  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
$\hat{A}$ with $\hat{A}^{2}=\hat{I}$ and $\hat{A}^{2}=\hat{A}$ for an arbitrary
interaction strength, where $\hat{I}$ represents 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 (SNR). 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.
