Failure of the Weakly Guiding Approximation for Few-Mode Fiber Index Profiles

We demonstrate that for some few-mode fiber index profiles, the weakly guiding approximation (WGA) can be grossly inaccurate in wavelength regions where the true vector modes undergo an HE <-> EH transition. Within this transition region, the true vector modes have unusual properties, so they cannot be combined with other modes to form LP pseudo-modes. The failure of the WGA in the transition region is likely related to the near degeneracy of the modes obtained under the WGA, signaling the breakdown of standard perturbation theory, under which the WGA modes serve as zeroth-order approximations. We also demonstrate that a small perturbation to a commercial few-mode fiber index profile can introduce an HE <-> EH transition which is not present in the unperturbed design. Because the WGA can be grossly inaccurate at some wavelengths, it would seem safer to avoid its use for few-mode optical fiber design and simulation, using instead the exact version of Maxwell's equations. At the least, the exact equations should be used to check results obtained by the WGA in wavelength regions of interest.