Interferometric weak value deflections: Quantum and classical treatments

We derive the weak value deflection given in an article by Dixon et al. [P. B. Dixon et al. Phys. Rev. Lett. 102 173601 (2009)] both quantum mechanically and classically, including diffraction effects. This article is meant to cover some of the mathematical details omitted in that article owing to space constraints.

Figure 1

Experimental setup. A fiber-coupled laser is launched into free space and collimated. The beam passes through a polarizing beam splitter (PBS) and then enters a Sagnac interferometer that consists of three mirrors: a 50:50 beam splitter (BS), a half wave plate (HWP), and a Soleil-Babinet compensator (SBC). The SBC and HWP in the interferometer allow the output intensity of the interferometer to be tuned. The output port is monitored with a split detector. The piezo-driven mirror gives a small beam deflection.