What Medium Does Light Travel Through in Space?

[Sagittarius A-Star]

The EM-wave function follows from Maxwells equations.

Derivation of the EM wave function (a linear, second-order partial differential equation) from Maxwells equations in (3+1) notation, Gaussian CGS units (see posting #107)

Write the $curl$ of Faradays law:
$\nabla \times (\nabla \times \mathbf{E}) = \nabla \times \left( - \frac{\partial \mathbf{B}}{\partial (ct)} \right)$
Apply the vector identity $\nabla \times (\nabla \times \mathbf{A}) = \nabla(\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}$ on the LHS and switch order of partial and time derivatives on the RHS:
$\nabla(\nabla \cdot \mathbf{E}) - \nabla^2 \mathbf{E} = -\frac{\partial}{\partial (ct)} (\nabla \times \mathbf{B})$
Substitute Gauss's law ($\nabla \cdot \mathbf{E} = 0$) and Ampere's law for ($\nabla \times \mathbf{B}$):
$$\nabla^2 \mathbf{E} - \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} = 0$$