Reciprocal waveguide coupled mode theory

Mode coupling is a common phenomenon in waveguides. The mode coupling among different guided modes in fiber-optic communication can cause crosstalk, and the mode coupling of guided mode and radiated mode can reduce the power of the guided mode. Application of mode coupling can guide the design of optical devices such as couplers and beam splitters with specific functions, which have been widely used in fiber optic communication and fiber sensing. So it is important to analyze how waveguide modes are coupled. The coupled-mode theory is a common method of studying mode coupling in waveguides. It provides not only an intuitive picture of how the photonic modes are hybridized, but also a quantitative assessment of how the hybridization among those relevant modes evolves. In recent years, non-Hermitian waveguides, represented by parity-time symmetrical structures, have become a research hotspot. However the conventional coupled-mode theory no longer works in this case. In this review, we briefly summarize the development history of coupled-mode theory and introduce the representative work in reciprocal waveguide coupled-mode theory in detail. Then the relationship among several coupled-mode theories is analyzed and their applications are briefly introduced.