Realizing the fictitious beam splitter -- A stationary implementation of semi-counterfactual interaction-free imaging

Based on quantum counterfactual interaction-free measurement, we propose an implementation scheme for a beam splitter with anomalous reflection and transmission properties that looks impossible at first glance. Our scheme is stationary without requiring switchable mirrors and polarization rotators. Using the scheme for imaging will ensure that the optical radiation received by the object being imaged can be arbitrarily low. Thus it enables applications such as stealthy night vision devices that can work without detectable ambient light, or being used as a hackware against some counterfactual quantum cryptographic protocols.