Complementary weak-value amplification with concatenated postselections

We measure a transverse momentum kick in a Sagnac interferometer using weak-value amplification with two postselections. The first postselection is controlled by a polarization-dependent phase mismatch between both paths of the interferometer, and the second postselection is controlled by a polarizer at the exit port. By monitoring the dark port of the interferometer, we study the complementary amplification of the concatenated postselections, where the polarization extinction ratio is greater than the contrast of the spatial interference. In this case, we find an improvement in the amplification of the signal of interest by introducing a second postselection to the system.