Nearly circular pump guides

How nearly circular can a double-clad fiber's pump guide be and still have good absorption in the core? D's and octagons have good absorption but can be hard to cleave and lose pump power or brightness through splices with circular fibers. Ray tracing cannot be trusted since the perturbations to the circle can be smaller than a transverse wavelength. Using an algorithm well suited to near-circular boundaries, we have computed statistics of core-overlap of the lowest 10,000 modes of many pump-guide shapes. Some with 3% radial modulation have nearly as good core-overlap as an octagon.