Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable  with A Î2 = and A Â2 = for an arbitrary interaction strength, where Ir epresents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak-and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.

We study the coherent propagation of light whose dynamics is governed by the effective Schrödinger equation derived in a magneto-optically-manipulated atomic ensemble with a fourlevel tripod configuration for electromagnetically induced transparency (EIT). The small transverse deflection of an optical beam, which is ultra-sensitive to the EIT effect, could be drastically amplified via a weak measurement with an appropriate preselection and postselection of the polarization state. The physical mechanism is explained as the effect of wavepacket reshaping, which results in an enlarged group velocity in the transverse direction.