Speaker:  Melanie Pierce

Title: “Vector Field Generator for a Direct Mapping of the First Order Poincaré Sphere”

Time:  9:00 am, Wednesday, May 6, 2015

Place:  P-250



This thesis presents an optical system able to generate all polarization states on the zero order Poincaré sphere.  An important characteristic of the zero order sphere is its spatial uniformity.  This means that the polarization of the beam is uniform.  This characterization can be proven using polarizers. Any change in the polarization of the beam will be consistent for all points in the beam. This is not necessarily true for all types of polarization states.  There are new polarization states that are spatially variant in which the polarization is no longer uniform.  The assumption that the polarization at one point in the beam is the same at all points is no longer valid, which allows for strange behavior.  These are defined as higher order polarization states which have their own Poincaré spheres that are similar to the zero order sphere but are spatially variant.  These states are the focus of this thesis. Maxwell’s equations are shown and the solution for light is derived. From this, Jones vectors are used to describe the polarization and how they relate to the Poincaré sphere.  Jones matrices are applied to the incoming polarization state to reflect the changes a waveplate causes to the system, and how to create a rotator to rotate the axis of polarization.  These matrices describe an optical system consisting of a variable waveplate and a rotator created from 2 quarter waveplates and an additional variable waveplate that able to change the latitude and longitude of a polarization state on the Poincaré sphere.  The system is able to achieve any coordinate on the surface of the sphere.  The system is applied to the zero order Poincaré sphere and the positive and negative first order Poincaré sphere.  The experimental results are presented.

Committee Chair:  Dr. Jeffrey Davis

Committee Members:  Dr. Fridolin Weber and Dr. Ricardo Carretero


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