Extraction of power transmission parameters from PT-symmetric waveguides

The PT-symmetric waveguides have been frequently discussed in the photonics community due to their extraordinary properties. Especially, the study of power transmission is significant for switching applications. The aim of this study is to extract the mode power transmission parameters based on the coupled mode equations and analyze the power properties of the PT-symmetric system. The equations relying on the coupled mode theory are constructed according to the two different orthogonality relations between the original and adjoint system. The results matching well with the finite difference simulations demonstrate the validity of our method, while the conventional coupled mode theory fails. The power properties in the PT-symmetric and PT-broken phases are also observed. Furthermore, a new integration is implemented from which the conserved quantity is defined and extracted, which reflects the Hamiltonian invariant of the system. Our method fully incorporates the properties of complex modes and allows the study of the power transmission properties based on the orthogonality relations, which is also applicable to other types of non-Hermitian optical systems. This work provides what we believe to be a new perspective for the power analysis of PT-symmetric waveguides and is helpful to design the switching devices.