We report the first complete set of measurements of a laser-plasma optical system's refractive index, as seen by a second probe laser beam, as a function of the relative wavelength shift between the two laser beams. Both the imaginary and real refractive index components are found to be in good agreement with linear theory using plasma parameters measured by optical Thomson scattering and interferometry; the former is in contrast to previous work and has implications for crossed-beam energy transfer in indirect-drive inertial confinement fusion, and the latter is measured for the first time. The data include the first demonstration of a laser-plasma polarizer with 85%-87% extinction for the particular laser and plasma parameters used in this experiment, complementing the existing suite of high-power, tunable, and ultrafast plasma-based photonic devices.