# Why the Divergence of Electric field is Zero?

I am studying nonlinear optics, specifically the wave equation of nonlinear optical media. During the derivation I came across a point where the divergence of electric field was zero for a linear isotropic medium. I couldn't understand the reason behind it.

• Hint: which of Maxwell’s equations tells you about divergence of E field, and what needs to be there for it to be nonzero? Aug 24 '20 at 14:24
• In English, only capitalize the first word of each sentence, names, and the word "I". English is not like German. Aug 24 '20 at 15:34

Usually, the derivations for wave equation of non linear optical media are done assuming, charge-free and current-free conditions, in which case $$\nabla \cdot \mathbf{D} = 0$$.
$$\nabla^2 \mathbf{E} - \frac{1}{c^2}\frac{\partial^2 \mathbf{E}}{\partial t^2} = \mu_0\frac{\partial^2 \mathbf{P}_{NL}}{\partial t^2},$$ where the $$\mathbf{P}_{NL}$$ is a non-linear function of $$\mathbf{E}$$. The term on RHS corresponds to source.