Birefringence in gradient-index media

Ion exchange is a common method used to fabricate gradient-index (GRIN) materials. Stress can result from this process by two means: (i) a size difference between the exchange and diffusing ions and (ii) a difference in thermal expansion coefficient across the ion-exchanged region. The temperature of the diffusion determines which mechanism dominates. The resulting birefringence causes the index profile to be polarization dependent which can significantly affect ray propagation. Anisotropy in GRIN optical glass has not been well characterized. This thesis analyzes stress birefringence in GRIN media through ray tracing and birefringence measurements.; Birefringence can be an important consideration in the design and use of GRIN optics, especially in radial-GRIN relay lenses with large optical path lengths. Birefringence can degrade image quality and alter the polarization state of input light. Therefore, if anisotropy is present, it must be taken into account to accurately predict optical performance. Current lens design software does not analyze media that are both anisotropic and inhomogeneous. Such media are often treated as isotropic for ray tracing purposes. The theory necessary to model ray propagation in anisotropic inhomogeneous media is developed for this thesis. Among the equations derived are the ray equation, the eikonal equation, and an expression for the Poynting vector direction. The model is applied to trace meridional rays in birefringent GRIN rods.; Two methods are used to measure the birefringence in GRIN rods. One method uses a phase-shifting Twyman-Green interferometer to measure the optical path difference with orthogonal input polarizations. The difference between the two data sets provides a measure of the birefringence as a function of radius. The second method has been developed specifically for this thesis to measure the change in optical path difference directly. The measurements are performed on samples fabricated with a variety of diffusion times and temperatures. This is the first systematic study of how changing the fabrication conditions affects the amount of residual birefringence in GRIN optical glass. The results from the ray-tracing model are compared with experimental data. Also, birefringence effects observed in the tilt fringes of the two measurement set-ups are modeled.