# What is the relationship between the nonlinear susceptibility and the effective nonlinear coefficient?

Oftentimes, I see equations for non-linear optics expressed in terms of the non-linear susceptibility tensor.

Other times, however, I see these same equations expressed in terms of an effective non-linear coefficient tensor.

What's the relationship between these two things? What am I missing here?

The nonlinear coefficient tensor $$d_{il}$$ is a contraction/approximation of the nonlinear susceptibility tensor $$\chi_{ijk}$$ under certain symmetries (here talking about second-order effects, $$\chi^{(2)}$$).