Supersymmetry in Optics: Beyond Traditional Supersymmetric Quantum Mechanics
Abstract
Supersymmetry in Optics: beyond Traditional Supersymmetric Quantum Mechanics Supersymmetry (SUSY) is a theoretical framework for extending the conventional spacetime symmetries. It has been commonly used in particle physics to relate bosonic and fermionic elementary particles, and the search for SUSY has been at the forefront of experimental efforts carried out by the Large Hadron Collider at CERN, which discovered the Higgs Boson in 2013. In the proposed research, SUSY will be viewed not as a fundamental symmetry of nature but employed as a powerful theoretical tool for optical design and implementation. The developed methods will bring in a new perspective on how optical design is carried out for specific device applications. The general framework and developed knowledge in this research can play an instrumental role in advancing the DoD mission in exploiting innovations to ensure the NationÕs technological superiority, especially in the strategic field of optics and photonics. Most recently, SUSY has been shown to play an instrumental role in controlling the propagation of light in certain classes of optical waveguides. The optical designs enabled by SUSY are quite novel and can potentially play an important role in advancing the future of optics and photonics. A specific form of SUSY dubbed as SUSY quantum mechanics (SUSY-QM) was first introduced as a toy model to study supersymmetry breaking. It has since evolved into a powerful theoretical framework with many applications in theoretical physics. It has helped with the classification of potentials with identical spectra, has facilitated the analytical derivation of the spectra in certain classes of quantum mechanical Hamiltonians, has provided useful extensions to the WKB approximation, has benefited the physics of non-quantum statistical mechanics explored with Fokker-Planck equation, and has found applications in random matrix theory, disorder, and chaos. Most recently, SUSY-QM has been shown to play an instrumental role in controlling the propagation of light in certain classes of optical waveguides. The optical designs enabled by SUSY-QM are quite novel and can potentially play an important role in advancing the future of optics and photonics. The objective of this research is to explore various applications of SUSY in optics. The focus will be on novel uncharted territories, which do not fall within the traditionally well-explored framework of SUSY-QM in guided-wave optics. The proposed areas of research include the application of SUSY in classical stochastic optics, the extension of the ideas to quantum nonlinear optics and applications of SUSY field theories, parasupersymmetry, and random matrix theory to optics and photonics. Special attention will be paid to optical device applications with importance to the DoD mission.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 17, 2019
- Source ID
- W911NF1910352
Entities
People
- Arash Mafi
Organizations
- Army Contracting Command
- United States Army
- University of New Mexico