Ultrasensitive Beam Deflection Measurement via Interferometric Weak Value Amplification

We report on the use of an interferometric weak value technique to amplify very small transverse deflections of an optical beam. By entangling the beam’s transverse degrees of freedom with the which-path states of a Sagnac interferometer, it is possible to realize an optical amplifier for polarization independent deflections. The theory for the interferometric weak value amplification method is presented along with the experimental results, which are in good agreement. Of particular interest, we measured the angular deflection of a mirror down to $400\pm 200\mathrm{\text{frad}}$ and the linear travel of a piezo actuator down to $14\pm 7\mathrm{\text{fm}}$.

Figure 1

Experimental Setup. The objective lens collimates a 780 nm beam. After passing through polarization optics, the beam enters a Sagnac interferometer consisting of three mirrors and a $50/50$ beam splitter arranged in a square. The output port is monitored by both a quadrant detector and a CCD camera. The SBC and half-wave plate in the interferometer allow the output intensity of the interferometer to be tuned. The piezo mirror gives a small beam deflection.

Figure 2

Measured beam deflection is plotted as a function of beam radius $\sigma$. SBC angle $\varphi$ for each data set is labeled. The scale on the left is the measured beam deflection $⟨x⟩$. The scale on the right is the amplification factor $\mathcal{A}$. The unamplified deflection is $\delta =2.95\mu \mathrm{m}$. The solid lines are theoretical predictions based on Eq. (6).

Figure 3

Angular displacement of the mirror is plotted versus piezo driving voltage. Weak value signal amplification allows small deflections to be measured. The solid line shows the expected deflection based on an extrapolation of calibrated measurements of the piezo actuator’s linear travel at higher voltages. These data were taken using a weak value amplification of approximately 86.