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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 extensively investigated in the literature, including recent work involving chiral metamaterials with material dispersion up to the first order. This paper examines the possible emergence of negative refractive index in dispersive chiral metamaterials with material dispersion up to the second order. The motivation is to determine if using second- as opposed to first-order dispersion may lead to more practical negative index behavior. 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 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 negative index material (NIM) behavior over information bandwidths in the low RF range. The second-order results are not significantly better than those for first-order results based on the theoretical analysis; however, greater parametric flexibility exists for the second-order system leading to the higher likelihood of achieving NIM over practical frequency bands. The velocities and indices computed using the Lorentzian and Condon models yield an NIM bandwidth around 200−400 Mrad/sec, about 2 orders of magnitude higher than that for the parametric approach; more importantly, NIM is found not to occur in the first order when using practical models.
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