Exact solution for the 3D bent step-index optical fiber (envelope Maxwell model)

Determine the exact time-harmonic electromagnetic field solution to the envelope Maxwell boundary value problem in a three-dimensional circularly coiled, weakly guiding step-index optical fiber with core–cladding–coating structure, subject to perfectly matched layer absorbing conditions in both the circumferential and radial directions and excited at the input facet by the LP02 mode of the corresponding straight fiber.

Background

The paper extends an envelope Maxwell formulation with perfectly matched layers to model propagation in circularly coiled optical fibers and validates the approach on two-dimensional bent slab waveguides, where semi-analytic benchmarks are available.

For the fully three-dimensional bent step-index fiber case, the authors emphasize that they cannot rely on a known closed-form or benchmark solution and therefore guide mesh adaptivity using the DPG residual indicator while exciting the fiber with the straight-fiber LP02 mode at the input facet.