It is known that constructive interference in one place must be compensated for by destructive interference in another. Take a simple Fabry Perot resonator for example. The interference occurring at both sides of the first mirror (assuming one incident electric field) compensate each other out, leading to the familiar transmissivity/reflectivity curves.
My question is, what about the interference between the forward and backward propagating fields in the resonator itself? If we choose the resonator length such that this interference is constructive/destructive on average, there doesn't seem to be a place where opposite interference can occur to cancel it out.
Edit: Still no luck finding an answer. Most simply take the absolute value squared of the individual fields when calculating the total intensity. While this does obey energy conservation, Maxwell's equations tell us that two counter-propagating waves undergo interference, and it doesn't seem like one can simply ignore this interference.