Complex notation for the dielectric response of ferroelectric materials beyond the small sinusoidal fields

For the polarization response beyond the small field range, Rayleigh's law has been introduced in the past to describe the field-dependent behavior (with loss) of ferroelectric materials with some success. We examine the relationship between Rayleigh's law and the complex dielectric constant notation that has been used widely in the scientific and engineering community; and we show that a modified complex notation can describe the field-dependent dielectric response with loss in the small and medium field range quite well. In addition, the modified complex notation easily can include a field independent dielectric loss that is, in fact, present in all the dielectric materials. The results also show that the alternating current (AC) field response is still predominantly linear with the amplitude and phase of the complex coefficient changing with the applied field amplitude