Electromagnetic wave cloaking and scattering around an antiresonance-resonance symmetrical pair in the frequency domain

Cloaking and scattering cancellation of electromagnetic waves have attracted much attention since they allow control of rf and light waves and are of scientific interest. The analytical results demonstrated in this paper reveal that plasmonic cloaking, which is one of the schemes for scattering cancellation, occurs in the vicinity of Tonks-Dattner resonances in the frequency domain, where resonances enhance wave scattering. This antiresonance-resonance pair for cloaking and scattering is cross-correlated by the symmetrical locations above and below the electron plasma frequency, respectively. However, the cloaking effect is almost independent of electron collisions with neutral particles, whereas scattering at resonance is fairly sensitive to them, leading to unclear resonance. An experimental verification of this analytical prediction is performed for the cloaking effect on working points passing through the cloaking condition and approaching resonance, which is dynamically controlled by changing the electron density. Numerical calculations based on a model configuration similar to the experimental setup confirm scattering cancellation and an increase in scattering as the points get close to the resonance condition. These results are direct evidence of scattering cancellation with a uniform epsilon-near-zero material and demonstrate the effectiveness of plasma as a cloaking material.

Figure 1

Schematic diagram of the metal cylinder coated with plasma layer.

Figure 2

Scattering width $Q_s$ as a function of electron elastic collision frequency ${\nu }_m$ and electron plasma frequency ${\omega }_{pe}$. Here, ${\nu }_m$ and ${\omega }_{pe}$ are normalized by a wave frequency ω/2π of 3 GHz.

Figure 3

Scattering width $Q_s$ as a function of plasma thickness $r_p\text{−}{r}_c$ and electron plasma frequency ${\omega }_{pe}$. Here, $r_p\text{−}{r}_c$ is normalized by the half wavelength λ/2 and ${\omega }_{pe}$ is normalized by a wave frequency ω/2π of 3 GHz. (a) ${\nu }_m/\omega =0$ and (b) ${\nu }_m/\omega =0.27$. White dashed lines show the contours of Eq. (7) and white dash-dotted lines show T-D resonances. The black dashed line in Fig. 3 corresponds to the experimental results in Fig. 10.

Figure 4

Schematic diagram of simulation model.

Figure 5

Dependence of scattering width on average electron density at 3 GHz.

Figure 6

Electromagnetic field distribution of scattered field and electric current obtained (a) without plasma ($n_{\mathrm{ave}}=0\mathrm{c}{\mathrm{m}}^{-3}$) and (b) with plasma $(n_{\mathrm{ave}}=3.8\times {10}^{10}\mathrm{c}{\mathrm{m}}^{-3})$.

Figure 7

Relation between scattering width and transmitted and reflected wave intensities.

Figure 8

Experimental setups: (a) schematic diagram of experimental setup and (b) photograph of plasma generated around the metal cylinder: D/C, directional coupler; M/B, matching box.

Figure 9

Time evolution of absorbed power and reflected wave intensity.

Figure 10

Absorbed power dependence of transmitted and reflected wave intensities.

Figure 11

Frequency dependence of transmitted wave intensity. (a) Experiment and (b) simulation.

Figure 12

Frequency dependence of reflected wave intensity. (a) Experiment and (b) simulation.

Figure 13

Scattering coefficient $c_n$ calculated from Eq. (5) as a function of plasma thickness under the condition of Eq. (7). $\omega /2\pi =3\mathrm{GHz}$, ${\nu }_m/\omega =0.27$, and $r_c=10\mathrm{mm}$. The blue solid line is $c_1$ calculated from Eq. (10).

Figure 14

Magnetic field distribution of $c_0$ resonance at point A in Fig. 3. ${\omega }_{pe}/\omega =4.79$, $r_c/\lambda =0.1$, and $2\left(r_p\text{−}{r}_c\right)/\lambda =0.18$.