Theoretical study of complex functions of the birefringence in alternating fields

In the case of a nonlinear stationary response resulting from the application of an alternating field superimposed on a continuous field in a dielectric liquid, the birefringence of that medium is well expressed as real and imaginary parts of two normalized complex birefringence functions Δ$N_j^{\mathrm{*}}$=$X_j$-${\mathrm{iY}}_j$, where j=1,2. By eliminating the angular frequency ω in the parametric equations $X_j$(ω) and $Y_j$(ω), Cartesian equations are obtained, which provide new quantitative interpretations of $Y_j$($X_j$) experimental plots. Moreover, for each harmonic term, a polar equation is established indicating that, in the complex plane, the end of the vector Δ${\mathrm{N}}_j$=($X_j$,$Y_j$) describes a set of quasiconchoids of circles whose radii vary with P, the ratio of the induced dipole moment to the permanent dipole moment. For any value of P, changes in phase angle ${\theta }_j$ with frequency are widely considered because of their very interesting use in Kramers-Kronig relations.