We theoretically study a two-dimensional electromagnetically induced phase grating in a four-level quantum system located near plasmonic metamaterials consisting of a periodic two-dimensional array of metal-coated dielectric nanospheres. The four-level quantum system interacts with a weak-probe laser field and a strong coherent coupling field with a standing-wave pattern. In the presence of plasmonic metamaterials the quantum system becomes sensitive to the relative phase between applied light. Therefore, the linear absorption and Kerr nonlinearity of the medium become phase dependent. Here, due to the standing-wave pattern of coupling light, an absorptive grating or phase grating can be formed in the quantum system. In our proposed model, we show that the diffraction efficiencies of the grating are related to the relative phase between applied fields, when the quantum system is located at different distances from plasmonic metamaterials.

我们从理论上研究了位于等离子超材料附近的四能级量子系统中的二维电磁感应相位光栅，该等离子超材料由金属包覆的电介质纳米球的周期性二维阵列组成。四能级量子系统与弱探针激光场和具有驻波模式的强相干耦合场相互作用。在等离子超材料的存在下，量子系统对施加的光之间的相对相位变得敏感。因此，介质的线性吸收和Kerr非线性变得与相位有关。在此，由于耦合光的驻波图案，可以在量子系统中形成吸收光栅或相位光栅。在我们提出的模型中