Some doped polymers, for example PMMA, present high third order nonlinearity (n_2), up to the order of 10^ 6 cm^2/W. Does the dopant affect seriously the linear refractive index of the polymer?
Also, are there cases of materials that while presenting high nonlinear index they do not possess a similarly high nonlinear absorption coefficient, which makes them improper for optical devices?
It is a question of magnitude.
When adding a nonlinear dopant in a polymer matrix you are indeed changing the index of refraction. But when increasing the nonlinearity by several factors, the average index is only changed by a small fraction (1E-3). You also often induces birefringence.
As for the nonlinear index vs absorption, they are indeed linked and you can find a bunch of article developing the theory. You will find however that the coupling can be week and shifted in wavelength which allow use of one of the other depending of the light frequency.
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