Abstract

Co-Author: Stanislav Maslovski Simultaneous localization of photons and phonons in optomechanical metamaterials offers a wide range of opportunities for enhancing light-matter interactions and exploring new physical phenomena. In this work, the Wiener-Hopf method is applied to address reflection and transmission problems at the interface of such metamaterials, including scenarios involving spatially dispersive media. This mathematical technique provides a rigorous framework for solving complex boundary value problems, allowing for precise analysis of the interactions at the interfaces of optomechanical structures. The results of this study can be used to optimize and design advanced optomechanical systems with improved performance and novel functionalities, paving the way for future technological innovations in photonics and quantum information processing.