One of the main motivation behind the current interest in magnetoelectric materials is that they can be building blocks of low-energy consumption nonvolatile memory devices. In this talk, I will demonstrate that simple optical absorption spectroscopy can be used to identify magnetoelectric (ME) antiferromagnetic (AFM) domains of LiCoPO4. In case of the THz spin-wave excitations this unusual contrast arising from the optical magnetoelectric effect as confirmed by our microscopic model, which also captures the characteristics of the observed static ME effect. Since these domains and the absorption difference are also present in zero magnetic field it may promote the development of ME memory devices based on AFM insulators.