In situ realization of particlelike scattering states in a microwave cavity

We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase- and amplitude-regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.

Figure 1

Sketch of the experimental setup. A two-dimensional microwave cavity is excited by 16 monopole antennas (left upper corner) placed in the incoming lead (red-colored area). The antennas are connected to IQ modulators controlling amplitude and phase of the microwave signal, whereas the IQ modulators themselves are fed by a vector network analyzer. The chaotic scattering region (light blue area) is connected to the incoming lead and an outgoing one (green area). Both leads are closed by absorbing foam material (LS-14, LS-16). The dotted line in the exit lead indicates the 27 positions where the movable monopole antenna is placed for the measurement of the complex transmission matrix $T$. The red square in the exit lead marks the area for the computation of $I_{\mathrm{ob}}$ and $I_{\mathrm{em}}$ (see text).

Figure 2

(a) Intensity of the particlelike scattering states which are experimentally created by wave-front shaping of the incident wave in the left upper lead. (b) Central path length of the corresponding classical trajectory bundles of the particlelike scattering states ($L_1=33.3\text{cm}, L_2=50.0\text{cm}, L_3=49.1\text{cm}$). (c) Typical intensity distribution when only one single antenna is excited (here: second antenna from top). Note that the intensities in panels (a) and (c) are normalized each to a maximum (minimum) value of 1 (0).

Figure 3

Autocorrelation function of the output profile of the three particlelike scattering states (PSS) and the random scattering state (RSS) according to Eq. (5). All three PSSs are more stable with respect to a change of the incident frequency $\nu$ as compared to the RSS.

Figure 4

(a) Change of the transmitted intensity $\mathrm{\Delta }{I}_{\mathrm{rel}}$ of the particlelike scattering states (PSS) and the random state while moving the rhombic obstacle between position 1 (Pos 1) to position 5 (Pos 5) [see panel (b)] operating at the center frequency ${\nu }_0=17.5\mathrm{GHz}$. PSS 1 and PSS 2 show a significant drop at only one position where the obstacle crosses the classical trajectory bundle. As expected, PSS 3, which is a superposition of two classical bundles, is affected by all obstacle positions. The RSS shows no indication of a particlelike pattern.