This dissertation addresses the creation of polarization vortex beams. Vortex retarders are components with uniform retardance but a fast axis which rotates around its center with can create polarization vortices. The goal was to develop a simple method for producing vortex retarders for visible wavelengths, with a continuous fast axis, and for multiple vortex modes.The approach was to use photo-aligned liquid crystal polymers (LCP). The target was a halfwave retardance for wavelengths in the range of 540~550nm. A photo-alignment layer was spin-coated onto a substrate, baked, and alignment was set through exposure to linear polarized UV (LPUV) light. The alignment layer was exposed through a narrow wedge shaped aperture located between the substrate and polarizer. Both the polarizer and substrate were continuously rotated during exposure process in order to create a continuous variation in photo-alignment orientation with respect to azimuthal locations on the substrate. The mode of the vortex retarder was determined by the relative rotation speeds. The LCP precursor was spin-coated and subsequently polymerized using a UV curing processes. Elements produced were analyzed by measuring the space variant Mueller Matrix of each component. Our measurements demonstrated that the vortex retarders were half wave plates with a continuous fast axis orientation. Measurement of the center region of the vortex retarders identifies a 100-200um region of disorientation. At 0.5mm resolution, a high depolarization index in the center of the vortex retarders was observed. The DOP was low in the center for a horizontal linear polarized input field but remained high for circular polarized input.The viability of these components was assessed by determining the point spread matrix (PSM) and the optical transfer matrix (OTM) and comparing these to theoretical calculations. The agreement between the measured and predicted PSM was excellent. The major difference was the non-zero response in the m03 and m30 elements indicating circular diattenuation. The OTM comparison between measured and predicted demonstrated an excellent quantitative match at lower spatial frequencies and a good qualitative match at higher spatial frequencies. Measured results confirm that vortex retarders produced using photo-aligned LCP produce near theoretical performance in an optical system.

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Die Arbeit untersucht planare optische Mikrokavitäten, welche aus einer beidseitig von Multischichtspiegeln umgebenen Kavitätsschicht bestehen. Im Rahmen einer Transfermatrixbeschreibung für ebene Wellen wird ein genereller Ansatz zur Berechnung von optischen Kavitätsmoden von planaren Mikrokavitäten entwickelt, welche aus optisch beliebig anisotropen Medien bestehen. Die zugrunde liegende Modenbedingung kommt ohne vorherige Einschränkungen bezüglich der betrachteten Lichtpolarisation aus. Basierend auf diesem Ansatz werden numerische Modenberechnungen von Mikrokavitäten mit optisch uniaxialen Kavitätsschichten vorgenommen. Generell sind die Moden in einem solchen System elliptisch polarisiert, und zudem i.A. nicht orthogonal. Ein besonderes Phänomen stellen sogenannte exzeptionelle Punkte dar. Dies sind Richtungen, für welche Energie und Verbreiterung der zwei Kavitätsphotonmoden zugleich entarten. Die Moden werden an solchen Punkten zirkular ko-polarisiert, die Orientierung der linearen Modenpolarisation windet sich im Impulsraum um diese Punkte herum. Die Eigenschaften der anisotropen Mikrokavitäten und exzeptionellen Punkte sind charakteristisch für singuläre, biaxiale Optik. So entsprechen die exzeptionellen Punkte Richtungen sogenannter singulärer optischer Achsen der effektiv biaxialen Strukturen, und können als Entartung nicht-Hermitescher Operatoren beschrieben werden. Die experimentelle Realisierung wird am Beispiel ZnO-basierter Mikrokavitäten gezeigt und bestätigt die theoretischen Vorhersagen im Wesentlichen, wenngleich im Experiment keine komplett zirkular polarisierten Zustände an den Entartungspunkten beobachtet wurden.:0 Introduction 1 Theory I: Linear optics principles 1.1 Maxwell theory 1.1.1 Plane-wave ansatz 1.1.2 Light polarization 1.1.3 Crystal optics 1.1.4 The polariton concept 1.2 Matrix formalisms for planar structures 1.2.1 Transfer-matrix approach 1.2.2 Scattering, Jones and Müller matrices 2 Theory II: Planar optical microcavities 2.1 Fabry-Pérot resonators and photonic modes 2.2 Practical mode computation 2.3 Quasi-particle approach 3 Computation: Exceptional points in anisotropic microcavities 3.1 Numerical methods 3.2 Model and findings for anisotropic, dielectric microcavities 3.3 Classification and discussion 3.3.1 General characteristics of exceptional points in anisotropic microcavities 3.3.2 Polarization vortices and singular optics 3.3.3 Net topology of the system 3.3.4 Effective-medium approaches 3.3.5 Quasi-particle approaches 3.3.6 Other familiar systems and phenomena 3.4 Anisotropic exciton-polaritons 4 Experiment: ZnO-based planar microcavities 4.1 Microcavity samples 4.2 Experimental methods 4.3 Experimental results vs. theoretical computations 4.4 Summary and discussion 5 Conclusion A Appendix A.1 Determining optic axes A.2 Exceptional points A.3 Expressions in Gaußian CGS units A.4 Polarization patterns of isotropic microcavities Bibliography Symbols and Abbreviations Authored and co-authored publications directly related to this thesis Acknowledgments Curriculum Vitae / In this thesis, planar optical cavities are investigated. They consist of a cavity layer which is surrounded by multi-layer mirrors. Using a transfer matrix technique for planar structures, a general mode condition is developed, which allows computation of cavity-photon modes for planar microcavities, which consist of optically arbitrarily anisotropic media. With this approach, no prior restriction of the considered light polarization is required. Based on this formalism, numerical computations of planar microcavities with optically uniaxial cavity layers are performed. Generally, the cavity-photon modes in such systems obtain elliptic polarization. Furthermore, they are in general not orthogonal to each other. A particular phenomenon is the occurrence of so called exceptional points. Here, the two cavity-photon modes degenerate in energy and broadening simultaneously, and the modes become circularly co-polarized. In addition, the exceptional points are vortex centers in momentum space for the orientation of the linear polarization of the modes. With this, anisotropic planar microcavities show typical characteristics of singular as well as biaxial optics. The exceptional points can be regarded as singular optic axes of the effectively biaxial structures. They can be described by the degeneracy of non-Hermitian operators. Experimental implementation is demonstrated by ZnO-based microcavities. In general, experimental findings prove the theoretical predictions, albeit the degree of circular polarization does not approach 100% at the exceptional points.:0 Introduction 1 Theory I: Linear optics principles 1.1 Maxwell theory 1.1.1 Plane-wave ansatz 1.1.2 Light polarization 1.1.3 Crystal optics 1.1.4 The polariton concept 1.2 Matrix formalisms for planar structures 1.2.1 Transfer-matrix approach 1.2.2 Scattering, Jones and Müller matrices 2 Theory II: Planar optical microcavities 2.1 Fabry-Pérot resonators and photonic modes 2.2 Practical mode computation 2.3 Quasi-particle approach 3 Computation: Exceptional points in anisotropic microcavities 3.1 Numerical methods 3.2 Model and findings for anisotropic, dielectric microcavities 3.3 Classification and discussion 3.3.1 General characteristics of exceptional points in anisotropic microcavities 3.3.2 Polarization vortices and singular optics 3.3.3 Net topology of the system 3.3.4 Effective-medium approaches 3.3.5 Quasi-particle approaches 3.3.6 Other familiar systems and phenomena 3.4 Anisotropic exciton-polaritons 4 Experiment: ZnO-based planar microcavities 4.1 Microcavity samples 4.2 Experimental methods 4.3 Experimental results vs. theoretical computations 4.4 Summary and discussion 5 Conclusion A Appendix A.1 Determining optic axes A.2 Exceptional points A.3 Expressions in Gaußian CGS units A.4 Polarization patterns of isotropic microcavities Bibliography Symbols and Abbreviations Authored and co-authored publications directly related to this thesis Acknowledgments Curriculum Vitae