Fabrication And Research On Optical Properties Of Gradient Refractive Index Ball Lenses

The terms gradient index (GRIN) or graded index (GI) are often used to describe an inhomogeneous medium in which the refractive index varies from point to point. There are three basic gradient index types that have been studied. The first one is the axial GRIN medium. In this case, the refractive index varies in a continuous way along the optics axis of the inhomogeneous medium. The isoindicial surfaces are planes perpendicular to the optical axis; the second one is the radial GRIN medium in which the index profile varies continuously from the optical axis to periphery along the transverse direction in such a way that isoindicial surfaces are concentric cylinders about the optical axis. In the special case of the index varying quadratically with the distance in the transverse direction, the medium is referred to as self-focusing lens; the last type is the spherical GRIN medium. Spherical GRIN medium may be thought of as a symmetric index around a point so that isoindicial surfaces are concentric spheres. Equations governing propagation of rays through a spherical gradient are similar to those of a geodesic lens. GRIN ball lens is a spherical optical element with refractive index is symmetric around a spherical point and varies in spherical radius direction. Because of simple geometry and excellent optical performance, it can be used in optical fiber communication system, and as imaging and sensing devices.Fabrication and optical performances of GRIN ball lens are studied in theory and experiment. Moreover, schematic eye models with GRIN ball lens and GRIN rod lens are designed at the aspect of eye optics, and the oxide composition model is given to analyze chromatic aberrations of GRIN rod lens. Which mainly include several parts:In Chapter 1, Development and fabrication technology of GRIN optics are depicted, and optical performances and research significance of GRIN ball lens are given, respectively.In Chapter 2, the refractive index distribution and ray trajectory of GRIN ball lens are studied in theory. The equations for calculating the refractive index and ray trajectory of GRIN ball lens based on the Fick's diffusion,the principle of Fermat and the equation of ray are established, respectively, and the refractive index profiles and the ray trajectory of GRIN ball lens with different radii are analyzed;In Chapter 3, basic glass manufacturing which includes glass formula design,glass melting procedure and optical parameter measuring is depicted in order to fabricate GRIN ball lens; GRIN ball lenses are fabricated using the method of combination of ion exchanging and sagging, and the surface profiles and transmittance of GRIN ball lens are tested.In Chapter 4, Thin slice interference method,lateral differential interference method and optical coherence tomography(OCT) are used for testing refractive index distributions of GRIN ball lens, respectively, and refractive index distributions of GRIN ball lens is verified in theory. Refractive index distributions and interferometer image of GRIN ball lens are tested using different method. Moreover, the equations for calculating the effect focal length and back focal length are established under paraxial approximation and the effect focal length,back focal length,numerical aperture and focusing intensity are rested, respectively.In Chapter 5, schematic eye models with GRIN ball lens and GRIN rod lens are designed at the aspect of eye optics and compared with four eye models and real eye model. Spherical aberration,sagittal and tangential power errors,astigmatism and field curvature of different eye models are analyzed;In Chapter 6, the oxide composition model is given to discuss chromatic aberrations of GRIN rod lenses. GRIN rod lenses are manufactured using K~+/Tl~+, Li~+/Na~+ and K~+/Cs~+ ion exchanges. Chromatic aberrations of GRIN rod lenses are analyzed using the oxide composition model and the Huggins-Sun-Davis (HSD) model in theory and experiment, respectively.In Chapter 7, all the work of the dissertation is summarized and predicted.Research results indicate: GRIN ball lens can be made of properly designed base glass by appropriate K~+/Tl~+ exchanging process and has better optical performances in theory and experiment, and obtains the smallest spherical aberration in eye model.