Nonlinear Polarization of Dielectric

Using the relation between polarization $\overrightarrow{\mathrm{P}}$ and electron displacement $\overrightarrow{\mathrm{\xi }}$ obtained by Prakash and Vachaspati, it is shown that Adler misses some terms in the polarization due to two simultaneously incident electromagnetic waves because he presumes a linear relation between $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{\xi }}$.