Question

what is the weak coupling approximation in optics

Answer 1

There are a number of things this could refer to, but one possibility is the following:

When electromagnetic waves travel through a waveguide, each mode is orthogonal to the others. However, when the dielectric permittivity of the medium is allowed to vary down the length of the waveguide, it is possible to have different modes couple to one another, i.e. exchange energy between them. The weak-coupling approximation in this context is the assumption that the coupling occurs only between two modes, and not simultaneously between three or four.