Investigation of Negative Index in Chiral Metamaterial and Dispersive Imaging Devices with Application to Efficiency Enhancement in Solar Cell Arrays

Date of Award


Degree Name

Ph.D. in Electrical Engineering


Department of Electrical and Computer Engineering


Advisor: Monish Chatterjee


In this dissertation, electromagnetic (EM) propagation in a chiral material with dispersion up to the first order is examined for possible emergence of negative refractive index under non-conductive losses. Three loss scenarios are considered, viz., dielectric losses (complex permittivity); magnetic losses (complex permeability); and a combination of both types of losses. A spectral approach combined with a slowly time-varying phasor analysis is applied, leading to the analytic derivation of EM phase and group velocities and corresponding indices. The velocities and indices are examined by selecting arbitrary dispersion parameters based on published practical values. The results indicate the emergence of negative index within specific RF modulation bands. The results presented are aimed at observing the polarization states of the fields under loss conditions. In addition to that, a method is suggested whereby the effects of dielectric and magnetic losses may be combined via appropriate Taylor coefficients such that the effective attenuation constant may be driven to zero via induced gain mechanisms arising from the dielectric and magnetic loss models. The second primary topic investigated in this work highlights the properties relative to thick lenses in the presence of chirality and material dispersion. A salient feature of a chiral thick lens is the inherent bimodal propagation via circular polarizations. Three different scenarios are considered, viz., first-order frequency-dependent material dispersion of the dielectric permittivity; the lens material being chiral; finally, the case of an airgap (shaped like a thick lens) 4 embedded in a chiral host. Under chirality, two sets of ABCD matrices are derived for right- and left-circularly polarized (RCP/LCP) modes. The analyses and results are compared with the standard achiral problem. For imaging purposes, a simple 1-D colored transparency is placed as an object before the thick lens in each scenario, with the transmission across the spherical boundaries examined via the ABCD parameters. Under dispersion, image characteristics such as foci, location, magnification and amplitude are controlled by narrow sidebands around a monochromatic carrier and the chirality. It turns out, that individual wavelengths of sunlight may be brought to focus by the lens to unique positions displaced in both Y and Z coordinates. Moreover, it is found that significant differences arise in the three imaging systems leading to comparisons with achiral thick lenses, which are discussed. In the third significant area of this research, extensions are made to the cases involving a 2-D polychromatic transparency serving as an object in front of a dispersive thick lens (for which, as described in this document, chirality has been dropped for reasons discussed later). The dispersive model, based on harmonic oscillator material dispersion characteristics, has been analyzed and applied in linear limits over the frequency/wavelength near-parabolic curves. The RGB based constituent colors are treated in terms of a center wavelength with a spectral spread by use of MATLAB simulations, thereby enabling the phasor interpretation and tracking along axial image planes. It turns out any individual color of the input transparency has a unique focal length or image position in the (meridional) observation plane after propagation through the lens. The analytical results (derived numerically) including image fidelity and mean squared error relative to original source transparency are compared with standard non-dispersive imaging. Particular attention is given to the nature of transverse paraxial images in fixed axial planes, whereby defocusing effects due to dispersion are demonstrated in the manner of spherical aberration. Such selective axial focusing of individual wavelengths may find applications in improving the conversion efficiency of solar cells and photodetectors exposed to white light illumination. This manner of wavelength splitting, and selectivity is used to minimize the spatial extent of the transmitted field at a specific wavelength near the focal planes (with maximal intensity) to improve the performance of a solar cell (pn junction) placed near the specific focal plane by increasing absorption and electron-hole generation efficiencies. The strategy for more efficient solar cell performance would be to place individual cells near the focal plane of each color (at specific (����,����) locations within the visible spectrum to absorb a single wavelength of the sunlight). The resulting solar cell array characteristics will be examined in ongoing work via absorption and photon generation under spatially separated spectra. Some results in this regard are presented herein, with the understanding that the impact of wavelength separation leading to highly efficient solar cells and related work are under further investigations.


Negative Index, Metamaterials, Chiral, Dispersion, Imaging, Solar cells

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