It is well known that if you have linearly polarized light impinging on a half-wave plate with an angle $\theta$ = 0 between the fast axis and the field polarization direction, then the output light will have the same polarization as the input. Now if you rotate the half-wave plate, such that $\theta$ is now non-zero,the output polarization of the beam will be along 2$\theta$.
However, it is not clear which direction the field should rotate. For example, if I rotate a half-wave plate $\theta$ clockwise (from the perspective of the propagating beam), then the field can be rotated either clockwise or counterclockwise to end up at 2$\theta$ relative to its initial state. Or is there always a fixed relationship between the two rotation directions (that of the plate and that of the field)?
According to a quick test I performed using a half-wave plate and a polarizer, the field rotates in the same direction as the plate. However, I am not sure if this generalizes to all half-wave plates, nor am I aware of an argument supporting that speculation.