2.7 Decoupling of the Electric and Magnetic Fields in Zero-Index Medium
49
(a)
(b)
Fig. 2.22 Nature of a electric and b magnetic fields inside a mu-near-zero (μ ≈ 0) medium
⎡
⎣
ˆ
i ˆ
j ˆ
k
∂
∂x
∂
∂ y
∂
∂z
E x 0 0
⎤
⎦ = iωμH y ˆ
j
(2.30)
or
∂ E x
∂z
= iωμH y
(2.31)
Now, for an MNZ medium (with μ ≈ 0)
∂ E x
∂z
≈ 0
(2.32)
From which it can be inferred that the electric field is spatially invariant (i.e., invariant with respect to z) inside a mu-near-zero medium. Please note that near-zero
permeability does not affect the variation of the magnetic field H , which remains
sinusoidal as usual. Figure 2.22 shows that the variation of the electric and magnetic
fields inside a medium having μ ≈ 0.
It can be noticed that the magnitude of the electric field (blue) remains constant
throughout the MNZ medium, while the magnetic field component (red) exhibits
sinusoidal variation. Moreover, the phase of the electric field at the emergence boundary is the same as that at the incidence boundary. This is evidence of the fact that
using an MNZ metamaterial the electric field of an electromagnetic wave can be
handled independently without disturbing the magnetic field component.
On performing a similar analysis using Eq. 2.28, it can be shown that for an E x –
H y –k z mode in an ENZ ( ≈ 0) medium, the magnetic field becomes uniform, while
the electric field remains sinusoidal. The corresponding plots for the variation of the
electric (blue) and magnetic fields (red) are shown in Fig. 2.23.
∂ H y
∂z
= 0
(2.33)