First order susceptability, χ(1)
The polarization, P, of light in a medium is related to the linear or first order susceptibility to the optical electric field, E, and describes its propagation through a medium.
In a rigorous mathematical treatment the susceptibility is considered in terms of a real and imaginary part. The speed in a medium comes from the real part of the susceptibility, while the imaginary part is related to absorption in the medium. The refractive index is also directly related to the linear susceptibility: