摘要
Group theory(GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles(such as parity-time invariance and supersymmetry) have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this status quo, here we present a brief overview of the application of GT in optics, deliberately choosing examples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.
Group theory （GT） provides a rigorous framework for studying symmetries in various disciplines in phy- sics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a powerful tool in optical physics remains limited. Over the past few years however, several quantum-inspired symmetry principles （such as parity-time invariance and supersym- metry） have been introduced in optics and photonics for the first time. Despite the intense activities in these new research directions, only few works utilized the power of group theory. Motivated by this sta- tus quo, here we present a brief overview of the application of GT in optics, deliberately choosing exam- ples that illustrate the power of this tool in both continuous and discrete setups. We hope that this review will stimulate further research that exploits the full potential of GT for investigating various symmetry paradigms in optics, eventually leading to new photonic devices.
基金
support from the Photonics and Mathematical Optics Group at Tecnologico de Monterrey and Consorcio enóptica Aplicada through CONACYT FORDECYT#290259 project grant
support from Henes Center for Quantum Phenomena,Michigan Technological University
support from Spanish MINECO projects FIS2014-57387-C3-3P and DPI2013-47100-C2-1-P
