Measurement of Mechanical Deformations Induced by Enhanced Electromagnetic Stress on a Parallel Metallic-Plate System

We measured the electromagnetic stress-induced local strain distribution on a centimeter-sized parallel-plate metallic resonant unit illuminated with microwave radiation. Using a fiber interferometer, we found that the strain changes sign across the resonant unit, in agreement with theoretical predictions that the attractive electric and repulsive magnetic forces act at different locations. The enhancement of the corresponding maximum local electromagnetic stress is stronger than the enhancement of the net force, reaching a factor of $>600$ compared to the ordinary radiation pressure.

Figure 1

(a) The double-plate resonating unit. The thick bottom plate is connected to the support by two rods. (b) Cross-sectional view of the double plate system (not to scale), showing induced antiparallel currents (red arrows) and charges at resonance. A silicon post supports the top plate at the middle. (c) The magnetic field (along the $y$ direction) distribution in the gap at resonance (top) and the corresponding electric field (along the $z$ direction) distribution along the middle of the plate (bottom). Both are normalized to the incident field amplitude. (d) Calculated deformation of the top plate in response to the time-averaged electromagnetic stress. The black arrows represent the directions of the stress at the middle of the four edges.

Figure 2

(a) Local deformation of the top plate is measured by a fiber interferometer. The location of measurement is controlled by an $X\text{−}Y$ positioning stage. (b) Vibration amplitude of the top plate in-phase ($U$, red) and out-of-phase ($V$, blue) with the intensity modulations of the microwave radiation at location ${\overrightarrow{r}}_1$ for normal mode 13. Inset: the measured mode shape for mode 13, normalized to the maximum vibration amplitude across the plate.

Figure 3

(a) Calculated vibration amplitude at location ${\overrightarrow{r}}_1$ in response to the electromagnetic stress as a function of microwave modulation frequency. Insets: the normalized mode profiles for normal modes 4, 5, and 7 for the 8 mm by 8 mm area at the center of the plate. (b) Measured vibration amplitude. The red (blue) peak represents a mode with the same (opposite) symmetry as the electromagnetic stress. Insets: measured mode profiles for modes 4, 5, and 7. (c) Response of modes 13 (red) and 7 (blue) at location ${\overrightarrow{r}}_2$ plotted in the $U\text{−}V$ phase space. The red (blue) arrow indicates the vibrations lag the microwave modulation by $3\pi /2(2\pi )$. (d) Measured phase lags of the first 14 normal modes, plotted in red (blue) for modes with the same (different) symmetry as the EM stress. Error bars are comparable to the symbol size.

Figure 4

(a) Measured and (b) calculated strain of the top plate induced by the electromagnetic stress. (c) Dependence of the deformation of the top plate at location ${\overrightarrow{r}}_1$ on the microwave frequency. The solid line shows the calculated results.