Читать книгу Introduction To Modern Planar Transmission Lines - Anand K. Verma - Страница 232

The above discussion shows that Maxwell's equations in the DNG medium are written in the LH‐coordinate system. However, the wave equation (4.5.32) of chapter 4 for the DPS medium remains valid for a lossless (σ = 0) DNG medium. It provides the following expressions for the propagation constant β = k^DPS and refraction index of a DPS medium:

(5.5.5)

The evaluation of the square root of negative permeability and negative permittivity is a critical issue in the DNG medium. The negative number (−1) is exp(±jπ). However, to meet the physical condition, discussed in subsection (5.5.3), we take {−1 = exp(−jπ)} [J.8, J.9]. Therefore, the square roots of negative permeability and negative permittivity are obtained as follows:

Using the above relations, the refractive index of a DNG medium, and also the propagation constant, are obtained as follows:

(5.5.6)

It is interesting to note that the refractive index for a DPS medium n^DPS is a positive quantity, whereas for a DNG medium n^DNG is a negative quantity. So the metamaterials are also known as the negative refractive index materials, i.e. the NIM. Snell's law of refraction for a DNG medium is also modified accordingly. The negative refractive index also shows the reversal of the direction of the phase velocity of the EM‐wave. However, first let us discuss the intrinsic impedance, i.e. the wave impedance for the DNG and SNG media.