Subject nonlinear dielectric

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

The nonlinear polarization Pi(fl, r ) of Eq. (10) is a pnrely local surface polarization because it only depends on the value of the fields at location r. Because it depends on the fundamental field inside the particle, it is subjected to resonances when the quantity s(ft)) + 2e , vanishes, where e(w) is the complex dielectric function of the metal and that of the surrounding medium. On the opposite, the nonlinear polarization 2( 2, E) of the form of Eq. (11) is a non local nonlinear polarization since it depends on spatially varying fields within the particle. Similarly to the first order contribution, it is subjected to resonances when the quantity 2e(w) + 3e vanishes. These resonances are the usual surface plasmon resonances of the particle. Within the condition of non magnetic media, the magnetic dipole field does not introduce any resonances. We neglect higher order terms. 

The dielectric polarization P of a medium with nonlinear susceptibility x. subject to an electric field E, can be written as an expansion in powers of the applied field... 

---