Colgate University

Rui: Three Dimensional Complex Light Forms -while Most Familiar Light Beams, Such as Those From a Laser Pointer, Have a Relatively Simple Structure and Intensity Pattern, Far More Complex Structures Are Possible. These Structures Are of Interest Both Intrinsically and for Potential Practical Applications. Deliberate Manipulation of the Phase and Intensity of Light Beams Can Create Patterns in Three Dimensions That Have Focal Lines Along Curved Paths, Rotate or Transform the Light's Transverse Pattern as It Travels, or Have Points Along Its Wavefront That Oscillate in Unison But With Patterned Orientations. the Goal of This Research Project Is to Explore Techniques for the Creation of Novel Three-dimensional Patterns Including Those That May Be of Interest for Applications. the Pi and His Undergraduate Research Team Will Look for Inspiration in the Connections Between Optical Beams in the Laboratory and Other Physical Systems, Such as - on the Cosmic Scale ? the Deflection of Light by Gravity Around Astrophysical Objects and ? on the Microscale ? Oscillations of a Pendulum Governed by Quantum Mechanics. Connecting These Diverse Physical Systems and Size Scales Is Possible Due to the Similarities in the Mathematical Structure of These Problems and the Wave Equation of the Light. Within This Framework, the Research Team Will Also Investigate Communication via the Rotation of Patterned Beams and New Types of Optical Beams With Low Divergence. Similarities Between Quantum Entanglement and Wave Behavior Also Give Rise to New Parallels That Are of Interest to Pursue. in Addition to Basic Research, the Team Will Incorporate Research Outcomes Into Undergraduate Laboratory Experiences Thereby Making a Direct Connection Between Research and Undergraduate Classroom/lab Instruction. the Training of Undergraduate Students in Basic Research, and the Development of Instructional Laboratories Which Can Be Used by Many Institutions, Will Help Prepare Students to Join the Emerging Quantum Workforce. the Manipulation of Light?s Degrees of Freedom in Polarization, Spatial Mode, Momentum, Energy, and Photon Number Can Lead to Novel Patterns in Three Dimensions That Are of Fundamental Interest and Can Lead to Applications in Biomedical Imaging and Communications. via Table-top Optics Experiments, Amenable to the Undergraduate Setting, the Pi and His Students Will Study Novel Problems That Harness the Similarity in Mathematical Structure Between Light?s Wave Equation and Other Physical Systems, Such as Cosmic Gravitational Lensing and Atomic and Molecular Nonlinear Oscillations. the Outcomes Are Three-dimensional Patterns That Carry Caustics and Vortex Singularities, Which Are Novel in Their Own Right and Can Be Exploited for New Applications. One Such Application Is in Communications Where the Information Is Encoded in the Rotation of Beam Patterns. at the Quantum Level, Parallels Between Photon Entanglement and Classical Optical Metrology Are Also Expected to Harness New Types of Non-local Metrology. This Award Will Support the Continuation of an Ongoing Program in the Development and Dissemination of Instructional Quantum Optics Laboratories Which Serve to Connect Research With Instruction. These Laboratories Will Help Educate the Emerging Quantum Information Workforce at and Beyond the Pi?s Home Institution. This Award Reflects NSF'S Statutory Mission and Has Been Deemed Worthy of Support Through Evaluation Using the Foundation's Intellectual Merit and Broader Impacts Review Criteria.- Subawards Are Not Planned for This Award.