RF and Microwave Engineering: Fundamentals of Wireless Communications

2.5 Electromagnetic Waves

2.5.1 Wave Equation and Plane Waves

Now we will take a look at wave propagation in homogeneous, lossless,¹⁴ non-conducting media. Again we start with Maxwell's first and second equation in differential form

2.88

2.89

We are interested in non-conducting media so the conductivity is zero (σ = 0) and there is no conduction current density . On the right-hand side of Ampere's law (Equation 2.88) only the displacement current density remains. First we apply the curl operator and the constitutive relation (with μ = μ₀μ_r) on Equation 2.89.

2.90

Now we insert Equation 2.88 into Equation 2.90 by using the constitutive relation (with ε = ε₀ε_r). Since we assume the medium to be time-invariant we can write the material parameters outside the derivative.

2.91

As in our discussion ...