Linear Susceptibility (χ(1)) is the susceptibility is associated with bound electrons (dipoles) moving around as the light propagates through a medium, referred to as the dipole moment. The following expression indicates how polarization, P, of light in a medium is related to the linear or first order susceptibility of the material to the optical electric field, E.
In a rigorous mathematical treatment the susceptibility is considered in terms of a real and imaginary part. The optical propagation 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: