In this thesis, we analyze the simplest optical imaging system: a ball lens. The traditional method of using a geometric optics analysis on an optical system only gives the roughest qualitative solution due to the lack of consideration of wave properties. Therefore, for accurate quantitative results, we need to analyze said system with a complete wave theory approach. The reason that we chose a ball lens as the focus of this research is due to its spherical symmetry properties which allows us to rigorously investigate it with different analytic methods. We will apply geometric optics, Fourier optics, scalar wave optics, and electromagnetic optics methods to compute the point spread functions (PSF) of a ball lens under the assumption that the point source is isotropic. We will follow up by predicting the spot sizes that correspond to each mean. First, with geometric optics (GO), we apply the analytic ray tracing method to correlate the origins of light rays passing through the ball lens to their respective positions on the receptive end. We can then evaluate the energy distribution function by gathering the density of rays on image plane. Second, in the theory of Fourier optics (FO), to obtain the analytic formula of the point spread function, the integral kernel can be approximated as the Fresnel integral kernel by means of paraxial approximation. Compared to GO, the results from FO are superior due to the inclusion of wave characteristics. Furthermore, we consider scalar wave optics by directly solving the inhomogeneous Helmholtz equation which the scalar light field should satisfy. However, the light field is not assigned to an exact physical meaning in the theory of scalar wave optics, so we reasonably require boundary conditions where the light field function and its first derivative are continuous everywhere on the surface of ball lens. Finally, in the theory of electromagnetic optics (EMO), we consider the polarization of the point source, and the two kinds of Hertz vectors and , both of which satisfy inhomogeneous Helmholtz equation, and are derived from Maxwell¡¦s equations in spherical structures. In contrast with the scalar wave optics, the two Hertz vectors are defined concretely thus allowing us to assign exact boundary conditions on the interface. Then the fields corresponding to and are averaged as the final point spread function.

<div>Aperiodic structures offer new functionalities for control, manipulation, and sensing that can benefit applications in all frequency ranges. We present a study of the influence of the degrees of freedom from a binary aperiodic nanostructure in free space, where each pixel is either the scatterer or the background, that uses a multivariate statistical analysis to examine the covariance matrix of the output field distributions. The total variance of the output fields and the rank can be evaluated to provide quantitative measurements of control. In addition, the field statistics provide an improved understanding of the scattering properties of aperiodic structures.</div><div><br></div><div><br></div><div><div>It has been proposed that structuring a metal surface can substantially increase the optical pressure over that possible with a planar interface. Based upon the forces on the mirrors of a one-dimensional asymmetric Fabry-Perot cavity, we show that the sum of the pressures on both mirrors increases through asymmetry and with quality factor. Using cavity quality factor as a measure, we present the physical basis of the enhanced pressure on a nanostructured metallic surface as being due to an array of asymmetric resonant cavities.</div></div><div><br></div><div><div>With use of optimized, aperiodic structures, more control and higher pressure should be possible. We present a design method by which the electromagnetic pressure on a nanostructured binary material can be controlled in terms of both the enhancement and the direction. This analysis offers new avenues for optomechanics.</div></div>