Analytical Framework for Tunable Spectral Permittivity in Polar Media under DC Bias

Abstract

A theoretical model is presented to describe the nonlinear dielectric response of a polar medium simultaneously subjected to a DC bias field and a harmonic AC excitation. Starting from a second-order anharmonic differential equation, the Homotopy Analysis Method (HAM) is applied to obtain closed-form analytical solutions for both transient and steady-state behavior up to the sixth order in the homotopy series. The results reveal the generation of $2 \omega$ and $3 \omega$ harmonics, temporal modulation of the induced polarization, and a quadratic tuning of the effective permittivity with the DC field. The work combines a complete analytical formulation of HAM, numerical validation, and a detailed physical analysis of the steady-state regime, emphasizing spectral dispersion, stability, and total harmonic distortion.