIMs, the primaxy-aberration-free lens systems composed of two thin lenses or two thick lenses based on the use of NIMs are intentionally presented. It is pointed out that NIMs can be used to reduce the number of lenses needed and simplify the surface shapes of lenses designed for a lens system with the same or superior imaging performance over those conventional PIM ones.4. A LC-loaded microstrip transmission line flat lens working at a higher microwave frequency and with an effective refractive index equal to -1 is designed according to the reported works and its subwavelength imaging ability is verified. The experimental results manifest that the evanescence waves is really amplified inner the planar negative-index section and the image of electrical field is observed in the imaging plane with a half-amplitude width about 0.42 time of the working wavelength, which is consistent with the simulation results calculated by the commercial software-Advanced Design Systems.