Total transmission of inhomogeneous electromagnetic waves at planar interfaces

We present the total transmission effect of inhomogeneous electromagnetic waves between dissipative media. The total transmission of a $p$-polarized plane wave at the interface between two lossless dielectrics happens at the Brewster angle. However, when a dielectric-conductor interface is considered, the effect cannot be achieved and there is only a minimum, different from zero, of the reflection coefficient. We prove that, by considering an inhomogeneous plane wave, the total transmission can be obtained both at the interface between two dissipative media and at the dielectric-conductor interface.

Figure 1

Geometry of the problem.

Figure 2

Magnitude of the Fresnel reflection coefficient for an interface between aluminum and gold at $\lambda =7.7$ $\mu \mathrm{m}$, with permittivities ${\varepsilon }_1=0.12+i0.04$ and ${\varepsilon }_2=0.84+i1.91$, respectively. Two cases are considered: when the incident wave is homogeneous (solid line) and when the incident wave is inhomogeneous with ${\eta }_1={\eta }_B$ (dashed line).

Figure 3

Magnitude of the Fresnel reflection coefficient for an interface between seawater and a loamy wet soil, with permittivities and conductivities ${\varepsilon }_1=81,{\sigma }_1=100\text{S}{\text{m}}^{-1}$ and ${\varepsilon }_2=15,{\sigma }_2=0.1\text{S}{\text{m}}^{-1}$, respectively. Two cases are considered: when the incident wave is homogeneous (solid line) and when the incident wave is inhomogeneous with ${\eta }_1={\eta }_B$ (dashed line).

Figure 4

Magnitude of the Fresnel reflection coefficient for an interface between air and gold at $\lambda =7.7$ $\mu \mathrm{m}$, with permittivity ${\epsilon }_2=0.84+i1.91$. Two cases are considered: when the incident wave is homogeneous (dashed line) and when the incident wave is inhomogeneous with ${\beta }_1={\beta }_B$ (solid line). In both cases the reflection coefficient has been computed by an electromagnetic simulation (circles).

Figure 5

Two-dimensional maps (plotted on the same scale) of the real part of the magnetic field of a plane wave in $p$ polarization incident at the interface between a vacuum and medium 2 with relative permittivity ${\varepsilon }_2$. (a) Medium 2 is lossless, with ${\varepsilon }_2=0.84$, the incident wave is homogeneous, and the incident angle is the Brewster angle. (b) Medium 2 is dissipative, with ${\varepsilon }_2=0.84+i1.91$ (gold at wavelength $\lambda =7.7$ $\mu \mathrm{m})$, the incident wave is homogeneous, and the incident angle is the pseudo-Brewster angle. (c) Medium 2 is dissipative [as in (b)], the incident wave is inhomogeneous with ${\beta }_1={\beta }_B$, and the incident angle is the Brewster angle.

Figure 6

Magnitude of the Fresnel reflection coefficient for an interface between air and seawater at a frequency of 100 MHz $({\varepsilon }_1=1,{\varepsilon }_2=81$, and ${\sigma }_2=100\text{S}{\text{m}}^{-1})$. Two cases are considered: when the incident wave is homogeneous (solid line) and when the incident wave is inhomogeneous with ${\beta }_1={\beta }_B$ (dashed line).