This five-year project studied novel liquid crystal polarization grating films and devices, each with complex 3D structure. Immensely useful and efficient holograms with surprising behaviour emerged from this work, with broad applicability throughout the field of optics and photonics. We developed modeling tools, breakthrough fabrication processes, and dramatically improved the viability and scope of a new class of photonic elements with remarkable control over the intensity, direction, orbital angular momentum, and polarization of light. In particular, we realized how to fabricate and more deeply understand Geometric-Phase Holograms (GPHs), also known as complex polarization grating based Fresnel optical elements. We also created ultra-efficient and agile vortex and vector beam generators and analyzers. Finally, we began an investigation of distributed-feedback effects in polarization gratings combined with semiconducting/fluorescent polymers.

This PECASE award has so far resulted in 12 journal articles, 16 conference proceedings, 2 PhD dissertations, 1 US patent application (licensed to an industrial partner), 2 invention disclosures, and 1 cover-feature magazine article. The award supported substantial portions of four PhD students' dissertations, including two US citizens. Four undergraduate students conducted substantial research efforts based on the topics in this award.

Many scientific and applied contributions arose out of the work supported by this award, including the following representative top seven. (1) We developed the most advanced Geometric Phase (GP) Lenses for visible and infrared light, i.e., with nearly 100% efficiency, fastest apertures down to F/1.8 and beyond, largest sizes of more than 100 mm diameter, and lowest reported aberration. Viable GP Lenses have immensely strong potential to enhance a wide range of applications in displays, telecommunications, imaging, and beyond. (2) In another thrust of this award, we developed novel vortex and orbital-angular-momentum (OAM) control elements, including a forked polarization grating and a stacked q-plate vortex beam generator/analyzer, useful to manipulate OAM in communication and microscopy systems with substantial simplifications of hardware. (3) Along with complementary support from industry, we were also able to develop the smallest period polarization gratings (by an order of magnitude), and still maintain the nearly 100% efficiency. (4) We also devised a way to apply distributed-feedback (DFB) principles to lead to dramatically smaller threshold and higher efficiency liquid crystal lasers. (5) Supporting all of the above, we invented a new type of laser printer/scanner, with the ability to print four-dimensions of information, in order to create the complex arbitrary orientational profiles in liquid crystal thin-films. (6) We also discovered how to employ multi-twist retarders (MTRs) to create high chromatic retardation effects, including creating diffractive elements that (e.g.) are transparent at visible wavelengths while strongly diffracting in the infrared. (7) Finally, the novel fabrication and simulation capabilities mentioned above facilitated partnerships with several astronomical instrumentation groups, most strongly with Leiden University (NL), who have designed and deployed some of the world's most advanced coronagraphs studying exosolar planets using elements fabricated by the PI and graduate students with the tools developed within this award.

This award supported a wide range of outreach activity. In partnership with the Science House and other NSF-supported STEM programs, the PI and graduate students engaged in afternoon-long sessions with over 100 high sch...

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