  The resonance wavelength, where a fiber mode converter grating written using
periodic external perturbations achieves phase matching, is both a critical
design parameter and a device parameter. However, a method to precisely predict
the resonance wavelength for any new fiber and grating writing apparatus has
been missing so far. The missing link was the lack of direct experimental
methods to estimate the modified intermodal phase after writing with external
perturbations. The presented method can make this estimation from a single
experiment, over a broad wavelength range, based on a novel mathematical
connection between two-mode interference and mode conversion. Using the novel
methods, experimentally measured resonance wavelengths for different pitch and
irradiation conditions have been predicted within relative errors of 0.004.
