  Intermodal interactions displayed through the phenomena of mode coupling and
conversion in optical systems are treated by means of the Lindstedt-Poincare
perturbation method of strained parameters more widely known in classical
quantum mechanics and quantum chemistry as the stationary perturbation
technique. The focus here is on the mode conversion at the points of virtual
phase matching (otherwise called anticrossings or avoided crossings) associated
with the maximum conversion efficiency. The method is shown to provide a
convenient tool to deal with intermodal interactions at anticrossings --
interactions induced by any kind of perturbation in dielectric index profile of
the waveguide, embracing optical inhomogeneity, magnetization of arbitrary
orientation, and nonlinearity. Closed-form analytic expressions are derived for
the minimum value of mode mismatch and for the length of complete mode
conversion (the coupling length, or the beat length) in generic waveguiding
systems exhibiting anticrossings. Demonstrating the effectiveness of the
method, these general expressions are further applied to the case of TE -- TM
mode conversion in (i) a multilayer gyrotropic waveguide under
piecewise-constant, arbitrarily oriented magnetization, and (ii) an
optically-inhomogeneous planar dielectric waveguide -- an example which the
standard coupled-mode theory fails to describe.
