Radiations by Finite-Sized Sources in Uniaxial Materials

Abstract

We present analytical results of fields radiated by finite-sized sources in unbounded uniaxial dielectric materials. Uniaxial materials are abundant in nature (rutile, calcite, quartz etc.) and can also be fabricated as periodic arrangement of thin sheets of different isotropic materials or as periodic arrangements of thin cylinders with their axis pointing in the same directions. Most modern metamaterials are also uniaxial due to dominant planar technology in electronics. Examples of uniaxial metamaterials include hyperbolic and zero-index materials. Analytical results of radiations from sources inside uniaxial materials are only available for point-sources. However, point-source is only a zeroth order approximation of actual radiators. In this thesis, the finite-sized sources are considered and approximate analytical results are derived. Finite-sized electric dipole and current loop are taken to find the next-order approximation of point-electric and point magnetic dipoles in uniaxial material. These results are obtained in the near zone and far zone for the two orientations of the finite-length dipole: when it is parallel to the optic axis and when it is perpendicular to the optic axis. These two orthogonal orientations can be used to construct solutions for an arbitrarily oriented dipole. When the electric dipole is parallel to the optic axis, only extraordinary waves are emitted. When the electric dipole is perpendicular this optic axis, both ordinary and extraordinary waves are emitted; however, the radiations are suppressed along the optic axis and no extraordinary waves are emitted in a direction perpendicular to both the electric dipole and the optic axis. A comparison with the point dipole showed that the directivity of the radiation pattern can be controlled using the length of the dipole. The radiations by a current loop in an unbounded uniaxial dielectric material with uniform current distribution are also studied. The closed-form expressions for the radiation in the far zone are found using the dyadic Green functions in the frequency domain. Analytical results are obtained when the axis of the loop was parallel to the optic axis and when it was perpendicular to the optic axis. Only ordinary waves are emitted when the axis of the loop is parallel to the optic axis in contrast to the electric dipole. When the axis of the loop is perpendicular to the optic axis, both the ordinary and the extraordinary waves are emitted. The results for different radii of the loop show that the radiation pattern strongly depends upon the size of the loop. A comparison of the finite-length dipole in the hyperbolic material with that of the uniaxial dielectric material showed that the radiation patterns are very different for the extraordinary waves but the patterns for the ordinary waves are similar. When the dipole and the optic axis are parallel, the extraordinary radiations are emitted along a cone in the hyperbolic material with the optic axis as its axis. When the dipole is perpendicular, no extraordinary radiation is emitted along the dipole, the optic axis, and perpendicular to the plane formed by the dipole and the optic axis. Furthermore, analytical results are obtained for the wire material in the zero-index regime. When the dipole is parallel, only the near field is significantly present and no radiations are emitted in the far field. When the dipole is perpendicular, the near field is negligible, but far field radiations are present, though only of the ordinary type.