How do I experimentally obtain the group index or phase index of waveguides? What kind of waveguide could help? Any literatures?
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.
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.
The group index can be measured with an interferometric device assymetric MZ or ring resonator. Positions of the different pics are only link to the optical path. If the length of the device is know, you can evaluate the effective index of the waveguide versus the wavelength. For example, in the case of a Mach-Zehnder, variation of the power is related to cos²(2*pi*neff*L/wavelength). You have a maximum when 2*pi*neff*L/wavelength = k*pi. If neff is modeling by neff = a+b*wavelenght, normaly with 3 position of the resonant wavelength, you can determine a, b and k, but the determinant of the linear system is 0 because a and k are link. In general, we perform the modeling with a mode solver and we fixe the parameter to the value obtain by the calculation. As the group index is link to the other parametr of the model (b in this example), the indetermination of a does not affect the result.
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