Investigation of negative refractive index in isotropic chiral metamaterials under first and second-order material dispersion with and without conductive loss

Date of Award


Degree Name

Ph.D. in Electrical Engineering


Department of Electrical and Computer Engineering


Advisor: Monish Ranjan Chatterjee


In recent years, considerable research has been carried out relative to the electromagnetic (EM) propagation and refraction characteristics in metamaterials with emphasis on the origins of negative refractive index. Negative refractive index may be introduced in metamaterials via different methods; one such is the condition whereby the Poynting vector of the EM wave is in opposition to the group velocity in the material. Alternatively, negative refractive index also occurs when the group and phase velocities in the medium are in opposition. The latter phenomenon has been investigated extensively in the literature, including recent work involving chiral metamaterials with material dispersion up to the first order. This dissertation examines the possible emergence of negative refractive index in dispersive chiral (lossless and lossy) metamaterials with material dispersion up to the first and second order. The motivation of this work has two parts- the first part is to determine if using second- as opposed to first-order material dispersion may lead to more practically realizable negative index behavior in the lossless material; the second part is to determine if including the conductive loss to the medium with material dispersion up to the first order (a feature likely to be present in most realistic cases; conductive losses in such materials as nanometals, or dielectric losses in a variety of other nanomaterials, such as lithium niobate and Sic+Ag) may lead to the emergence of negative index. This dissertation investigates the above problems (with the exception of lossy dielectrics, the determination of which is currently ongoing) by using spectral and phasor plane-wave based analytical approaches as well as alternative analysis incorporating practical physical models into the electromagnetic equations. In this work, a spectral approach combined with slowly time-varying phasor analysis is applied leading to the derivation of EM phase and group velocities analytically, and the resulting phase and group velocities and the corresponding phase and group indices are evaluated by selecting somewhat arbitrary dispersive parameters. The results indicate the emergence of negative index (via negative phase indices along with positive group indices, as reported in the literature) or NIM behavior over information bandwidths in the low RF range. The second-order results are not significantly better than those for first-order based on the theoretical analysis; however, greater parametric flexibility exists for the second order system leading to higher likelihood of achieving NIM over practical frequency bands. The velocities and indices computed using the Lorentzian and Condon models. More importantly, NIM is found not to occur in first-order when using practical models. Also we have revisited the first order calculations and it is seen that (In the lossless -first order calculations) to match up with all negative index conditions or requirements, the relative electric permittivity and relative magnetic permeability must be negative in the NIM region. We investigated that the relative electric permittivity and magnetic permeability just can be negative in the negative sideband frequency. In the lossy case, the loss is introduced via the material's dispersive conductivity, and its effect in achieving NIM is carefully explored. Emergence of NIM is again established. Interestingly, it is found that the usual circular (RCP and LCP) spatial polarization states for the lossless material morph into right-handed spiral states once loss is introduced. These results derived via dispersive spectral analyses are in overall good agreement with corresponding findings in the literature.


Negative refractive index, Electromagnetic waves, Wave mechanics, Metamaterials, Electrical Engineering, Electromagnetics, Physics, Negative index, phase velocity, phase index, group velocity, group index, negative relative electric permittivity, negative relative magnetic permeability, polarization state, right circular polarization, lossy chiral material

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