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    • 3.3: Wave Equations for Lossy Regions
      https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/03%3A_Wave_Propagation_in_General_Media/3.03%3A_Wave_Equations_for_Lossy_Regions
      We wish to upgrade the wave equations for electromagnetic propagation in lossless and source-free media  to account for the possibility of loss. First, let’s be clear on what we mean by “loss.” Specif...We wish to upgrade the wave equations for electromagnetic propagation in lossless and source-free media  to account for the possibility of loss. First, let’s be clear on what we mean by “loss.” Specifically, we mean the possibility of conversion of energy from the propagating wave into current, and subsequently to heat. This mechanism is described by Ohm’s law.
    • 3.4: Complex Permittivity
      https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/03%3A_Wave_Propagation_in_General_Media/3.04%3A_Complex_Permittivity
      \[\begin{align} \widetilde{\bf D} &= a_0\widetilde{\bf E} + a_1\left(j\omega\right)\widetilde{\bf E} + a_2\left(j\omega\right)^2\widetilde{\bf E} + a_3\left(j\omega\right)^3\widetilde{\bf E} + ... \no...˜D=a0˜E+a1(jω)˜E+a2(jω)2˜E+a3(jω)3˜E+...=a0˜E+jωa1˜E−ω2a2˜E−jω3a3˜E+...=(a0+jωa1−ω2a2−jω3a3+...)˜E

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