Description and applications of space-variant polarization states and elements

Thesis (Ph. D.)--University of Rochester. The Institute of Optics, 2018.Space-variant polarization states and elements have received significant interest in recent years for their interesting physical properties and widespread applications. This thesis is primarily focused on the optimization of spatially-varying polarization distributions and birefringent media for three applications: semiconductor metrology, star test polarimetry, and optical bottle field generation. These analyses are supported by additional chapters discussing a geometrical representation for spatially-varying birefringence on the Poincaré sphere and an overview of maximum likelihood estimation in the context of an optical measurement. The first application is a focused beam scatterometry experiment for simultaneous retrieval of multiple parameters of a subwavelength structure. As a variation of traditional Fourier scatterometry, a tailored spatially-varying polarization distribution is used to achieve heightened sensitivity to variations in each parameter. This measurement technique has practical uses in the semiconductor industry, where there is a high demand for fast and accurate measurements of silicon transistor components. As an example, initial two-parameter measurements of a silicon lamellar grating are presented, leading to parameter estimates with sub-nanometer precision, on par with current industry needs. Additionally, simulations are performed to predict the improvement in accuracy in future experiments with refined polarization control. The second application is star test polarimetry, in which an element with spatiallyvarying birefringence is used to encode polarization information into the point-spread function (PSF) of an imaging system. A variational calculation is performed to optimize the birefringence distribution to produce the smallest possible PSF, thus maximizing the resolution for imaging polarimetry measurements. The optimal solution is found to be nearly identical to the birefringence distribution of a stressengineered optic (SEO) with three stress points, which has been used in previous star test polarimetry experiments. The third and final application is a method for generating an optical bottle field containing a three-dimensional null in intensity at the focal point, which is useful for optical trapping and microscopy. The spatial variation of a birefringent mask, placed in the pupil plane of a high-NA focusing system, is optimized to produce a bottle field with the sharpest possible minimum in intensity. The optimal solution is shown to be closely approximated by an SEO