POLARIZATION OF DIELECTRIC

The electric polarization P has been expressed in terms of ξ, the displacement of the electrons, and its space and time derivatives. It is found to have a very complicated dependence and only in the first order of approximation it reduces to the expression P=-eN 0 ξ, where N 0 is the density of the electrons of charge -e. The use of this relation by Kronig and Boukema and by Adler for the second-order terms in P and ξ is not justified; this has been discussed. Also, it is shown that the polarization cannot be expressed as a power series in the electric field. If the field consists of only the plane waves, the Fourier amplitudes of the polarization can be expressed as a power series in the electric field but the expression is not very satisfactory as i) the coefficients are different for different combinations of the Fourier amplitudes of electric field and ii) they are not constants and have dependence on both the frequencies and directions of propagation in the medium of the Fourier amplitudes of the electric field associated with them. © 1968 Società Italiana di Fisica.