Consider a charged particle moving relativistically along x -axis in a medium with refraction index n ( ω ω ) = ε ε ( ω ω ) with a constant velocity v → → = ( v , 0 , 0 ) . Start with Maxwell's equations (in Gaussian units) in the wave forms (also known as the Lorenz gauge condition) and take the Fourier transform: ( k 2 − − ω ω 2 c 2 ε ε ( ω ω ) ) Φ Φ ( k → → , ω ω ) = 4 π π ε ε ( ω ω ) ρ ρ ( k → → , ω ω ) ( k 2 − − ω ω 2 c 2 ε ε ( ω ω ) ) A → → ( k → → , ω ω ) = 4 π π c J → → ( k → → , ω ω )