Miguel Angel Ruphuy
Electrically Thin Lenses and Reflectors
In physics, specially in optics, ray models are commonly used to simplify problems and further design devices for a diverse variety of applications. This diversity runs from mass-oriented products, such as cameras, to more sophisticated needs, such as wireless communications. These ray models frequently make use of Snell Law to further describe the rays' trajectories. The importance of Snell Law is out of question. However, its applicability is limited to homogeneous half spaces.
Nowadays, advanced materials could further improve the characteristics of current devices and expand the applications by using inhomogeneous medium. Designers and scientists typically avoid working with inhomogeneous medium due to the difficulties on predicting the wave behaviour. In this manuscript, I present a general and simple formulation to predict refraction over inhomogeneous electrically-thin media. This formulation is found to be highly accurate and describes refraction over inhomogeneous slabs just as Snell Law predicts the refracted ray in a half space system.
Naturally, the first application that comes to mind are lenses to form an images and concentrate energy. Similarly, parabolic reflectors could potentially be substituted by inhomogeneous media devices with simpler geometries. In particular, the possibility of having flat lenses lead to envision improved images. In this work, a flat lens and reflector are proposed. An electrically thin lens and a reflector are designed to exhibit a refractive index profile, which results in a radial phase shift dependence. The concept of phase shifting to converge energy is proven with a case of study at 10 GHz with a lens and a reflector with a diameter of 8 $\lambda$. High contrast in the fields around the focal point demonstrates the remarkable performance of the lens. Additionally, the lens demonstrates to be free of spherical aberration. To obtain this characteristic, in the proposed design methodology, the electrical thinness of the lens is crucial. A complete analysis of monochromatic spherical aberration is performed and compared to classical gradient index rods. Given the expensive computation of large structures in full wave simulations, a model based on infinite line currents is proposed to model 2D (refractive index constant in one direction) inhomogeneous electrically-thin media. Similarly, infinitesimal dipoles are used to model 3D inhomogeneous electrically-thin media. This model exhibits good agreement and requires of lower computation resources than that of numerical simulations.
Besides lenses and reflectors, there are several applications for thin inhomogeneous films. For instance, monostatic cloaking to conceal objects from radars is proposed here. An important decrease in the radar cross-section ratio is demonstrated.
In summary, in this thesis I present a formulation to predict refraction in inhomogeneous thin media. High performance is shown for classical applications (lenses and reflectors) whereas other applications such as cloaking shows promising results. Application possibilities are much broader than the ones presented here. I consider this work to be the seed of many possible applications. For instance, some medical devices that use gradient index rods which are bulky and subject to aberration could be replaced. Also, an inhomogeneous sheet could be designed for hyperthermia which is a technique used to heat cancer cells within the body, enhancing the power performance of current antenna systems. Or to electromagnetically decouple antennas located close to each other, just to name a few.