  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 standard coupled coupled mode theory fails. We generalize the
coupled mode theory with a properly defined inner product based on reaction
conservation. We apply our theory to the non-Hermitian parity-time symmetric
waveguides, and obtain excellent agreement with results obtained by finite
element fullwave simulations. The theory presented here is typically formulated
in space to study coupling between waveguides, which can be transformed into
time domain by proper reformulation to study coupling between non-Hermitian
resonators. Our theory has the strength of studying non-Hermitian optical
systems with inclusion of the full vector fields, thus is useful to study and
design non-Hermitian devices that support asymmetric and even nonreciprocal
light propagations
