text permittivity tilde varepsilon varepsilon frac i sigma omega varep

Question

\text { permittivity, } \tilde{\varepsilon}=\varepsilon+\frac{i \sigma}{\omega \varepsilon_{0}} \text {, where } \sigma \text { is the electric conductivity: } \left(\nabla \times \varepsilon^{-1} \nabla \times \mathbf{H}-\frac{\omega^{-}}{c^{2}} \mu \mathbf{H}=\nabla \times \varepsilon^{-1} \mathbf{j}_{s}\right) 2. In class we have derived the wave eq. for E-field using the concept of complex \nabla \times \mu^{-1} \nabla \times \mathbf{E}-\frac{\omega^{2}}{c^{2}} \tilde{\varepsilon} \mathbf{E}=i \omega \mu_{0} \mathbf{j}_{s} \text {. Derive another one for the H-field. Does these eqs. work in } the case of an inhomogeneous structure? Nonlinear structure? Explain your answer?