Wave propagation in negative index materials

Date of Award


Degree Name

Ph.D. in Electrical Engineering


Department of Electrical and Computer Engineering


Advisor: Partha P. Banerjee


Properties of electromagnetic propagation in materials with negative permittivities and permeabilities were first studied in 1968. In such metamaterials, the electric field vector, the magnetic field vector, and the propagation vector form a left hand triad, thus the name left hand materials. Research in this area was practically non-existent, until about 10 years ago, a composite material consisting of periodic metallic rods and split-ring resonators showed left-handed properties. Because the dimension of the constituents of the metamaterial are small compared to the operating wavelength, it is possible to describe the electromagnetic properties of the composite using the concept of effective permittivity and permeability. In this dissertation, the basic properties of electromagnetic propagation through homogenous left hand materials are first studied. Many of the basic properties of left hand materials are in contrast to those in right hand materials, viz., negative refraction, perfect lensing, and the inverse Doppler effect. Dispersion relations are used to study wave propagation in negative index materials. For the first time to the best of our knowledge, we show that a reduced dispersion relation, obtained from the frequency dependence of the propagation constant by neglecting a linear frequency dependent term, obeys causality. Causality of the propagation constant enables us to use a novel and simple operator formalism approach to derive the underlying partial differential equations for baseband and envelope wave propagation. Various tools for understanding and characterizing left-handed materials are thereafter presented. The transfer matrix method is used to analyze periodic and random structures composed of positive and negative index materials. By random structures we mean randomness in layer position, index of refraction, and thickness. As an application of alternating periodic negative index and positive index structures, we propose a novel sensor using the zero average gap that only appears in such structures which has different properties from the usual Bragg gap occurring in alternating positive index structures. Also in this dissertation, we propose a novel negative index material in the visible range based on nanoparticle dispersed liquid crystal cells. The extended Maxwell Garnett theory, which is combination of the regular Maxwell Garnett and Mie scattering theories, is used to find the effective refractive index of the proposed cell. Nanoparticle dispersed liquid crystal cells can also be used as plasmonic sensors. A theoretical study of such sensors is presented. Finally, fabrication and testing of such cells is proposed and initial progress in fabrication is reported. The final assembly and testing of nanoparticle dispersed liquid crystal cells constitute ongoing and future work.


Metamaterials Optical properties, Metamaterials Structure, Electromagnetism

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