Propagation of Electromagnetic Waves in Structured Metamaterials and System of Two-Level Atoms

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Ahmed, Abdurahman

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Addis Ababa University


Metamaterials are artificially engineered composites that exhibit superior properties not observed in nature or in the constituent materials. Because of the sub-wavelength periodicity of their constituent materials, metamaterials appear as homogeneous entity to an incident wave and can be described by effective parameters, such as electric and magnetic material properties, that are controlled by the unit cells geometry and the type of its constituent parts. These controllable material properties, in turn, makes structured metamaterials (SMMs) more interesting for diverse potential device applications. Consequently, it is of vital importance to investigate the responses of SMMs to electromagnetic waves (EMWs). In this dissertation, the dispersion properties of SMMs consisting of strips of a copper wire (electron subsystem) and square copper split-ring-resonators (magnetic subsystem) with different and coinciding resonant frequencies are studied. In a narrow frequency band above the resonant frequency of the electron subsystem, the structured metamaterial is described by a negative refractive index. In addition to this, there are some peculiar properties observed in these metamaterials. Among these properties is the nonanalytic behavior of the real part of the refractive index as a function of the frequency with a discontinuity of its derivative in the metamaterial with two resonances. It is also shown that the superluminal, slow, and backward microwaves can exist in the structured metamaterials. However, in the absence of gain components, only the slow microwaves can propagate considerably. In addition, we investigated the propagation of narrow packets of EMWs in frequency dispersive medium with the consideration of the complex refractive index. It xiv xv is shown that taking into account of the dispersion of the complex refractive index within the context of the conventional expression of the group velocity of narrow wave packets of EMWs propagating in a dispersive medium results in the appearance of additional constraints on the group velocity, which dictates that the physically acceptable group velocity can only be realized in the case of a negligible imaginary part of the group index. The conditions that allow one to realize the physically acceptable group velocity are formulated and analyzed numerically for the relevant model of the refractive index of a system of two-level atoms in the optical frequency range. It is shown that in the frequency band where superluminal light propagation is expected, there is a strong dispersion of the refractive index that is accompanied with strong absorption, resulting in a strongly attenuated superluminal light



Propagation of Electromagnetic Waves