Excitation of two-dimensional plasmon polaritons by an incident electromagnetic wave at a contact

We consider the scattering of an incident electromagnetic radiation on a two-dimensional (2D) electron layer with an imbedded metallic contact. We show that the incident wave excites in the system the 2D plasmon polaritons running along the 2D layer and localized near it, and electromagnetic waves reflected back from the system. The ratio of the energy transformed to the 2D plasmon polaritons and reflected back from the layer depends on the frequency and the value of a retardation parameter, which characterizes the importance of retardation effects. When the retardation parameter is large, the energy of the incident radiation is mainly reflected from the 2D electron system and the excitation of the 2D plasmon polaritons is less effective. The results obtained are discussed in connection with recent experiments on the microwave response of the 2D electron systems.

Figure 1

Geometry of the considered structure. The width of the contact stripe is $W$.

Figure 2

The normalized absorption cross section vs the normalized frequency with (a) $\alpha ⩽0.5$ and (b) $\alpha ⩾0.5$. The inset in (b) depicts the curve for $\alpha =5$.

Figure 3

(Color online) The distribution of the 2D plasmon-polariton electric field $\mathrm{Re}{E}_x^{2\mathrm{DP}}∕E_x^0$ at $\alpha =0.1$ and the frequency $\omega ∕{\omega }_0=1$.

Figure 4

(Color online) The distribution of the 2D plasmon-polariton electric field $\mathrm{Re}{E}_x^{2\mathrm{DP}}∕E_x^0$ at different values of the retardation parameter with the frequency corresponding to the first maximum of the absorption cross section (Fig. 2).

Figure 5

The energy flow in the induced electromagnetic wave ${\mathbf{S}}^{2\mathrm{DP}}∕S_z^0$ at $\alpha =0.1$ and $\omega ∕{\omega }_0=1$. The quantity $c$ is the scaling factor of vectors, so that the actual value of a vector is equal to the length in coordinates divided by $c$.

Figure 6

The energy flow ${\mathbf{S}}^{2\mathrm{DP}}∕S_z^0$ at $\alpha =0.5$ and the frequencies corresponding to the maximum $(\omega ∕{\omega }_0=1.46)$ and to the miminum $(\omega ∕{\omega }_0=3.94)$ of the absorption cross section, see Fig. 2.

Figure 7

The energy flow in the induced electromagnetic wave ${\mathbf{S}}^{2\mathrm{DP}}∕S_z^0$ at $\alpha =2$ and frequencies, corresponding to maxima (left panels) and minima (right panels) of the absorption cross-section (Fig. 2).