Is the index of refraction for LCP/RCP light any different from that for linearly polarized light?
Not in an isotropic material. Anisotropic materials have permittivities and/or permeabilities that depend upon the orientation of the incident fields. As such, the polarization of the light will affect the apparent index of refraction. Take as an example a birefringent material. You can take a circularly polarized light as being the superposition of two normal linearly polarized waves. So the CP light will behave differently from a LP wave since it will have a component normal to the LP wave. Though this would imply that the transmitted and reflected waves will not preserve circular polarization.
In chiral media (even isotropic ones like a solution of sugar) the index of refraction is different for LCP and RCP waves. One speaks of circular birefringence.
In these media, the index of refraction is not well defined for linear polarized waves as they are superpositions of LCP and RCP waves.
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