The group index and group velocity dispersion of waveguides have been measured by employing an integrated Mach-Zehnder interferometer [Optics Express 14(9), 3853 (2016)] or a free-space Mach-Zehnder interferometer [Appl. Phys. Lett. 80, 416 (2002)]. There are also works in which the propagation constant and dispersion parameter were measured in microrings [Optics Express 17(16), 14098 (2009); Optics Express 26(3), 2807 (2018)], but in this case I don't know what is the influence of the bending. Qualitatively speaking, I suppose that if the bending radious is big and bending losses are small the difference compared to a straight waveguide is small. I hope it was of any help. I am really interested if someone knows more about it.

The group index and group velocity dispersion of waveguides have been measured by employing an integrated Mach-Zehnder interferometer [Optics Express 14(9), 3853 (2016)] or a free-space Mach-Zehnder interferometer [Appl. Phys. Lett. 80, 416 (2002)]. There are also works in which the propagation constant and dispersion parameter were measured in microrings [Optics Express 17(16), 14098 (2009); Optics Express 26(3), 2807 (2018)], but in this case I don't know what is the influence of the bending. Qualitatively speaking, I suppose that if the bending radious is big and bending losses are small the difference compared to a straight waveguide is small. I hope it was of any help. I am really interested if someone knows more about it.

Thanks Alberto. It is very helpful.

I think you can make MZI structure with length difference between the two arms. You can obtain the phase difference from the curve-fitting, from which you can extract the group index.