The challenge
A fiber carries a signal over long distances with low loss, but every bend degrades its performance. Bending deforms the guided-mode field distribution relative to that of a straight waveguide, so part of the optical power leaks from the core into the cladding and radiates outward. Accurately modeling these losses is key when designing fibers, maintaining signal integrity in optical networks, and in compact photonic integration, where tight bends can sometimes be unavoidable. The question is: at what bend radius do the losses become unacceptable?
The solution
SMF-28 fiber was modeled in the FEM solver of OptiMode at a wavelength of λ = 1550 nm: a doped-silica core (n = 1.44916, diameter 8.3 μm) in a pure-silica cladding (n = 1.44346), with PML boundary conditions absorbing the fields far from the core. Bend loss follows directly from the imaginary part of the mode's complex effective refractive index:
Loss (dB/m) = 4.343 · (4π · Im(n_eff) / λ)
The key technique is "stepping" through the bend radius: the simulation starts from a very large radius (a well-guided mode) and then steps down to the target radius in small increments, using the mode coefficient from the previous step as the estimate for the next one. This keeps the solver locked onto the same mode branch and prevents it from jumping to unphysical states. Repeating this across a range of radii yields the full loss characteristic.
Field amplitude distribution |Ex| at R = 6 mm — the mode field shifted from the core toward the cladding (radiation).
Bend loss as a function of radius — OptiMode (FEM) results match the analytical model.
Results
- Loss as a function of bend radius — below 0.5 dB/m at R = 14 mm, rising to hundreds of dB/m at R = 6 mm.
- Excellent agreement with the analytical model — the FEM results match the analytical solution (Faustini and Martini, 1997), confirming the reliability of the method.
- A visible loss mechanism — at R = 6 mm the mode field clearly shifts from the core toward the cladding, and the radiation shows up as the imaginary part of n_eff.
- A basis for design decisions — an unambiguous choice of minimum bend radius for a given loss budget, before production.
Software used
Dlaczego to narzędzie. OptiMode is Optiwave's FEM mode solver for analyzing waveguide and fiber modes. It calculates the complex effective refractive index, from which bend loss follows directly — this is the domain of finite-element mode analysis.
Want to determine the minimum bend radius for your fiber or waveguide at a given loss budget? Request an OptiMode trial or get in touch with us — we'll show you how to build this kind of mode analysis.
Uwaga. An example based on an Optiwave application note for OptiMode; the results were verified for agreement with the analytical model (L. Faustini, G. Martini, "Bend loss in single-mode fibers," J. Lightwave Technol., 1997).