Measurement of electromagnetic radiation force using a capacitance-bridge interferometer

Abstract

We present a mechanical cantilever-based tabletop interferometer to measure the radiation force exerted by light. Using a high-power (~ 1W) pulsed laser beam, we excite mechanical oscillations of a thin metallic cantilever. The cantilever forms a parallel plate capacitor with a printed circuit board trace. Using a capacitance-bridge geometry, we measure small capacitance changes of the order of femto-Farads, induced by the radiation forces of a few nano-Newtons. This experiment uses equipment commonly found in an undergraduate teaching laboratory for physics and electronics while providing insight into electromagnetic wave theory, circuit design for low-noise measurements, and Fourier analysis.

Figures (10)

• Figure 1: (a) Physical layout of the capacitance bridge consisting of two air capacitors, made with brass cantilevers parallel to the PCB traces with plate separations less than $1\,\mathrm{mm}$. (b) Schematic of the capacitance bridge circuit. The voltage amplitudes of the signal are used to label the nodes in the circuit.
• Figure 2: Image of the assembled PCB, with the capacitance bridge circuit and an integrated Op-Amp (LF411C) based inverting amplifier block. Inset: zoomed-in image of $C_{\text{DUT}}$.
• Figure 3: (a) Experimental setup with the laser focused on the tip of the cantilever ($C_{\text{DUT}}$), (b) schematic of the experimental setup, and (c) a schematic of the laser setup.
• Figure 4: (a) Circuit schematic consisting the capacitance bridge and the amplifier block. We used LTSpice to simulate the circuit and match it with experiments to find capacitance $C_\text{G2}$. (b) Frequency dependence of amplification: measured ($\circ$) and simulated ($\square$) values of output voltage $V_{\text{Out}}$, for constant in-phase input signals with amplitudes $V_{\text{Ref}} = V_{\text{DUT}} = 1\,\mathrm{V_{pp}}$.
• Figure 5: Oscilloscope data for the balanced bridge: $V_{\text{Ref}}$ = $19\,\mathrm{V_{pp}}$ (left panel), $V_{\text{DUT}}$ = $20\,\mathrm{V_{pp}}$ (left panel), and $V_{\text{Out}}$ = $120\,\mathrm{mV_{pp}}$ (right panel).