Comparative Computational Analysis of Electromagnetic Wave Propagation in Conducting, Dielectric, and Plasma Media within the Extended Maxwell Formalism

The propagation of electromagnetic waves in conducting, dielectric, and plasma media is traditionally treated in separate theoretical frameworks — Drude theory of metals, Lorentz oscillator theory of dielectrics, and Appleton–Hartree theory of ionospheric plasmas. This separation, while pedagogically convenient, obscures the underlying unity of the wave-propagation problem in linear isotropic media. The present work develops a single computational framework, based on the complex-permittivity form of Maxwell's equations, that treats all three classes of media on equal footing. We compute the complex refractive index ñ(ω) = n(ω) + i k(ω), penetration depth δ(ω), phase velocity v_φ(ω), and group velocity v_g(ω) for representative media — copper (Drude), fused silica (single-oscillator Lorentz), and the daytime F2 ionospheric layer (cold collisional plasma) — across six decades of frequency from 10⁶ Hz to 10¹² Hz. Headline numerical results include a skin depth of 0.79 μm for copper at 10 GHz, an F2 plasma cutoff at 8.98 MHz, and an evanescent decay length of approximately 5 m for waves at 3 MHz in the daytime F2 plasma. A regime map summarizing the propagation behaviour of each medium across the full frequency range is presented as the central original contribution. All numerical results are validated against limiting-case analytical formulas. Limitations of single-oscillator fits are discussed and an extension toward polarised media via the formalism of Rasulov is outlined.