General coupled mode theory in non-Hermitian waveguides

Coupled mode theory (CMT) can be traced back to 3 decades ago, and has been an indispensable tool of analyzing and designing waveguides, resonators, couplers or many other devices from microwave frequency to optical frequency [1], in both time and space domain. In the presence of loss and gain, the coupled mode equation on describing the mode hybridization of various waveguides or cavities, or cavities coupled to waveguides becomes intrinsically non- Hermitian. In such non-Hermitian waveguides, the conventional coupled mode theory (CCMT, see [1]) fails.