Reflection and Transmission of Electromagnetic Waves by a Layered Structure Containing Left-Handed Material

Abstract

Left-handed materials (LHMs) are artificial materials whose electric permittivity and magnetic permeability are both negative and consequently have negative index of refraction. Such materials, first studied theoretically in 1968 have very unusual properties, such as negative refraction, inverse Doppler effect and reversed Čerenkov radiation. The first practical realization of them, consisting of split-ring resonators and continuous wires occurred in 2000. After this time a large number of both theoretical and experimental reports confirmed the existence and the main properties of these materials. Regular materials are materials whose permittivity and permeability are both positive and termed right handed materials (RHMs). In this thesis, the propagation of electromagnetic waves through multilayered structures containing LHM is investigated theoretically. Maxwell's equations are used to determine the electric and magnetic fields of the incident waves at each layer. Snell's law is applied and the boundary conditions are imposed at each layer interface to calculate the reflected, transmitted and loss powers of the structure. Numerical results are illustrated to show the variation of these powers with frequency, angle of incidence and LHM thickness. Two cases of the LHM are considered, loss-less case and loss case. To verify the performed computations, the law of conservation of energy is satisfied for all examples. The thesis is also concerned with the reflection and transmission properties of a structure consisting of N identical pairs of left- and right-handed materials. Maximum and minimum transmission (minimum and maximum reflection) of the structure are demonstrated on the rule that, LHM has negative index of refraction while RHM has positive index of refraction. Minimum transmission (maximum reflection) is obtained by using high ratio of refractive indices and different thicknesses of LH and RH materials constituted each pair of the structure. The total thickness of each pair is quarter wavelength of the incident waves at the operation frequency. Maximum transmission (minimum reflection) is realized by two slabs of the same thickness and opposite refractive indices, one is LHM and the other is RHM. The overall reflectance and transmittance of the structure are formulated in terms of Fresnel coefficients. A recursive method is applied on the computations under the mentioned conditions to show the variation of transmittance and reflectance with frequency. Also in this thesis, we propose an additional novel LHM based on magnetized ferrite-wire structure. Ferrites to provide negative permeability and wire array to provide negative permittivity. The structure forms LHM with negative refractive index. The negative frequency band (the frequency range at which the permittivity and permeability of the structure are both negative) can be tuned by changing the applied magnetic field. Thus by considering this structure embedded in vacuum, the propagation of electromagnetic waves through it is analyzed theoretically. The properties and the required equations for the effective permittivity and permeability of the structure are given in detail. After the construction of the problem, the reflection and transmission coefficients for the incident waves are derived. Then the reflected, transmitted and loss powers are determined using these coefficients. Finally, in the numerical results, the mentioned powers of the structure are computed and illustrated as a function of frequency, ferrite thickness etc. when the applied magnetic field changes.